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added libtomcrypt-1.12

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Tom St Denis 2006-05-29 23:12:56 +00:00 committed by Steffen Jaeckel
parent 64d7ebe166
commit 2945dea3e2
40 changed files with 1376 additions and 122 deletions
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2
Doxyfile
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@ -23,7 +23,7 @@ PROJECT_NAME = LibTomCrypt
# This could be handy for archiving the generated documentation or
# if some version control system is used.
PROJECT_NUMBER = 1.11
PROJECT_NUMBER = 1.12
# The OUTPUT_DIRECTORY tag is used to specify the (relative or absolute)
# base path where the generated documentation will be put.

3
TODO
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@ -1,3 +1,6 @@
- document new math function count_lsb_bits
- add BOOLEAN type to the ASN world
- ECC fixed point accelerator
- look into X9.63 support [in addition to the LTC style ecc_encrypt_key() not replacing]

21
changes
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@ -1,3 +1,20 @@
May 29th, 2006
v1.12 -- Fixed OID encoder/decoder/length to properly handle the first two parts of an OID, matches 2002 X.690 now.
-- [Wesley Shields] Allows both GMP/LTM and TFM to be defined now.
-- [Wesley Shields] GMP pluggin is cleaner now and doesn't use deprecated symbols. Yipee
-- Added count_lsb_bits to get the number of leading LSB zero bits there are.
-- Fixed a bug in the INTEGER encoders for values of -(256**k)/2
-- Added BOOLEAN type to ASN.1 thingy-ma-do-hicky
-- Testprof doesn't strictly require GMP ... oops [Nils Durner]
-- Added LTC_CALL and LTC_EXPORT macros in tomcrypt_cfg.h to support various calling and linker conventions
(Thanks to John Kirk from Demonware)
-- In what has to be the best thing since sliced bread I bring you MECC_FP which is the fixed point
ECC point multiplier. It's fast, it's sexy and what's more it's hella fast [did I mention it's fast?]
You can tune it somewhat with FP_LUT (default to 8) for look-up width.
Read section 8.2 of the manual for more info.
It is disabled by default, you'll have to build LTC with it defined to get it.
-- Fixed bug in ecc_test.c (from testprof) to include the 521 [not 512] bit curve. :-)
April 4th, 2006
v1.11 -- Removed printf's from lrw_test ... whoops
-- lrw_process now checks the return of the cipher ecb encrypt/decrypt calls
@ -1436,6 +1453,6 @@ v0.02 -- Changed RC5 to only allow 12 to 24 rounds
v0.01 -- We will call this the first version.
/* $Source: /cvs/libtom/libtomcrypt/changes,v $ */
/* $Revision: 1.194 $ */
/* $Date: 2006/04/05 02:51:41 $ */
/* $Revision: 1.206 $ */
/* $Date: 2006/05/29 11:21:25 $ */

47
crypt.tex
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@ -47,7 +47,7 @@
\def\gap{\vspace{0.5ex}}
\makeindex
\begin{document}
\title{LibTomCrypt \\ Version 1.11}
\title{LibTomCrypt \\ Version 1.12}
\author{Tom St Denis \\
\\
tomstdenis@gmail.com \\
@ -2909,6 +2909,40 @@ provided are very close to $p$ that is $\vert \vert \phi(\beta) \vert \vert \app
range in order from $\approx 2^{192}$ points to $\approx 2^{521}$. According to the source document any key size greater
than or equal to 256-bits is sufficient for long term security.
\section{Fixed Point Optimizations}
\index{Fixed Point ECC}
As of v1.12 of LibTomCrypt, support for Fixed Point ECC point multiplication has been added. It is a generic optimization that is
supported by any conformant math plugin. It is enabled by defining \textbf{MECC\_FP} during the build, such as
\begin{verbatim}
CFLAGS="-DTFM_DESC -DMECC_FP" make
\end{verbatim}
which will build LTC using the TFM math library and enabling this new feature. The feature is not enabled by default as it is \textbf{NOT} thread
safe (by default). It supports the LTC locking macros (such as by enabling LTC\_PTHREAD), but by default is not locked.
\index{FP\_ENTRIES}
The optimization works by using a Fixed Point point multiplier on any base point you use twice or more in a short period of time. It has a limited size
cache (of FP\_ENTRIES entries) which it uses to hold recent bases passed to ltc\_ecc\_mulmod(). Any base detected to be used twice is sent through the
pre--computation phase and then the fixed point algorithm can be used. For example, if you use a NIST base point twice in a row, the 2nd and
all subsequence point multiplications with that point will use the faster algorithm.
\index{FP\_LUT}
The optimization uses a window on the multiplicand of FP\_LUT bits (default: 8, min: 2, max: 12) and controls the memory/time tradeoff. The larger the
value the faster the algorithm will be but the more memory it will take. The memory usage is $3 \cdot 2^{FP\_LUT}$ integers which by default
with TFM amounts to about 400kB of memory. Tuning TFM (by changing FP\_SIZE) can decrease the usage by a fair amount. Memory is only used by a cache entry
if it is active. Both FP\_ENTRIES and FP\_LUT are definable on the command line if you wish to override them. For instance,
\begin{verbatim}
CFLAGS="-DTFM_DESC -DMECC_FP -DFP_ENTRIES=8 -DFP_LUT=6" make
\end{verbatim}
\begin{flushleft}
would define a window of 6 bits and limit the cache to 8 entries. Generally it's better to first tune TFM by adjusting FP\_SIZE (from tfm.h). It defaults
to 4096 bits (512 bytes) which is way more than what is required by ECC. At most, you need 1152 bits to accommodate ECC--521. If you're only using (say)
ECC--256 you will only need 576 bits, which would reduce the memory usage by 700\%.
\end{flushleft}
\section{Key Format}
LibTomCrypt uses it's own format for ECC public and private keys. While ANSI X9.62 partially specifies key formats (it covers public keys) it does it in a less
than ideally simple manner. In the case of LibTomCrypt it is meant \textbf{solely} for NIST $GF(p)$ curves. The format of the keys is as follows:
@ -3320,6 +3354,7 @@ LTC_SET_ASN1(sequence, x++, LTC_ASN1_NULL, NULL, 0);
\begin{tabular}{|l|l|}
\hline \textbf{Definition} & \textbf{ASN.1 Type} \\
\hline LTC\_ASN1\_EOL & End of a ASN.1 list structure. \\
\hline LTC\_ASN1\_BOOLEAN & BOOLEAN type \\
\hline LTC\_ASN1\_INTEGER & INTEGER (uses mp\_int) \\
\hline LTC\_ASN1\_SHORT\_INTEGER & INTEGER (32--bit using unsigned long) \\
\hline LTC\_ASN1\_BIT\_STRING & BIT STRING (one bit per char) \\
@ -4825,6 +4860,12 @@ typedef struct {
*/
int (*count_bits)(void * a);
/** Count the number of LSB bits which are zero
@param a The integer to count
@return The number of contiguous zero LSB bits
*/
int (*count_lsb_bits)(void *a);
/** Compute a power of two
@param a The integer to store the power in
@param n The power of two you want to store (a = 2^n)
@ -5190,5 +5231,5 @@ Since the function is given the entire RSA key (for private keys only) CRT is po
\end{document}
% $Source: /cvs/libtom/libtomcrypt/crypt.tex,v $
% $Revision: 1.67 $
% $Date: 2006/03/31 14:16:09 $
% $Revision: 1.71 $
% $Date: 2006/05/29 11:19:08 $

2
demos/test.c
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@ -24,7 +24,7 @@ int main(void)
printf("\nmac_test......"); fflush(stdout); x = mac_test(); printf(x ? "failed" : "passed");if (x) exit(EXIT_FAILURE);
printf("\npkcs_1_test..."); fflush(stdout); x = pkcs_1_test(); printf(x ? "failed" : "passed");if (x) exit(EXIT_FAILURE);
printf("\nrsa_test......"); fflush(stdout); x = rsa_test(); printf(x ? "failed" : "passed");if (x) exit(EXIT_FAILURE);
printf("\necc_test......"); fflush(stdout); x = ecc_tests(); printf(x ? "failed" : "passed");if (x) exit(EXIT_FAILURE);
printf("\necc_test......"); fflush(stdout); x = ecc_tests(); printf(x ? "failed" : "passed");if (x) exit(EXIT_FAILURE);
printf("\ndsa_test......"); fflush(stdout); x = dsa_test(); printf(x ? "failed" : "passed");if (x) exit(EXIT_FAILURE);
printf("\nkatja_test...."); fflush(stdout); x = katja_test(); printf(x ? "failed" : "passed");if (x) exit(EXIT_FAILURE);
printf("\n");

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24
makefile
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@ -4,7 +4,7 @@
# Modified by Clay Culver
# The version
VERSION=1.11
VERSION=1.12
# Compiler and Linker Names
#CC=gcc
@ -128,10 +128,10 @@ src/mac/omac/omac_memory_multi.o src/mac/omac/omac_process.o src/mac/omac/omac_t
src/mac/pelican/pelican.o src/mac/pelican/pelican_memory.o src/mac/pelican/pelican_test.o \
src/mac/pmac/pmac_done.o src/mac/pmac/pmac_file.o src/mac/pmac/pmac_init.o src/mac/pmac/pmac_memory.o \
src/mac/pmac/pmac_memory_multi.o src/mac/pmac/pmac_ntz.o src/mac/pmac/pmac_process.o \
src/mac/pmac/pmac_shift_xor.o src/mac/pmac/pmac_test.o src/math/gmp_desc.o src/math/ltm_desc.o \
src/math/multi.o src/math/rand_prime.o src/math/tfm_desc.o src/misc/base64/base64_decode.o \
src/misc/base64/base64_encode.o src/misc/burn_stack.o src/misc/crypt/crypt.o \
src/misc/crypt/crypt_argchk.o src/misc/crypt/crypt_cipher_descriptor.o \
src/mac/pmac/pmac_shift_xor.o src/mac/pmac/pmac_test.o src/math/fp/ltc_ecc_fp_mulmod.o \
src/math/gmp_desc.o src/math/ltm_desc.o src/math/multi.o src/math/rand_prime.o src/math/tfm_desc.o \
src/misc/base64/base64_decode.o src/misc/base64/base64_encode.o src/misc/burn_stack.o \
src/misc/crypt/crypt.o src/misc/crypt/crypt_argchk.o src/misc/crypt/crypt_cipher_descriptor.o \
src/misc/crypt/crypt_cipher_is_valid.o src/misc/crypt/crypt_find_cipher.o \
src/misc/crypt/crypt_find_cipher_any.o src/misc/crypt/crypt_find_cipher_id.o \
src/misc/crypt/crypt_find_hash.o src/misc/crypt/crypt_find_hash_any.o \
@ -156,10 +156,12 @@ src/modes/lrw/lrw_setiv.o src/modes/lrw/lrw_start.o src/modes/lrw/lrw_test.o \
src/modes/ofb/ofb_decrypt.o src/modes/ofb/ofb_done.o src/modes/ofb/ofb_encrypt.o \
src/modes/ofb/ofb_getiv.o src/modes/ofb/ofb_setiv.o src/modes/ofb/ofb_start.o \
src/pk/asn1/der/bit/der_decode_bit_string.o src/pk/asn1/der/bit/der_encode_bit_string.o \
src/pk/asn1/der/bit/der_length_bit_string.o src/pk/asn1/der/choice/der_decode_choice.o \
src/pk/asn1/der/ia5/der_decode_ia5_string.o src/pk/asn1/der/ia5/der_encode_ia5_string.o \
src/pk/asn1/der/ia5/der_length_ia5_string.o src/pk/asn1/der/integer/der_decode_integer.o \
src/pk/asn1/der/integer/der_encode_integer.o src/pk/asn1/der/integer/der_length_integer.o \
src/pk/asn1/der/bit/der_length_bit_string.o src/pk/asn1/der/boolean/der_decode_boolean.o \
src/pk/asn1/der/boolean/der_encode_boolean.o src/pk/asn1/der/boolean/der_length_boolean.o \
src/pk/asn1/der/choice/der_decode_choice.o src/pk/asn1/der/ia5/der_decode_ia5_string.o \
src/pk/asn1/der/ia5/der_encode_ia5_string.o src/pk/asn1/der/ia5/der_length_ia5_string.o \
src/pk/asn1/der/integer/der_decode_integer.o src/pk/asn1/der/integer/der_encode_integer.o \
src/pk/asn1/der/integer/der_length_integer.o \
src/pk/asn1/der/object_identifier/der_decode_object_identifier.o \
src/pk/asn1/der/object_identifier/der_encode_object_identifier.o \
src/pk/asn1/der/object_identifier/der_length_object_identifier.o \
@ -364,5 +366,5 @@ zipup: no_oops docs
# $Source: /cvs/libtom/libtomcrypt/makefile,v $
# $Revision: 1.119 $
# $Date: 2006/03/22 20:48:57 $
# $Revision: 1.123 $
# $Date: 2006/05/25 10:33:01 $

22
makefile.icc
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@ -120,10 +120,10 @@ src/mac/omac/omac_memory_multi.o src/mac/omac/omac_process.o src/mac/omac/omac_t
src/mac/pelican/pelican.o src/mac/pelican/pelican_memory.o src/mac/pelican/pelican_test.o \
src/mac/pmac/pmac_done.o src/mac/pmac/pmac_file.o src/mac/pmac/pmac_init.o src/mac/pmac/pmac_memory.o \
src/mac/pmac/pmac_memory_multi.o src/mac/pmac/pmac_ntz.o src/mac/pmac/pmac_process.o \
src/mac/pmac/pmac_shift_xor.o src/mac/pmac/pmac_test.o src/math/gmp_desc.o src/math/ltm_desc.o \
src/math/multi.o src/math/rand_prime.o src/math/tfm_desc.o src/misc/base64/base64_decode.o \
src/misc/base64/base64_encode.o src/misc/burn_stack.o src/misc/crypt/crypt.o \
src/misc/crypt/crypt_argchk.o src/misc/crypt/crypt_cipher_descriptor.o \
src/mac/pmac/pmac_shift_xor.o src/mac/pmac/pmac_test.o src/math/fp/ltc_ecc_fp_mulmod.o \
src/math/gmp_desc.o src/math/ltm_desc.o src/math/multi.o src/math/rand_prime.o src/math/tfm_desc.o \
src/misc/base64/base64_decode.o src/misc/base64/base64_encode.o src/misc/burn_stack.o \
src/misc/crypt/crypt.o src/misc/crypt/crypt_argchk.o src/misc/crypt/crypt_cipher_descriptor.o \
src/misc/crypt/crypt_cipher_is_valid.o src/misc/crypt/crypt_find_cipher.o \
src/misc/crypt/crypt_find_cipher_any.o src/misc/crypt/crypt_find_cipher_id.o \
src/misc/crypt/crypt_find_hash.o src/misc/crypt/crypt_find_hash_any.o \
@ -148,10 +148,12 @@ src/modes/lrw/lrw_setiv.o src/modes/lrw/lrw_start.o src/modes/lrw/lrw_test.o \
src/modes/ofb/ofb_decrypt.o src/modes/ofb/ofb_done.o src/modes/ofb/ofb_encrypt.o \
src/modes/ofb/ofb_getiv.o src/modes/ofb/ofb_setiv.o src/modes/ofb/ofb_start.o \
src/pk/asn1/der/bit/der_decode_bit_string.o src/pk/asn1/der/bit/der_encode_bit_string.o \
src/pk/asn1/der/bit/der_length_bit_string.o src/pk/asn1/der/choice/der_decode_choice.o \
src/pk/asn1/der/ia5/der_decode_ia5_string.o src/pk/asn1/der/ia5/der_encode_ia5_string.o \
src/pk/asn1/der/ia5/der_length_ia5_string.o src/pk/asn1/der/integer/der_decode_integer.o \
src/pk/asn1/der/integer/der_encode_integer.o src/pk/asn1/der/integer/der_length_integer.o \
src/pk/asn1/der/bit/der_length_bit_string.o src/pk/asn1/der/boolean/der_decode_boolean.o \
src/pk/asn1/der/boolean/der_encode_boolean.o src/pk/asn1/der/boolean/der_length_boolean.o \
src/pk/asn1/der/choice/der_decode_choice.o src/pk/asn1/der/ia5/der_decode_ia5_string.o \
src/pk/asn1/der/ia5/der_encode_ia5_string.o src/pk/asn1/der/ia5/der_length_ia5_string.o \
src/pk/asn1/der/integer/der_decode_integer.o src/pk/asn1/der/integer/der_encode_integer.o \
src/pk/asn1/der/integer/der_length_integer.o \
src/pk/asn1/der/object_identifier/der_decode_object_identifier.o \
src/pk/asn1/der/object_identifier/der_encode_object_identifier.o \
src/pk/asn1/der/object_identifier/der_length_object_identifier.o \
@ -274,6 +276,6 @@ install: library
install -g $(GROUP) -o $(USER) $(HEADERS) $(DESTDIR)$(INCPATH)
# $Source: /cvs/libtom/libtomcrypt/makefile.icc,v $
# $Revision: 1.53 $
# $Date: 2006/04/02 13:23:20 $
# $Revision: 1.56 $
# $Date: 2006/05/25 10:33:01 $

22
makefile.msvc
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@ -30,10 +30,10 @@ src/mac/omac/omac_memory_multi.obj src/mac/omac/omac_process.obj src/mac/omac/om
src/mac/pelican/pelican.obj src/mac/pelican/pelican_memory.obj src/mac/pelican/pelican_test.obj \
src/mac/pmac/pmac_done.obj src/mac/pmac/pmac_file.obj src/mac/pmac/pmac_init.obj src/mac/pmac/pmac_memory.obj \
src/mac/pmac/pmac_memory_multi.obj src/mac/pmac/pmac_ntz.obj src/mac/pmac/pmac_process.obj \
src/mac/pmac/pmac_shift_xor.obj src/mac/pmac/pmac_test.obj src/math/gmp_desc.obj src/math/ltm_desc.obj \
src/math/multi.obj src/math/rand_prime.obj src/math/tfm_desc.obj src/misc/base64/base64_decode.obj \
src/misc/base64/base64_encode.obj src/misc/burn_stack.obj src/misc/crypt/crypt.obj \
src/misc/crypt/crypt_argchk.obj src/misc/crypt/crypt_cipher_descriptor.obj \
src/mac/pmac/pmac_shift_xor.obj src/mac/pmac/pmac_test.obj src/math/fp/ltc_ecc_fp_mulmod.obj \
src/math/gmp_desc.obj src/math/ltm_desc.obj src/math/multi.obj src/math/rand_prime.obj src/math/tfm_desc.obj \
src/misc/base64/base64_decode.obj src/misc/base64/base64_encode.obj src/misc/burn_stack.obj \
src/misc/crypt/crypt.obj src/misc/crypt/crypt_argchk.obj src/misc/crypt/crypt_cipher_descriptor.obj \
src/misc/crypt/crypt_cipher_is_valid.obj src/misc/crypt/crypt_find_cipher.obj \
src/misc/crypt/crypt_find_cipher_any.obj src/misc/crypt/crypt_find_cipher_id.obj \
src/misc/crypt/crypt_find_hash.obj src/misc/crypt/crypt_find_hash_any.obj \
@ -58,10 +58,12 @@ src/modes/lrw/lrw_setiv.obj src/modes/lrw/lrw_start.obj src/modes/lrw/lrw_test.o
src/modes/ofb/ofb_decrypt.obj src/modes/ofb/ofb_done.obj src/modes/ofb/ofb_encrypt.obj \
src/modes/ofb/ofb_getiv.obj src/modes/ofb/ofb_setiv.obj src/modes/ofb/ofb_start.obj \
src/pk/asn1/der/bit/der_decode_bit_string.obj src/pk/asn1/der/bit/der_encode_bit_string.obj \
src/pk/asn1/der/bit/der_length_bit_string.obj src/pk/asn1/der/choice/der_decode_choice.obj \
src/pk/asn1/der/ia5/der_decode_ia5_string.obj src/pk/asn1/der/ia5/der_encode_ia5_string.obj \
src/pk/asn1/der/ia5/der_length_ia5_string.obj src/pk/asn1/der/integer/der_decode_integer.obj \
src/pk/asn1/der/integer/der_encode_integer.obj src/pk/asn1/der/integer/der_length_integer.obj \
src/pk/asn1/der/bit/der_length_bit_string.obj src/pk/asn1/der/boolean/der_decode_boolean.obj \
src/pk/asn1/der/boolean/der_encode_boolean.obj src/pk/asn1/der/boolean/der_length_boolean.obj \
src/pk/asn1/der/choice/der_decode_choice.obj src/pk/asn1/der/ia5/der_decode_ia5_string.obj \
src/pk/asn1/der/ia5/der_encode_ia5_string.obj src/pk/asn1/der/ia5/der_length_ia5_string.obj \
src/pk/asn1/der/integer/der_decode_integer.obj src/pk/asn1/der/integer/der_encode_integer.obj \
src/pk/asn1/der/integer/der_length_integer.obj \
src/pk/asn1/der/object_identifier/der_decode_object_identifier.obj \
src/pk/asn1/der/object_identifier/der_encode_object_identifier.obj \
src/pk/asn1/der/object_identifier/der_length_object_identifier.obj \
@ -132,5 +134,5 @@ timing: demos/timing.c library
cl $(CFLAGS) demos/timing.c testprof/tomcrypt_prof.lib tomcrypt.lib advapi32.lib $(EXTRALIBS)
# $Source: /cvs/libtom/libtomcrypt/makefile.msvc,v $
# $Revision: 1.31 $
# $Date: 2006/03/18 03:48:32 $
# $Revision: 1.34 $
# $Date: 2006/05/25 10:33:01 $

24
makefile.shared
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@ -6,7 +6,7 @@
# Tom St Denis
# The version
VERSION=0:111
VERSION=0:112
# Compiler and Linker Names
CC=libtool --mode=compile --tag=CC gcc
@ -125,10 +125,10 @@ src/mac/omac/omac_memory_multi.o src/mac/omac/omac_process.o src/mac/omac/omac_t
src/mac/pelican/pelican.o src/mac/pelican/pelican_memory.o src/mac/pelican/pelican_test.o \
src/mac/pmac/pmac_done.o src/mac/pmac/pmac_file.o src/mac/pmac/pmac_init.o src/mac/pmac/pmac_memory.o \
src/mac/pmac/pmac_memory_multi.o src/mac/pmac/pmac_ntz.o src/mac/pmac/pmac_process.o \
src/mac/pmac/pmac_shift_xor.o src/mac/pmac/pmac_test.o src/math/gmp_desc.o src/math/ltm_desc.o \
src/math/multi.o src/math/rand_prime.o src/math/tfm_desc.o src/misc/base64/base64_decode.o \
src/misc/base64/base64_encode.o src/misc/burn_stack.o src/misc/crypt/crypt.o \
src/misc/crypt/crypt_argchk.o src/misc/crypt/crypt_cipher_descriptor.o \
src/mac/pmac/pmac_shift_xor.o src/mac/pmac/pmac_test.o src/math/fp/ltc_ecc_fp_mulmod.o \
src/math/gmp_desc.o src/math/ltm_desc.o src/math/multi.o src/math/rand_prime.o src/math/tfm_desc.o \
src/misc/base64/base64_decode.o src/misc/base64/base64_encode.o src/misc/burn_stack.o \
src/misc/crypt/crypt.o src/misc/crypt/crypt_argchk.o src/misc/crypt/crypt_cipher_descriptor.o \
src/misc/crypt/crypt_cipher_is_valid.o src/misc/crypt/crypt_find_cipher.o \
src/misc/crypt/crypt_find_cipher_any.o src/misc/crypt/crypt_find_cipher_id.o \
src/misc/crypt/crypt_find_hash.o src/misc/crypt/crypt_find_hash_any.o \
@ -153,10 +153,12 @@ src/modes/lrw/lrw_setiv.o src/modes/lrw/lrw_start.o src/modes/lrw/lrw_test.o \
src/modes/ofb/ofb_decrypt.o src/modes/ofb/ofb_done.o src/modes/ofb/ofb_encrypt.o \
src/modes/ofb/ofb_getiv.o src/modes/ofb/ofb_setiv.o src/modes/ofb/ofb_start.o \
src/pk/asn1/der/bit/der_decode_bit_string.o src/pk/asn1/der/bit/der_encode_bit_string.o \
src/pk/asn1/der/bit/der_length_bit_string.o src/pk/asn1/der/choice/der_decode_choice.o \
src/pk/asn1/der/ia5/der_decode_ia5_string.o src/pk/asn1/der/ia5/der_encode_ia5_string.o \
src/pk/asn1/der/ia5/der_length_ia5_string.o src/pk/asn1/der/integer/der_decode_integer.o \
src/pk/asn1/der/integer/der_encode_integer.o src/pk/asn1/der/integer/der_length_integer.o \
src/pk/asn1/der/bit/der_length_bit_string.o src/pk/asn1/der/boolean/der_decode_boolean.o \
src/pk/asn1/der/boolean/der_encode_boolean.o src/pk/asn1/der/boolean/der_length_boolean.o \
src/pk/asn1/der/choice/der_decode_choice.o src/pk/asn1/der/ia5/der_decode_ia5_string.o \
src/pk/asn1/der/ia5/der_encode_ia5_string.o src/pk/asn1/der/ia5/der_length_ia5_string.o \
src/pk/asn1/der/integer/der_decode_integer.o src/pk/asn1/der/integer/der_encode_integer.o \
src/pk/asn1/der/integer/der_length_integer.o \
src/pk/asn1/der/object_identifier/der_decode_object_identifier.o \
src/pk/asn1/der/object_identifier/der_encode_object_identifier.o \
src/pk/asn1/der/object_identifier/der_length_object_identifier.o \
@ -262,5 +264,5 @@ timing: library testprof/$(LIBTEST) $(TIMINGS)
gcc -o $(TIMING) $(TIMINGS) -ltomcrypt_prof -ltomcrypt $(EXTRALIBS)
# $Source: /cvs/libtom/libtomcrypt/makefile.shared,v $
# $Revision: 1.51 $
# $Date: 2006/03/31 05:46:53 $
# $Revision: 1.55 $
# $Date: 2006/05/25 10:33:01 $

2
mess.sh
View File

@ -1,4 +1,4 @@
#!/bin/bash
if cvs log $1 >/dev/null 2>/dev/null; then exit 0; else echo "$1 shouldn't be here" ; exit 1; fi
if cvs log $1 >/dev/null 2>/dev/null; then exit 0; else echo "$1 shouldn't be here, removed"; rm -f $1 ; fi

4
src/headers/tomcrypt.h
View File

@ -16,8 +16,8 @@ extern "C" {
#endif
/* version */
#define CRYPT 0x0111
#define SCRYPT "1.11"
#define CRYPT 0x0112
#define SCRYPT "1.12"
/* max size of either a cipher/hash block or symmetric key [largest of the two] */
#define MAXBLOCKSIZE 128

32
src/headers/tomcrypt_cfg.h
View File

@ -7,22 +7,34 @@
#ifndef TOMCRYPT_CFG_H
#define TOMCRYPT_CFG_H
/* you can change how memory allocation works ... */
void *XMALLOC(size_t n);
void *XREALLOC(void *p, size_t n);
void *XCALLOC(size_t n, size_t s);
void XFREE(void *p);
#if defined(_WIN32) || defined(_MSC_VER)
#define LTC_CALL __cdecl
#else
#ifndef LTC_CALL
#define LTC_CALL
#endif
#endif
void XQSORT(void *base, size_t nmemb, size_t size, int(*compar)(const void *, const void *));
#ifndef LTC_EXPORT
#define LTC_EXPORT
#endif
/* you can change how memory allocation works ... */
LTC_EXPORT void * LTC_CALL XMALLOC(size_t n);
LTC_EXPORT void * LTC_CALL XREALLOC(void *p, size_t n);
LTC_EXPORT void * LTC_CALL XCALLOC(size_t n, size_t s);
LTC_EXPORT void LTC_CALL XFREE(void *p);
LTC_EXPORT void LTC_CALL XQSORT(void *base, size_t nmemb, size_t size, int(*compar)(const void *, const void *));
/* change the clock function too */
clock_t XCLOCK(void);
LTC_EXPORT clock_t LTC_CALL XCLOCK(void);
/* various other functions */
void *XMEMCPY(void *dest, const void *src, size_t n);
int XMEMCMP(const void *s1, const void *s2, size_t n);
void *XMEMSET(void *s, int c, size_t n);
LTC_EXPORT void * LTC_CALL XMEMCPY(void *dest, const void *src, size_t n);
LTC_EXPORT int LTC_CALL XMEMCMP(const void *s1, const void *s2, size_t n);
LTC_EXPORT void * LTC_CALL XMEMSET(void *s, int c, size_t n);
/* type of argument checking, 0=default, 1=fatal and 2=error+continue, 3=nothing */
#ifndef ARGTYPE

3
src/headers/tomcrypt_custom.h
View File

@ -269,6 +269,9 @@
#define MECC_ACCEL
#endif
/* do we want fixed point ECC */
/* #define MECC_FP */
/* Timing Resistant? */
/* #define LTC_ECC_TIMING_RESISTANT */

7
src/headers/tomcrypt_math.h
View File

@ -108,6 +108,12 @@ typedef struct {
*/
int (*count_bits)(void * a);
/** Count the number of LSB bits which are zero
@param a The integer to count
@return The number of contiguous zero LSB bits
*/
int (*count_lsb_bits)(void *a);
/** Compute a power of two
@param a The integer to store the power in
@param n The power of two you want to store (a = 2^n)
@ -424,6 +430,7 @@ extern const ltc_math_descriptor gmp_desc;
#define mp_cmp(a, b) ltc_mp.compare(a, b)
#define mp_cmp_d(a, b) ltc_mp.compare_d(a, b)
#define mp_count_bits(a) ltc_mp.count_bits(a)
#define mp_cnt_lsb(a) ltc_mp.count_lsb_bits(a)
#define mp_2expt(a, b) ltc_mp.twoexpt(a, b)
#define mp_read_radix(a, b, c) ltc_mp.read_radix(a, b, c)

17
src/headers/tomcrypt_pk.h
View File

@ -226,9 +226,8 @@ ecc_point *ltc_ecc_new_point(void);
void ltc_ecc_del_point(ecc_point *p);
int ltc_ecc_is_valid_idx(int n);
/* point ops (mp == montgomery digit) */
#ifndef MECC_ACCEL
#if !defined(MECC_ACCEL) || defined(LTM_DESC) || defined(GMP_DESC)
/* R = 2P */
int ltc_ecc_projective_dbl_point(ecc_point *P, ecc_point *R, void *modulus, void *mp);
@ -236,6 +235,13 @@ int ltc_ecc_projective_dbl_point(ecc_point *P, ecc_point *R, void *modulus, void
int ltc_ecc_projective_add_point(ecc_point *P, ecc_point *Q, ecc_point *R, void *modulus, void *mp);
#endif
#if defined(MECC_FP)
int ltc_ecc_fp_mulmod(void *k, ecc_point *G, ecc_point *R, void *modulus, int map);
int ltc_ecc_fp_save_state(unsigned char **out, unsigned long *outlen);
int ltc_ecc_fp_restore_state(unsigned char *in, unsigned long inlen);
void ltc_ecc_fp_free(void);
#endif
/* R = kG */
int ltc_ecc_mulmod(void *k, ecc_point *G, ecc_point *R, void *modulus, int map);
@ -318,6 +324,7 @@ int dsa_shared_secret(void *private_key, void *base,
enum {
LTC_ASN1_EOL,
LTC_ASN1_BOOLEAN,
LTC_ASN1_INTEGER,
LTC_ASN1_SHORT_INTEGER,
LTC_ASN1_BIT_STRING,
@ -389,6 +396,12 @@ int der_decode_sequence_flexi(const unsigned char *in, unsigned long *inlen, lt
void der_free_sequence_flexi(ltc_asn1_list *list);
void der_sequence_free(ltc_asn1_list *in);
/* BOOLEAN */
int der_length_boolean(unsigned long *outlen);
int der_encode_boolean(int in,
unsigned char *out, unsigned long *outlen);
int der_decode_boolean(const unsigned char *in, unsigned long inlen,
int *out);
/* INTEGER */
int der_encode_integer(void *num, unsigned char *out, unsigned long *outlen);
int der_decode_integer(const unsigned char *in, unsigned long inlen, void *num);

936
src/math/fp/ltc_ecc_fp_mulmod.c Normal file
View File

@ -0,0 +1,936 @@
/* LibTomCrypt, modular cryptographic library -- Tom St Denis
*
* LibTomCrypt is a library that provides various cryptographic
* algorithms in a highly modular and flexible manner.
*
* The library is free for all purposes without any express
* guarantee it works.
*
* Tom St Denis, tomstdenis@gmail.com, http://libtomcrypt.com
*/
#include "tomcrypt.h"
/**
@file ltc_ecc_fp_mulmod.c
ECC Crypto, Tom St Denis
*/
#if defined(MECC) && defined(MECC_FP)
#include <limits.h>
/* number of entries in the cache */
#ifndef FP_ENTRIES
#define FP_ENTRIES 16
#endif
/* number of bits in LUT */
#ifndef FP_LUT
#define FP_LUT 8U
#endif
#if (FP_LUT > 12) || (FP_LUT < 2)
#error FP_LUT must be between 2 and 12 inclusively
#endif
/** Our FP cache */
static struct {
ecc_point *g, /* cached COPY of base point */
*LUT[1<<FP_LUT]; /* fixed point lookup */
int lru_count; /* amount of times this entry has been used */
} fp_cache[FP_ENTRIES];
LTC_MUTEX_GLOBAL(ltc_ecc_fp_lock);
/* simple table to help direct the generation of the LUT */
static const struct {
int ham, terma, termb;
} lut_orders[] = {
{ 0, 0, 0 }, { 1, 0, 0 }, { 1, 0, 0 }, { 2, 1, 2 }, { 1, 0, 0 }, { 2, 1, 4 }, { 2, 2, 4 }, { 3, 3, 4 },
{ 1, 0, 0 }, { 2, 1, 8 }, { 2, 2, 8 }, { 3, 3, 8 }, { 2, 4, 8 }, { 3, 5, 8 }, { 3, 6, 8 }, { 4, 7, 8 },
{ 1, 0, 0 }, { 2, 1, 16 }, { 2, 2, 16 }, { 3, 3, 16 }, { 2, 4, 16 }, { 3, 5, 16 }, { 3, 6, 16 }, { 4, 7, 16 },
{ 2, 8, 16 }, { 3, 9, 16 }, { 3, 10, 16 }, { 4, 11, 16 }, { 3, 12, 16 }, { 4, 13, 16 }, { 4, 14, 16 }, { 5, 15, 16 },
{ 1, 0, 0 }, { 2, 1, 32 }, { 2, 2, 32 }, { 3, 3, 32 }, { 2, 4, 32 }, { 3, 5, 32 }, { 3, 6, 32 }, { 4, 7, 32 },
{ 2, 8, 32 }, { 3, 9, 32 }, { 3, 10, 32 }, { 4, 11, 32 }, { 3, 12, 32 }, { 4, 13, 32 }, { 4, 14, 32 }, { 5, 15, 32 },
{ 2, 16, 32 }, { 3, 17, 32 }, { 3, 18, 32 }, { 4, 19, 32 }, { 3, 20, 32 }, { 4, 21, 32 }, { 4, 22, 32 }, { 5, 23, 32 },
{ 3, 24, 32 }, { 4, 25, 32 }, { 4, 26, 32 }, { 5, 27, 32 }, { 4, 28, 32 }, { 5, 29, 32 }, { 5, 30, 32 }, { 6, 31, 32 },
#if FP_LUT > 6
{ 1, 0, 0 }, { 2, 1, 64 }, { 2, 2, 64 }, { 3, 3, 64 }, { 2, 4, 64 }, { 3, 5, 64 }, { 3, 6, 64 }, { 4, 7, 64 },
{ 2, 8, 64 }, { 3, 9, 64 }, { 3, 10, 64 }, { 4, 11, 64 }, { 3, 12, 64 }, { 4, 13, 64 }, { 4, 14, 64 }, { 5, 15, 64 },
{ 2, 16, 64 }, { 3, 17, 64 }, { 3, 18, 64 }, { 4, 19, 64 }, { 3, 20, 64 }, { 4, 21, 64 }, { 4, 22, 64 }, { 5, 23, 64 },
{ 3, 24, 64 }, { 4, 25, 64 }, { 4, 26, 64 }, { 5, 27, 64 }, { 4, 28, 64 }, { 5, 29, 64 }, { 5, 30, 64 }, { 6, 31, 64 },
{ 2, 32, 64 }, { 3, 33, 64 }, { 3, 34, 64 }, { 4, 35, 64 }, { 3, 36, 64 }, { 4, 37, 64 }, { 4, 38, 64 }, { 5, 39, 64 },
{ 3, 40, 64 }, { 4, 41, 64 }, { 4, 42, 64 }, { 5, 43, 64 }, { 4, 44, 64 }, { 5, 45, 64 }, { 5, 46, 64 }, { 6, 47, 64 },
{ 3, 48, 64 }, { 4, 49, 64 }, { 4, 50, 64 }, { 5, 51, 64 }, { 4, 52, 64 }, { 5, 53, 64 }, { 5, 54, 64 }, { 6, 55, 64 },
{ 4, 56, 64 }, { 5, 57, 64 }, { 5, 58, 64 }, { 6, 59, 64 }, { 5, 60, 64 }, { 6, 61, 64 }, { 6, 62, 64 }, { 7, 63, 64 },
#if FP_LUT > 7
{ 1, 0, 0 }, { 2, 1, 128 }, { 2, 2, 128 }, { 3, 3, 128 }, { 2, 4, 128 }, { 3, 5, 128 }, { 3, 6, 128 }, { 4, 7, 128 },
{ 2, 8, 128 }, { 3, 9, 128 }, { 3, 10, 128 }, { 4, 11, 128 }, { 3, 12, 128 }, { 4, 13, 128 }, { 4, 14, 128 }, { 5, 15, 128 },
{ 2, 16, 128 }, { 3, 17, 128 }, { 3, 18, 128 }, { 4, 19, 128 }, { 3, 20, 128 }, { 4, 21, 128 }, { 4, 22, 128 }, { 5, 23, 128 },
{ 3, 24, 128 }, { 4, 25, 128 }, { 4, 26, 128 }, { 5, 27, 128 }, { 4, 28, 128 }, { 5, 29, 128 }, { 5, 30, 128 }, { 6, 31, 128 },
{ 2, 32, 128 }, { 3, 33, 128 }, { 3, 34, 128 }, { 4, 35, 128 }, { 3, 36, 128 }, { 4, 37, 128 }, { 4, 38, 128 }, { 5, 39, 128 },
{ 3, 40, 128 }, { 4, 41, 128 }, { 4, 42, 128 }, { 5, 43, 128 }, { 4, 44, 128 }, { 5, 45, 128 }, { 5, 46, 128 }, { 6, 47, 128 },
{ 3, 48, 128 }, { 4, 49, 128 }, { 4, 50, 128 }, { 5, 51, 128 }, { 4, 52, 128 }, { 5, 53, 128 }, { 5, 54, 128 }, { 6, 55, 128 },
{ 4, 56, 128 }, { 5, 57, 128 }, { 5, 58, 128 }, { 6, 59, 128 }, { 5, 60, 128 }, { 6, 61, 128 }, { 6, 62, 128 }, { 7, 63, 128 },
{ 2, 64, 128 }, { 3, 65, 128 }, { 3, 66, 128 }, { 4, 67, 128 }, { 3, 68, 128 }, { 4, 69, 128 }, { 4, 70, 128 }, { 5, 71, 128 },
{ 3, 72, 128 }, { 4, 73, 128 }, { 4, 74, 128 }, { 5, 75, 128 }, { 4, 76, 128 }, { 5, 77, 128 }, { 5, 78, 128 }, { 6, 79, 128 },
{ 3, 80, 128 }, { 4, 81, 128 }, { 4, 82, 128 }, { 5, 83, 128 }, { 4, 84, 128 }, { 5, 85, 128 }, { 5, 86, 128 }, { 6, 87, 128 },
{ 4, 88, 128 }, { 5, 89, 128 }, { 5, 90, 128 }, { 6, 91, 128 }, { 5, 92, 128 }, { 6, 93, 128 }, { 6, 94, 128 }, { 7, 95, 128 },
{ 3, 96, 128 }, { 4, 97, 128 }, { 4, 98, 128 }, { 5, 99, 128 }, { 4, 100, 128 }, { 5, 101, 128 }, { 5, 102, 128 }, { 6, 103, 128 },
{ 4, 104, 128 }, { 5, 105, 128 }, { 5, 106, 128 }, { 6, 107, 128 }, { 5, 108, 128 }, { 6, 109, 128 }, { 6, 110, 128 }, { 7, 111, 128 },
{ 4, 112, 128 }, { 5, 113, 128 }, { 5, 114, 128 }, { 6, 115, 128 }, { 5, 116, 128 }, { 6, 117, 128 }, { 6, 118, 128 }, { 7, 119, 128 },
{ 5, 120, 128 }, { 6, 121, 128 }, { 6, 122, 128 }, { 7, 123, 128 }, { 6, 124, 128 }, { 7, 125, 128 }, { 7, 126, 128 }, { 8, 127, 128 },
#if FP_LUT > 8
{ 1, 0, 0 }, { 2, 1, 256 }, { 2, 2, 256 }, { 3, 3, 256 }, { 2, 4, 256 }, { 3, 5, 256 }, { 3, 6, 256 }, { 4, 7, 256 },
{ 2, 8, 256 }, { 3, 9, 256 }, { 3, 10, 256 }, { 4, 11, 256 }, { 3, 12, 256 }, { 4, 13, 256 }, { 4, 14, 256 }, { 5, 15, 256 },
{ 2, 16, 256 }, { 3, 17, 256 }, { 3, 18, 256 }, { 4, 19, 256 }, { 3, 20, 256 }, { 4, 21, 256 }, { 4, 22, 256 }, { 5, 23, 256 },
{ 3, 24, 256 }, { 4, 25, 256 }, { 4, 26, 256 }, { 5, 27, 256 }, { 4, 28, 256 }, { 5, 29, 256 }, { 5, 30, 256 }, { 6, 31, 256 },
{ 2, 32, 256 }, { 3, 33, 256 }, { 3, 34, 256 }, { 4, 35, 256 }, { 3, 36, 256 }, { 4, 37, 256 }, { 4, 38, 256 }, { 5, 39, 256 },
{ 3, 40, 256 }, { 4, 41, 256 }, { 4, 42, 256 }, { 5, 43, 256 }, { 4, 44, 256 }, { 5, 45, 256 }, { 5, 46, 256 }, { 6, 47, 256 },
{ 3, 48, 256 }, { 4, 49, 256 }, { 4, 50, 256 }, { 5, 51, 256 }, { 4, 52, 256 }, { 5, 53, 256 }, { 5, 54, 256 }, { 6, 55, 256 },
{ 4, 56, 256 }, { 5, 57, 256 }, { 5, 58, 256 }, { 6, 59, 256 }, { 5, 60, 256 }, { 6, 61, 256 }, { 6, 62, 256 }, { 7, 63, 256 },
{ 2, 64, 256 }, { 3, 65, 256 }, { 3, 66, 256 }, { 4, 67, 256 }, { 3, 68, 256 }, { 4, 69, 256 }, { 4, 70, 256 }, { 5, 71, 256 },
{ 3, 72, 256 }, { 4, 73, 256 }, { 4, 74, 256 }, { 5, 75, 256 }, { 4, 76, 256 }, { 5, 77, 256 }, { 5, 78, 256 }, { 6, 79, 256 },
{ 3, 80, 256 }, { 4, 81, 256 }, { 4, 82, 256 }, { 5, 83, 256 }, { 4, 84, 256 }, { 5, 85, 256 }, { 5, 86, 256 }, { 6, 87, 256 },
{ 4, 88, 256 }, { 5, 89, 256 }, { 5, 90, 256 }, { 6, 91, 256 }, { 5, 92, 256 }, { 6, 93, 256 }, { 6, 94, 256 }, { 7, 95, 256 },
{ 3, 96, 256 }, { 4, 97, 256 }, { 4, 98, 256 }, { 5, 99, 256 }, { 4, 100, 256 }, { 5, 101, 256 }, { 5, 102, 256 }, { 6, 103, 256 },
{ 4, 104, 256 }, { 5, 105, 256 }, { 5, 106, 256 }, { 6, 107, 256 }, { 5, 108, 256 }, { 6, 109, 256 }, { 6, 110, 256 }, { 7, 111, 256 },
{ 4, 112, 256 }, { 5, 113, 256 }, { 5, 114, 256 }, { 6, 115, 256 }, { 5, 116, 256 }, { 6, 117, 256 }, { 6, 118, 256 }, { 7, 119, 256 },
{ 5, 120, 256 }, { 6, 121, 256 }, { 6, 122, 256 }, { 7, 123, 256 }, { 6, 124, 256 }, { 7, 125, 256 }, { 7, 126, 256 }, { 8, 127, 256 },
{ 2, 128, 256 }, { 3, 129, 256 }, { 3, 130, 256 }, { 4, 131, 256 }, { 3, 132, 256 }, { 4, 133, 256 }, { 4, 134, 256 }, { 5, 135, 256 },
{ 3, 136, 256 }, { 4, 137, 256 }, { 4, 138, 256 }, { 5, 139, 256 }, { 4, 140, 256 }, { 5, 141, 256 }, { 5, 142, 256 }, { 6, 143, 256 },
{ 3, 144, 256 }, { 4, 145, 256 }, { 4, 146, 256 }, { 5, 147, 256 }, { 4, 148, 256 }, { 5, 149, 256 }, { 5, 150, 256 }, { 6, 151, 256 },
{ 4, 152, 256 }, { 5, 153, 256 }, { 5, 154, 256 }, { 6, 155, 256 }, { 5, 156, 256 }, { 6, 157, 256 }, { 6, 158, 256 }, { 7, 159, 256 },
{ 3, 160, 256 }, { 4, 161, 256 }, { 4, 162, 256 }, { 5, 163, 256 }, { 4, 164, 256 }, { 5, 165, 256 }, { 5, 166, 256 }, { 6, 167, 256 },
{ 4, 168, 256 }, { 5, 169, 256 }, { 5, 170, 256 }, { 6, 171, 256 }, { 5, 172, 256 }, { 6, 173, 256 }, { 6, 174, 256 }, { 7, 175, 256 },
{ 4, 176, 256 }, { 5, 177, 256 }, { 5, 178, 256 }, { 6, 179, 256 }, { 5, 180, 256 }, { 6, 181, 256 }, { 6, 182, 256 }, { 7, 183, 256 },
{ 5, 184, 256 }, { 6, 185, 256 }, { 6, 186, 256 }, { 7, 187, 256 }, { 6, 188, 256 }, { 7, 189, 256 }, { 7, 190, 256 }, { 8, 191, 256 },
{ 3, 192, 256 }, { 4, 193, 256 }, { 4, 194, 256 }, { 5, 195, 256 }, { 4, 196, 256 }, { 5, 197, 256 }, { 5, 198, 256 }, { 6, 199, 256 },
{ 4, 200, 256 }, { 5, 201, 256 }, { 5, 202, 256 }, { 6, 203, 256 }, { 5, 204, 256 }, { 6, 205, 256 }, { 6, 206, 256 }, { 7, 207, 256 },
{ 4, 208, 256 }, { 5, 209, 256 }, { 5, 210, 256 }, { 6, 211, 256 }, { 5, 212, 256 }, { 6, 213, 256 }, { 6, 214, 256 }, { 7, 215, 256 },
{ 5, 216, 256 }, { 6, 217, 256 }, { 6, 218, 256 }, { 7, 219, 256 }, { 6, 220, 256 }, { 7, 221, 256 }, { 7, 222, 256 }, { 8, 223, 256 },
{ 4, 224, 256 }, { 5, 225, 256 }, { 5, 226, 256 }, { 6, 227, 256 }, { 5, 228, 256 }, { 6, 229, 256 }, { 6, 230, 256 }, { 7, 231, 256 },
{ 5, 232, 256 }, { 6, 233, 256 }, { 6, 234, 256 }, { 7, 235, 256 }, { 6, 236, 256 }, { 7, 237, 256 }, { 7, 238, 256 }, { 8, 239, 256 },
{ 5, 240, 256 }, { 6, 241, 256 }, { 6, 242, 256 }, { 7, 243, 256 }, { 6, 244, 256 }, { 7, 245, 256 }, { 7, 246, 256 }, { 8, 247, 256 },
{ 6, 248, 256 }, { 7, 249, 256 }, { 7, 250, 256 }, { 8, 251, 256 }, { 7, 252, 256 }, { 8, 253, 256 }, { 8, 254, 256 }, { 9, 255, 256 },
#if FP_LUT > 9
{ 1, 0, 0 }, { 2, 1, 512 }, { 2, 2, 512 }, { 3, 3, 512 }, { 2, 4, 512 }, { 3, 5, 512 }, { 3, 6, 512 }, { 4, 7, 512 },
{ 2, 8, 512 }, { 3, 9, 512 }, { 3, 10, 512 }, { 4, 11, 512 }, { 3, 12, 512 }, { 4, 13, 512 }, { 4, 14, 512 }, { 5, 15, 512 },
{ 2, 16, 512 }, { 3, 17, 512 }, { 3, 18, 512 }, { 4, 19, 512 }, { 3, 20, 512 }, { 4, 21, 512 }, { 4, 22, 512 }, { 5, 23, 512 },
{ 3, 24, 512 }, { 4, 25, 512 }, { 4, 26, 512 }, { 5, 27, 512 }, { 4, 28, 512 }, { 5, 29, 512 }, { 5, 30, 512 }, { 6, 31, 512 },
{ 2, 32, 512 }, { 3, 33, 512 }, { 3, 34, 512 }, { 4, 35, 512 }, { 3, 36, 512 }, { 4, 37, 512 }, { 4, 38, 512 }, { 5, 39, 512 },
{ 3, 40, 512 }, { 4, 41, 512 }, { 4, 42, 512 }, { 5, 43, 512 }, { 4, 44, 512 }, { 5, 45, 512 }, { 5, 46, 512 }, { 6, 47, 512 },
{ 3, 48, 512 }, { 4, 49, 512 }, { 4, 50, 512 }, { 5, 51, 512 }, { 4, 52, 512 }, { 5, 53, 512 }, { 5, 54, 512 }, { 6, 55, 512 },
{ 4, 56, 512 }, { 5, 57, 512 }, { 5, 58, 512 }, { 6, 59, 512 }, { 5, 60, 512 }, { 6, 61, 512 }, { 6, 62, 512 }, { 7, 63, 512 },
{ 2, 64, 512 }, { 3, 65, 512 }, { 3, 66, 512 }, { 4, 67, 512 }, { 3, 68, 512 }, { 4, 69, 512 }, { 4, 70, 512 }, { 5, 71, 512 },
{ 3, 72, 512 }, { 4, 73, 512 }, { 4, 74, 512 }, { 5, 75, 512 }, { 4, 76, 512 }, { 5, 77, 512 }, { 5, 78, 512 }, { 6, 79, 512 },
{ 3, 80, 512 }, { 4, 81, 512 }, { 4, 82, 512 }, { 5, 83, 512 }, { 4, 84, 512 }, { 5, 85, 512 }, { 5, 86, 512 }, { 6, 87, 512 },
{ 4, 88, 512 }, { 5, 89, 512 }, { 5, 90, 512 }, { 6, 91, 512 }, { 5, 92, 512 }, { 6, 93, 512 }, { 6, 94, 512 }, { 7, 95, 512 },
{ 3, 96, 512 }, { 4, 97, 512 }, { 4, 98, 512 }, { 5, 99, 512 }, { 4, 100, 512 }, { 5, 101, 512 }, { 5, 102, 512 }, { 6, 103, 512 },
{ 4, 104, 512 }, { 5, 105, 512 }, { 5, 106, 512 }, { 6, 107, 512 }, { 5, 108, 512 }, { 6, 109, 512 }, { 6, 110, 512 }, { 7, 111, 512 },
{ 4, 112, 512 }, { 5, 113, 512 }, { 5, 114, 512 }, { 6, 115, 512 }, { 5, 116, 512 }, { 6, 117, 512 }, { 6, 118, 512 }, { 7, 119, 512 },
{ 5, 120, 512 }, { 6, 121, 512 }, { 6, 122, 512 }, { 7, 123, 512 }, { 6, 124, 512 }, { 7, 125, 512 }, { 7, 126, 512 }, { 8, 127, 512 },
{ 2, 128, 512 }, { 3, 129, 512 }, { 3, 130, 512 }, { 4, 131, 512 }, { 3, 132, 512 }, { 4, 133, 512 }, { 4, 134, 512 }, { 5, 135, 512 },
{ 3, 136, 512 }, { 4, 137, 512 }, { 4, 138, 512 }, { 5, 139, 512 }, { 4, 140, 512 }, { 5, 141, 512 }, { 5, 142, 512 }, { 6, 143, 512 },
{ 3, 144, 512 }, { 4, 145, 512 }, { 4, 146, 512 }, { 5, 147, 512 }, { 4, 148, 512 }, { 5, 149, 512 }, { 5, 150, 512 }, { 6, 151, 512 },
{ 4, 152, 512 }, { 5, 153, 512 }, { 5, 154, 512 }, { 6, 155, 512 }, { 5, 156, 512 }, { 6, 157, 512 }, { 6, 158, 512 }, { 7, 159, 512 },
{ 3, 160, 512 }, { 4, 161, 512 }, { 4, 162, 512 }, { 5, 163, 512 }, { 4, 164, 512 }, { 5, 165, 512 }, { 5, 166, 512 }, { 6, 167, 512 },
{ 4, 168, 512 }, { 5, 169, 512 }, { 5, 170, 512 }, { 6, 171, 512 }, { 5, 172, 512 }, { 6, 173, 512 }, { 6, 174, 512 }, { 7, 175, 512 },
{ 4, 176, 512 }, { 5, 177, 512 }, { 5, 178, 512 }, { 6, 179, 512 }, { 5, 180, 512 }, { 6, 181, 512 }, { 6, 182, 512 }, { 7, 183, 512 },
{ 5, 184, 512 }, { 6, 185, 512 }, { 6, 186, 512 }, { 7, 187, 512 }, { 6, 188, 512 }, { 7, 189, 512 }, { 7, 190, 512 }, { 8, 191, 512 },
{ 3, 192, 512 }, { 4, 193, 512 }, { 4, 194, 512 }, { 5, 195, 512 }, { 4, 196, 512 }, { 5, 197, 512 }, { 5, 198, 512 }, { 6, 199, 512 },
{ 4, 200, 512 }, { 5, 201, 512 }, { 5, 202, 512 }, { 6, 203, 512 }, { 5, 204, 512 }, { 6, 205, 512 }, { 6, 206, 512 }, { 7, 207, 512 },
{ 4, 208, 512 }, { 5, 209, 512 }, { 5, 210, 512 }, { 6, 211, 512 }, { 5, 212, 512 }, { 6, 213, 512 }, { 6, 214, 512 }, { 7, 215, 512 },
{ 5, 216, 512 }, { 6, 217, 512 }, { 6, 218, 512 }, { 7, 219, 512 }, { 6, 220, 512 }, { 7, 221, 512 }, { 7, 222, 512 }, { 8, 223, 512 },
{ 4, 224, 512 }, { 5, 225, 512 }, { 5, 226, 512 }, { 6, 227, 512 }, { 5, 228, 512 }, { 6, 229, 512 }, { 6, 230, 512 }, { 7, 231, 512 },
{ 5, 232, 512 }, { 6, 233, 512 }, { 6, 234, 512 }, { 7, 235, 512 }, { 6, 236, 512 }, { 7, 237, 512 }, { 7, 238, 512 }, { 8, 239, 512 },
{ 5, 240, 512 }, { 6, 241, 512 }, { 6, 242, 512 }, { 7, 243, 512 }, { 6, 244, 512 }, { 7, 245, 512 }, { 7, 246, 512 }, { 8, 247, 512 },
{ 6, 248, 512 }, { 7, 249, 512 }, { 7, 250, 512 }, { 8, 251, 512 }, { 7, 252, 512 }, { 8, 253, 512 }, { 8, 254, 512 }, { 9, 255, 512 },
{ 2, 256, 512 }, { 3, 257, 512 }, { 3, 258, 512 }, { 4, 259, 512 }, { 3, 260, 512 }, { 4, 261, 512 }, { 4, 262, 512 }, { 5, 263, 512 },
{ 3, 264, 512 }, { 4, 265, 512 }, { 4, 266, 512 }, { 5, 267, 512 }, { 4, 268, 512 }, { 5, 269, 512 }, { 5, 270, 512 }, { 6, 271, 512 },
{ 3, 272, 512 }, { 4, 273, 512 }, { 4, 274, 512 }, { 5, 275, 512 }, { 4, 276, 512 }, { 5, 277, 512 }, { 5, 278, 512 }, { 6, 279, 512 },
{ 4, 280, 512 }, { 5, 281, 512 }, { 5, 282, 512 }, { 6, 283, 512 }, { 5, 284, 512 }, { 6, 285, 512 }, { 6, 286, 512 }, { 7, 287, 512 },
{ 3, 288, 512 }, { 4, 289, 512 }, { 4, 290, 512 }, { 5, 291, 512 }, { 4, 292, 512 }, { 5, 293, 512 }, { 5, 294, 512 }, { 6, 295, 512 },
{ 4, 296, 512 }, { 5, 297, 512 }, { 5, 298, 512 }, { 6, 299, 512 }, { 5, 300, 512 }, { 6, 301, 512 }, { 6, 302, 512 }, { 7, 303, 512 },
{ 4, 304, 512 }, { 5, 305, 512 }, { 5, 306, 512 }, { 6, 307, 512 }, { 5, 308, 512 }, { 6, 309, 512 }, { 6, 310, 512 }, { 7, 311, 512 },
{ 5, 312, 512 }, { 6, 313, 512 }, { 6, 314, 512 }, { 7, 315, 512 }, { 6, 316, 512 }, { 7, 317, 512 }, { 7, 318, 512 }, { 8, 319, 512 },
{ 3, 320, 512 }, { 4, 321, 512 }, { 4, 322, 512 }, { 5, 323, 512 }, { 4, 324, 512 }, { 5, 325, 512 }, { 5, 326, 512 }, { 6, 327, 512 },
{ 4, 328, 512 }, { 5, 329, 512 }, { 5, 330, 512 }, { 6, 331, 512 }, { 5, 332, 512 }, { 6, 333, 512 }, { 6, 334, 512 }, { 7, 335, 512 },
{ 4, 336, 512 }, { 5, 337, 512 }, { 5, 338, 512 }, { 6, 339, 512 }, { 5, 340, 512 }, { 6, 341, 512 }, { 6, 342, 512 }, { 7, 343, 512 },
{ 5, 344, 512 }, { 6, 345, 512 }, { 6, 346, 512 }, { 7, 347, 512 }, { 6, 348, 512 }, { 7, 349, 512 }, { 7, 350, 512 }, { 8, 351, 512 },
{ 4, 352, 512 }, { 5, 353, 512 }, { 5, 354, 512 }, { 6, 355, 512 }, { 5, 356, 512 }, { 6, 357, 512 }, { 6, 358, 512 }, { 7, 359, 512 },
{ 5, 360, 512 }, { 6, 361, 512 }, { 6, 362, 512 }, { 7, 363, 512 }, { 6, 364, 512 }, { 7, 365, 512 }, { 7, 366, 512 }, { 8, 367, 512 },
{ 5, 368, 512 }, { 6, 369, 512 }, { 6, 370, 512 }, { 7, 371, 512 }, { 6, 372, 512 }, { 7, 373, 512 }, { 7, 374, 512 }, { 8, 375, 512 },
{ 6, 376, 512 }, { 7, 377, 512 }, { 7, 378, 512 }, { 8, 379, 512 }, { 7, 380, 512 }, { 8, 381, 512 }, { 8, 382, 512 }, { 9, 383, 512 },
{ 3, 384, 512 }, { 4, 385, 512 }, { 4, 386, 512 }, { 5, 387, 512 }, { 4, 388, 512 }, { 5, 389, 512 }, { 5, 390, 512 }, { 6, 391, 512 },
{ 4, 392, 512 }, { 5, 393, 512 }, { 5, 394, 512 }, { 6, 395, 512 }, { 5, 396, 512 }, { 6, 397, 512 }, { 6, 398, 512 }, { 7, 399, 512 },
{ 4, 400, 512 }, { 5, 401, 512 }, { 5, 402, 512 }, { 6, 403, 512 }, { 5, 404, 512 }, { 6, 405, 512 }, { 6, 406, 512 }, { 7, 407, 512 },
{ 5, 408, 512 }, { 6, 409, 512 }, { 6, 410, 512 }, { 7, 411, 512 }, { 6, 412, 512 }, { 7, 413, 512 }, { 7, 414, 512 }, { 8, 415, 512 },
{ 4, 416, 512 }, { 5, 417, 512 }, { 5, 418, 512 }, { 6, 419, 512 }, { 5, 420, 512 }, { 6, 421, 512 }, { 6, 422, 512 }, { 7, 423, 512 },
{ 5, 424, 512 }, { 6, 425, 512 }, { 6, 426, 512 }, { 7, 427, 512 }, { 6, 428, 512 }, { 7, 429, 512 }, { 7, 430, 512 }, { 8, 431, 512 },
{ 5, 432, 512 }, { 6, 433, 512 }, { 6, 434, 512 }, { 7, 435, 512 }, { 6, 436, 512 }, { 7, 437, 512 }, { 7, 438, 512 }, { 8, 439, 512 },
{ 6, 440, 512 }, { 7, 441, 512 }, { 7, 442, 512 }, { 8, 443, 512 }, { 7, 444, 512 }, { 8, 445, 512 }, { 8, 446, 512 }, { 9, 447, 512 },
{ 4, 448, 512 }, { 5, 449, 512 }, { 5, 450, 512 }, { 6, 451, 512 }, { 5, 452, 512 }, { 6, 453, 512 }, { 6, 454, 512 }, { 7, 455, 512 },
{ 5, 456, 512 }, { 6, 457, 512 }, { 6, 458, 512 }, { 7, 459, 512 }, { 6, 460, 512 }, { 7, 461, 512 }, { 7, 462, 512 }, { 8, 463, 512 },
{ 5, 464, 512 }, { 6, 465, 512 }, { 6, 466, 512 }, { 7, 467, 512 }, { 6, 468, 512 }, { 7, 469, 512 }, { 7, 470, 512 }, { 8, 471, 512 },
{ 6, 472, 512 }, { 7, 473, 512 }, { 7, 474, 512 }, { 8, 475, 512 }, { 7, 476, 512 }, { 8, 477, 512 }, { 8, 478, 512 }, { 9, 479, 512 },
{ 5, 480, 512 }, { 6, 481, 512 }, { 6, 482, 512 }, { 7, 483, 512 }, { 6, 484, 512 }, { 7, 485, 512 }, { 7, 486, 512 }, { 8, 487, 512 },
{ 6, 488, 512 }, { 7, 489, 512 }, { 7, 490, 512 }, { 8, 491, 512 }, { 7, 492, 512 }, { 8, 493, 512 }, { 8, 494, 512 }, { 9, 495, 512 },
{ 6, 496, 512 }, { 7, 497, 512 }, { 7, 498, 512 }, { 8, 499, 512 }, { 7, 500, 512 }, { 8, 501, 512 }, { 8, 502, 512 }, { 9, 503, 512 },
{ 7, 504, 512 }, { 8, 505, 512 }, { 8, 506, 512 }, { 9, 507, 512 }, { 8, 508, 512 }, { 9, 509, 512 }, { 9, 510, 512 }, { 10, 511, 512 },
#if FP_LUT > 10
{ 1, 0, 0 }, { 2, 1, 1024 }, { 2, 2, 1024 }, { 3, 3, 1024 }, { 2, 4, 1024 }, { 3, 5, 1024 }, { 3, 6, 1024 }, { 4, 7, 1024 },
{ 2, 8, 1024 }, { 3, 9, 1024 }, { 3, 10, 1024 }, { 4, 11, 1024 }, { 3, 12, 1024 }, { 4, 13, 1024 }, { 4, 14, 1024 }, { 5, 15, 1024 },
{ 2, 16, 1024 }, { 3, 17, 1024 }, { 3, 18, 1024 }, { 4, 19, 1024 }, { 3, 20, 1024 }, { 4, 21, 1024 }, { 4, 22, 1024 }, { 5, 23, 1024 },
{ 3, 24, 1024 }, { 4, 25, 1024 }, { 4, 26, 1024 }, { 5, 27, 1024 }, { 4, 28, 1024 }, { 5, 29, 1024 }, { 5, 30, 1024 }, { 6, 31, 1024 },
{ 2, 32, 1024 }, { 3, 33, 1024 }, { 3, 34, 1024 }, { 4, 35, 1024 }, { 3, 36, 1024 }, { 4, 37, 1024 }, { 4, 38, 1024 }, { 5, 39, 1024 },
{ 3, 40, 1024 }, { 4, 41, 1024 }, { 4, 42, 1024 }, { 5, 43, 1024 }, { 4, 44, 1024 }, { 5, 45, 1024 }, { 5, 46, 1024 }, { 6, 47, 1024 },
{ 3, 48, 1024 }, { 4, 49, 1024 }, { 4, 50, 1024 }, { 5, 51, 1024 }, { 4, 52, 1024 }, { 5, 53, 1024 }, { 5, 54, 1024 }, { 6, 55, 1024 },
{ 4, 56, 1024 }, { 5, 57, 1024 }, { 5, 58, 1024 }, { 6, 59, 1024 }, { 5, 60, 1024 }, { 6, 61, 1024 }, { 6, 62, 1024 }, { 7, 63, 1024 },
{ 2, 64, 1024 }, { 3, 65, 1024 }, { 3, 66, 1024 }, { 4, 67, 1024 }, { 3, 68, 1024 }, { 4, 69, 1024 }, { 4, 70, 1024 }, { 5, 71, 1024 },
{ 3, 72, 1024 }, { 4, 73, 1024 }, { 4, 74, 1024 }, { 5, 75, 1024 }, { 4, 76, 1024 }, { 5, 77, 1024 }, { 5, 78, 1024 }, { 6, 79, 1024 },
{ 3, 80, 1024 }, { 4, 81, 1024 }, { 4, 82, 1024 }, { 5, 83, 1024 }, { 4, 84, 1024 }, { 5, 85, 1024 }, { 5, 86, 1024 }, { 6, 87, 1024 },
{ 4, 88, 1024 }, { 5, 89, 1024 }, { 5, 90, 1024 }, { 6, 91, 1024 }, { 5, 92, 1024 }, { 6, 93, 1024 }, { 6, 94, 1024 }, { 7, 95, 1024 },
{ 3, 96, 1024 }, { 4, 97, 1024 }, { 4, 98, 1024 }, { 5, 99, 1024 }, { 4, 100, 1024 }, { 5, 101, 1024 }, { 5, 102, 1024 }, { 6, 103, 1024 },
{ 4, 104, 1024 }, { 5, 105, 1024 }, { 5, 106, 1024 }, { 6, 107, 1024 }, { 5, 108, 1024 }, { 6, 109, 1024 }, { 6, 110, 1024 }, { 7, 111, 1024 },
{ 4, 112, 1024 }, { 5, 113, 1024 }, { 5, 114, 1024 }, { 6, 115, 1024 }, { 5, 116, 1024 }, { 6, 117, 1024 }, { 6, 118, 1024 }, { 7, 119, 1024 },
{ 5, 120, 1024 }, { 6, 121, 1024 }, { 6, 122, 1024 }, { 7, 123, 1024 }, { 6, 124, 1024 }, { 7, 125, 1024 }, { 7, 126, 1024 }, { 8, 127, 1024 },
{ 2, 128, 1024 }, { 3, 129, 1024 }, { 3, 130, 1024 }, { 4, 131, 1024 }, { 3, 132, 1024 }, { 4, 133, 1024 }, { 4, 134, 1024 }, { 5, 135, 1024 },
{ 3, 136, 1024 }, { 4, 137, 1024 }, { 4, 138, 1024 }, { 5, 139, 1024 }, { 4, 140, 1024 }, { 5, 141, 1024 }, { 5, 142, 1024 }, { 6, 143, 1024 },
{ 3, 144, 1024 }, { 4, 145, 1024 }, { 4, 146, 1024 }, { 5, 147, 1024 }, { 4, 148, 1024 }, { 5, 149, 1024 }, { 5, 150, 1024 }, { 6, 151, 1024 },
{ 4, 152, 1024 }, { 5, 153, 1024 }, { 5, 154, 1024 }, { 6, 155, 1024 }, { 5, 156, 1024 }, { 6, 157, 1024 }, { 6, 158, 1024 }, { 7, 159, 1024 },
{ 3, 160, 1024 }, { 4, 161, 1024 }, { 4, 162, 1024 }, { 5, 163, 1024 }, { 4, 164, 1024 }, { 5, 165, 1024 }, { 5, 166, 1024 }, { 6, 167, 1024 },
{ 4, 168, 1024 }, { 5, 169, 1024 }, { 5, 170, 1024 }, { 6, 171, 1024 }, { 5, 172, 1024 }, { 6, 173, 1024 }, { 6, 174, 1024 }, { 7, 175, 1024 },
{ 4, 176, 1024 }, { 5, 177, 1024 }, { 5, 178, 1024 }, { 6, 179, 1024 }, { 5, 180, 1024 }, { 6, 181, 1024 }, { 6, 182, 1024 }, { 7, 183, 1024 },
{ 5, 184, 1024 }, { 6, 185, 1024 }, { 6, 186, 1024 }, { 7, 187, 1024 }, { 6, 188, 1024 }, { 7, 189, 1024 }, { 7, 190, 1024 }, { 8, 191, 1024 },
{ 3, 192, 1024 }, { 4, 193, 1024 }, { 4, 194, 1024 }, { 5, 195, 1024 }, { 4, 196, 1024 }, { 5, 197, 1024 }, { 5, 198, 1024 }, { 6, 199, 1024 },
{ 4, 200, 1024 }, { 5, 201, 1024 }, { 5, 202, 1024 }, { 6, 203, 1024 }, { 5, 204, 1024 }, { 6, 205, 1024 }, { 6, 206, 1024 }, { 7, 207, 1024 },
{ 4, 208, 1024 }, { 5, 209, 1024 }, { 5, 210, 1024 }, { 6, 211, 1024 }, { 5, 212, 1024 }, { 6, 213, 1024 }, { 6, 214, 1024 }, { 7, 215, 1024 },
{ 5, 216, 1024 }, { 6, 217, 1024 }, { 6, 218, 1024 }, { 7, 219, 1024 }, { 6, 220, 1024 }, { 7, 221, 1024 }, { 7, 222, 1024 }, { 8, 223, 1024 },
{ 4, 224, 1024 }, { 5, 225, 1024 }, { 5, 226, 1024 }, { 6, 227, 1024 }, { 5, 228, 1024 }, { 6, 229, 1024 }, { 6, 230, 1024 }, { 7, 231, 1024 },
{ 5, 232, 1024 }, { 6, 233, 1024 }, { 6, 234, 1024 }, { 7, 235, 1024 }, { 6, 236, 1024 }, { 7, 237, 1024 }, { 7, 238, 1024 }, { 8, 239, 1024 },
{ 5, 240, 1024 }, { 6, 241, 1024 }, { 6, 242, 1024 }, { 7, 243, 1024 }, { 6, 244, 1024 }, { 7, 245, 1024 }, { 7, 246, 1024 }, { 8, 247, 1024 },
{ 6, 248, 1024 }, { 7, 249, 1024 }, { 7, 250, 1024 }, { 8, 251, 1024 }, { 7, 252, 1024 }, { 8, 253, 1024 }, { 8, 254, 1024 }, { 9, 255, 1024 },
{ 2, 256, 1024 }, { 3, 257, 1024 }, { 3, 258, 1024 }, { 4, 259, 1024 }, { 3, 260, 1024 }, { 4, 261, 1024 }, { 4, 262, 1024 }, { 5, 263, 1024 },
{ 3, 264, 1024 }, { 4, 265, 1024 }, { 4, 266, 1024 }, { 5, 267, 1024 }, { 4, 268, 1024 }, { 5, 269, 1024 }, { 5, 270, 1024 }, { 6, 271, 1024 },
{ 3, 272, 1024 }, { 4, 273, 1024 }, { 4, 274, 1024 }, { 5, 275, 1024 }, { 4, 276, 1024 }, { 5, 277, 1024 }, { 5, 278, 1024 }, { 6, 279, 1024 },
{ 4, 280, 1024 }, { 5, 281, 1024 }, { 5, 282, 1024 }, { 6, 283, 1024 }, { 5, 284, 1024 }, { 6, 285, 1024 }, { 6, 286, 1024 }, { 7, 287, 1024 },
{ 3, 288, 1024 }, { 4, 289, 1024 }, { 4, 290, 1024 }, { 5, 291, 1024 }, { 4, 292, 1024 }, { 5, 293, 1024 }, { 5, 294, 1024 }, { 6, 295, 1024 },
{ 4, 296, 1024 }, { 5, 297, 1024 }, { 5, 298, 1024 }, { 6, 299, 1024 }, { 5, 300, 1024 }, { 6, 301, 1024 }, { 6, 302, 1024 }, { 7, 303, 1024 },
{ 4, 304, 1024 }, { 5, 305, 1024 }, { 5, 306, 1024 }, { 6, 307, 1024 }, { 5, 308, 1024 }, { 6, 309, 1024 }, { 6, 310, 1024 }, { 7, 311, 1024 },
{ 5, 312, 1024 }, { 6, 313, 1024 }, { 6, 314, 1024 }, { 7, 315, 1024 }, { 6, 316, 1024 }, { 7, 317, 1024 }, { 7, 318, 1024 }, { 8, 319, 1024 },
{ 3, 320, 1024 }, { 4, 321, 1024 }, { 4, 322, 1024 }, { 5, 323, 1024 }, { 4, 324, 1024 }, { 5, 325, 1024 }, { 5, 326, 1024 }, { 6, 327, 1024 },
{ 4, 328, 1024 }, { 5, 329, 1024 }, { 5, 330, 1024 }, { 6, 331, 1024 }, { 5, 332, 1024 }, { 6, 333, 1024 }, { 6, 334, 1024 }, { 7, 335, 1024 },
{ 4, 336, 1024 }, { 5, 337, 1024 }, { 5, 338, 1024 }, { 6, 339, 1024 }, { 5, 340, 1024 }, { 6, 341, 1024 }, { 6, 342, 1024 }, { 7, 343, 1024 },
{ 5, 344, 1024 }, { 6, 345, 1024 }, { 6, 346, 1024 }, { 7, 347, 1024 }, { 6, 348, 1024 }, { 7, 349, 1024 }, { 7, 350, 1024 }, { 8, 351, 1024 },
{ 4, 352, 1024 }, { 5, 353, 1024 }, { 5, 354, 1024 }, { 6, 355, 1024 }, { 5, 356, 1024 }, { 6, 357, 1024 }, { 6, 358, 1024 }, { 7, 359, 1024 },
{ 5, 360, 1024 }, { 6, 361, 1024 }, { 6, 362, 1024 }, { 7, 363, 1024 }, { 6, 364, 1024 }, { 7, 365, 1024 }, { 7, 366, 1024 }, { 8, 367, 1024 },
{ 5, 368, 1024 }, { 6, 369, 1024 }, { 6, 370, 1024 }, { 7, 371, 1024 }, { 6, 372, 1024 }, { 7, 373, 1024 }, { 7, 374, 1024 }, { 8, 375, 1024 },
{ 6, 376, 1024 }, { 7, 377, 1024 }, { 7, 378, 1024 }, { 8, 379, 1024 }, { 7, 380, 1024 }, { 8, 381, 1024 }, { 8, 382, 1024 }, { 9, 383, 1024 },
{ 3, 384, 1024 }, { 4, 385, 1024 }, { 4, 386, 1024 }, { 5, 387, 1024 }, { 4, 388, 1024 }, { 5, 389, 1024 }, { 5, 390, 1024 }, { 6, 391, 1024 },
{ 4, 392, 1024 }, { 5, 393, 1024 }, { 5, 394, 1024 }, { 6, 395, 1024 }, { 5, 396, 1024 }, { 6, 397, 1024 }, { 6, 398, 1024 }, { 7, 399, 1024 },
{ 4, 400, 1024 }, { 5, 401, 1024 }, { 5, 402, 1024 }, { 6, 403, 1024 }, { 5, 404, 1024 }, { 6, 405, 1024 }, { 6, 406, 1024 }, { 7, 407, 1024 },
{ 5, 408, 1024 }, { 6, 409, 1024 }, { 6, 410, 1024 }, { 7, 411, 1024 }, { 6, 412, 1024 }, { 7, 413, 1024 }, { 7, 414, 1024 }, { 8, 415, 1024 },
{ 4, 416, 1024 }, { 5, 417, 1024 }, { 5, 418, 1024 }, { 6, 419, 1024 }, { 5, 420, 1024 }, { 6, 421, 1024 }, { 6, 422, 1024 }, { 7, 423, 1024 },
{ 5, 424, 1024 }, { 6, 425, 1024 }, { 6, 426, 1024 }, { 7, 427, 1024 }, { 6, 428, 1024 }, { 7, 429, 1024 }, { 7, 430, 1024 }, { 8, 431, 1024 },
{ 5, 432, 1024 }, { 6, 433, 1024 }, { 6, 434, 1024 }, { 7, 435, 1024 }, { 6, 436, 1024 }, { 7, 437, 1024 }, { 7, 438, 1024 }, { 8, 439, 1024 },
{ 6, 440, 1024 }, { 7, 441, 1024 }, { 7, 442, 1024 }, { 8, 443, 1024 }, { 7, 444, 1024 }, { 8, 445, 1024 }, { 8, 446, 1024 }, { 9, 447, 1024 },
{ 4, 448, 1024 }, { 5, 449, 1024 }, { 5, 450, 1024 }, { 6, 451, 1024 }, { 5, 452, 1024 }, { 6, 453, 1024 }, { 6, 454, 1024 }, { 7, 455, 1024 },
{ 5, 456, 1024 }, { 6, 457, 1024 }, { 6, 458, 1024 }, { 7, 459, 1024 }, { 6, 460, 1024 }, { 7, 461, 1024 }, { 7, 462, 1024 }, { 8, 463, 1024 },
{ 5, 464, 1024 }, { 6, 465, 1024 }, { 6, 466, 1024 }, { 7, 467, 1024 }, { 6, 468, 1024 }, { 7, 469, 1024 }, { 7, 470, 1024 }, { 8, 471, 1024 },
{ 6, 472, 1024 }, { 7, 473, 1024 }, { 7, 474, 1024 }, { 8, 475, 1024 }, { 7, 476, 1024 }, { 8, 477, 1024 }, { 8, 478, 1024 }, { 9, 479, 1024 },
{ 5, 480, 1024 }, { 6, 481, 1024 }, { 6, 482, 1024 }, { 7, 483, 1024 }, { 6, 484, 1024 }, { 7, 485, 1024 }, { 7, 486, 1024 }, { 8, 487, 1024 },
{ 6, 488, 1024 }, { 7, 489, 1024 }, { 7, 490, 1024 }, { 8, 491, 1024 }, { 7, 492, 1024 }, { 8, 493, 1024 }, { 8, 494, 1024 }, { 9, 495, 1024 },
{ 6, 496, 1024 }, { 7, 497, 1024 }, { 7, 498, 1024 }, { 8, 499, 1024 }, { 7, 500, 1024 }, { 8, 501, 1024 }, { 8, 502, 1024 }, { 9, 503, 1024 },
{ 7, 504, 1024 }, { 8, 505, 1024 }, { 8, 506, 1024 }, { 9, 507, 1024 }, { 8, 508, 1024 }, { 9, 509, 1024 }, { 9, 510, 1024 }, { 10, 511, 1024 },
{ 2, 512, 1024 }, { 3, 513, 1024 }, { 3, 514, 1024 }, { 4, 515, 1024 }, { 3, 516, 1024 }, { 4, 517, 1024 }, { 4, 518, 1024 }, { 5, 519, 1024 },
{ 3, 520, 1024 }, { 4, 521, 1024 }, { 4, 522, 1024 }, { 5, 523, 1024 }, { 4, 524, 1024 }, { 5, 525, 1024 }, { 5, 526, 1024 }, { 6, 527, 1024 },
{ 3, 528, 1024 }, { 4, 529, 1024 }, { 4, 530, 1024 }, { 5, 531, 1024 }, { 4, 532, 1024 }, { 5, 533, 1024 }, { 5, 534, 1024 }, { 6, 535, 1024 },
{ 4, 536, 1024 }, { 5, 537, 1024 }, { 5, 538, 1024 }, { 6, 539, 1024 }, { 5, 540, 1024 }, { 6, 541, 1024 }, { 6, 542, 1024 }, { 7, 543, 1024 },
{ 3, 544, 1024 }, { 4, 545, 1024 }, { 4, 546, 1024 }, { 5, 547, 1024 }, { 4, 548, 1024 }, { 5, 549, 1024 }, { 5, 550, 1024 }, { 6, 551, 1024 },
{ 4, 552, 1024 }, { 5, 553, 1024 }, { 5, 554, 1024 }, { 6, 555, 1024 }, { 5, 556, 1024 }, { 6, 557, 1024 }, { 6, 558, 1024 }, { 7, 559, 1024 },
{ 4, 560, 1024 }, { 5, 561, 1024 }, { 5, 562, 1024 }, { 6, 563, 1024 }, { 5, 564, 1024 }, { 6, 565, 1024 }, { 6, 566, 1024 }, { 7, 567, 1024 },
{ 5, 568, 1024 }, { 6, 569, 1024 }, { 6, 570, 1024 }, { 7, 571, 1024 }, { 6, 572, 1024 }, { 7, 573, 1024 }, { 7, 574, 1024 }, { 8, 575, 1024 },
{ 3, 576, 1024 }, { 4, 577, 1024 }, { 4, 578, 1024 }, { 5, 579, 1024 }, { 4, 580, 1024 }, { 5, 581, 1024 }, { 5, 582, 1024 }, { 6, 583, 1024 },
{ 4, 584, 1024 }, { 5, 585, 1024 }, { 5, 586, 1024 }, { 6, 587, 1024 }, { 5, 588, 1024 }, { 6, 589, 1024 }, { 6, 590, 1024 }, { 7, 591, 1024 },
{ 4, 592, 1024 }, { 5, 593, 1024 }, { 5, 594, 1024 }, { 6, 595, 1024 }, { 5, 596, 1024 }, { 6, 597, 1024 }, { 6, 598, 1024 }, { 7, 599, 1024 },
{ 5, 600, 1024 }, { 6, 601, 1024 }, { 6, 602, 1024 }, { 7, 603, 1024 }, { 6, 604, 1024 }, { 7, 605, 1024 }, { 7, 606, 1024 }, { 8, 607, 1024 },
{ 4, 608, 1024 }, { 5, 609, 1024 }, { 5, 610, 1024 }, { 6, 611, 1024 }, { 5, 612, 1024 }, { 6, 613, 1024 }, { 6, 614, 1024 }, { 7, 615, 1024 },
{ 5, 616, 1024 }, { 6, 617, 1024 }, { 6, 618, 1024 }, { 7, 619, 1024 }, { 6, 620, 1024 }, { 7, 621, 1024 }, { 7, 622, 1024 }, { 8, 623, 1024 },
{ 5, 624, 1024 }, { 6, 625, 1024 }, { 6, 626, 1024 }, { 7, 627, 1024 }, { 6, 628, 1024 }, { 7, 629, 1024 }, { 7, 630, 1024 }, { 8, 631, 1024 },
{ 6, 632, 1024 }, { 7, 633, 1024 }, { 7, 634, 1024 }, { 8, 635, 1024 }, { 7, 636, 1024 }, { 8, 637, 1024 }, { 8, 638, 1024 }, { 9, 639, 1024 },
{ 3, 640, 1024 }, { 4, 641, 1024 }, { 4, 642, 1024 }, { 5, 643, 1024 }, { 4, 644, 1024 }, { 5, 645, 1024 }, { 5, 646, 1024 }, { 6, 647, 1024 },
{ 4, 648, 1024 }, { 5, 649, 1024 }, { 5, 650, 1024 }, { 6, 651, 1024 }, { 5, 652, 1024 }, { 6, 653, 1024 }, { 6, 654, 1024 }, { 7, 655, 1024 },
{ 4, 656, 1024 }, { 5, 657, 1024 }, { 5, 658, 1024 }, { 6, 659, 1024 }, { 5, 660, 1024 }, { 6, 661, 1024 }, { 6, 662, 1024 }, { 7, 663, 1024 },
{ 5, 664, 1024 }, { 6, 665, 1024 }, { 6, 666, 1024 }, { 7, 667, 1024 }, { 6, 668, 1024 }, { 7, 669, 1024 }, { 7, 670, 1024 }, { 8, 671, 1024 },
{ 4, 672, 1024 }, { 5, 673, 1024 }, { 5, 674, 1024 }, { 6, 675, 1024 }, { 5, 676, 1024 }, { 6, 677, 1024 }, { 6, 678, 1024 }, { 7, 679, 1024 },
{ 5, 680, 1024 }, { 6, 681, 1024 }, { 6, 682, 1024 }, { 7, 683, 1024 }, { 6, 684, 1024 }, { 7, 685, 1024 }, { 7, 686, 1024 }, { 8, 687, 1024 },
{ 5, 688, 1024 }, { 6, 689, 1024 }, { 6, 690, 1024 }, { 7, 691, 1024 }, { 6, 692, 1024 }, { 7, 693, 1024 }, { 7, 694, 1024 }, { 8, 695, 1024 },
{ 6, 696, 1024 }, { 7, 697, 1024 }, { 7, 698, 1024 }, { 8, 699, 1024 }, { 7, 700, 1024 }, { 8, 701, 1024 }, { 8, 702, 1024 }, { 9, 703, 1024 },
{ 4, 704, 1024 }, { 5, 705, 1024 }, { 5, 706, 1024 }, { 6, 707, 1024 }, { 5, 708, 1024 }, { 6, 709, 1024 }, { 6, 710, 1024 }, { 7, 711, 1024 },
{ 5, 712, 1024 }, { 6, 713, 1024 }, { 6, 714, 1024 }, { 7, 715, 1024 }, { 6, 716, 1024 }, { 7, 717, 1024 }, { 7, 718, 1024 }, { 8, 719, 1024 },
{ 5, 720, 1024 }, { 6, 721, 1024 }, { 6, 722, 1024 }, { 7, 723, 1024 }, { 6, 724, 1024 }, { 7, 725, 1024 }, { 7, 726, 1024 }, { 8, 727, 1024 },
{ 6, 728, 1024 }, { 7, 729, 1024 }, { 7, 730, 1024 }, { 8, 731, 1024 }, { 7, 732, 1024 }, { 8, 733, 1024 }, { 8, 734, 1024 }, { 9, 735, 1024 },
{ 5, 736, 1024 }, { 6, 737, 1024 }, { 6, 738, 1024 }, { 7, 739, 1024 }, { 6, 740, 1024 }, { 7, 741, 1024 }, { 7, 742, 1024 }, { 8, 743, 1024 },
{ 6, 744, 1024 }, { 7, 745, 1024 }, { 7, 746, 1024 }, { 8, 747, 1024 }, { 7, 748, 1024 }, { 8, 749, 1024 }, { 8, 750, 1024 }, { 9, 751, 1024 },
{ 6, 752, 1024 }, { 7, 753, 1024 }, { 7, 754, 1024 }, { 8, 755, 1024 }, { 7, 756, 1024 }, { 8, 757, 1024 }, { 8, 758, 1024 }, { 9, 759, 1024 },
{ 7, 760, 1024 }, { 8, 761, 1024 }, { 8, 762, 1024 }, { 9, 763, 1024 }, { 8, 764, 1024 }, { 9, 765, 1024 }, { 9, 766, 1024 }, { 10, 767, 1024 },
{ 3, 768, 1024 }, { 4, 769, 1024 }, { 4, 770, 1024 }, { 5, 771, 1024 }, { 4, 772, 1024 }, { 5, 773, 1024 }, { 5, 774, 1024 }, { 6, 775, 1024 },
{ 4, 776, 1024 }, { 5, 777, 1024 }, { 5, 778, 1024 }, { 6, 779, 1024 }, { 5, 780, 1024 }, { 6, 781, 1024 }, { 6, 782, 1024 }, { 7, 783, 1024 },
{ 4, 784, 1024 }, { 5, 785, 1024 }, { 5, 786, 1024 }, { 6, 787, 1024 }, { 5, 788, 1024 }, { 6, 789, 1024 }, { 6, 790, 1024 }, { 7, 791, 1024 },
{ 5, 792, 1024 }, { 6, 793, 1024 }, { 6, 794, 1024 }, { 7, 795, 1024 }, { 6, 796, 1024 }, { 7, 797, 1024 }, { 7, 798, 1024 }, { 8, 799, 1024 },
{ 4, 800, 1024 }, { 5, 801, 1024 }, { 5, 802, 1024 }, { 6, 803, 1024 }, { 5, 804, 1024 }, { 6, 805, 1024 }, { 6, 806, 1024 }, { 7, 807, 1024 },
{ 5, 808, 1024 }, { 6, 809, 1024 }, { 6, 810, 1024 }, { 7, 811, 1024 }, { 6, 812, 1024 }, { 7, 813, 1024 }, { 7, 814, 1024 }, { 8, 815, 1024 },
{ 5, 816, 1024 }, { 6, 817, 1024 }, { 6, 818, 1024 }, { 7, 819, 1024 }, { 6, 820, 1024 }, { 7, 821, 1024 }, { 7, 822, 1024 }, { 8, 823, 1024 },
{ 6, 824, 1024 }, { 7, 825, 1024 }, { 7, 826, 1024 }, { 8, 827, 1024 }, { 7, 828, 1024 }, { 8, 829, 1024 }, { 8, 830, 1024 }, { 9, 831, 1024 },
{ 4, 832, 1024 }, { 5, 833, 1024 }, { 5, 834, 1024 }, { 6, 835, 1024 }, { 5, 836, 1024 }, { 6, 837, 1024 }, { 6, 838, 1024 }, { 7, 839, 1024 },
{ 5, 840, 1024 }, { 6, 841, 1024 }, { 6, 842, 1024 }, { 7, 843, 1024 }, { 6, 844, 1024 }, { 7, 845, 1024 }, { 7, 846, 1024 }, { 8, 847, 1024 },
{ 5, 848, 1024 }, { 6, 849, 1024 }, { 6, 850, 1024 }, { 7, 851, 1024 }, { 6, 852, 1024 }, { 7, 853, 1024 }, { 7, 854, 1024 }, { 8, 855, 1024 },
{ 6, 856, 1024 }, { 7, 857, 1024 }, { 7, 858, 1024 }, { 8, 859, 1024 }, { 7, 860, 1024 }, { 8, 861, 1024 }, { 8, 862, 1024 }, { 9, 863, 1024 },
{ 5, 864, 1024 }, { 6, 865, 1024 }, { 6, 866, 1024 }, { 7, 867, 1024 }, { 6, 868, 1024 }, { 7, 869, 1024 }, { 7, 870, 1024 }, { 8, 871, 1024 },
{ 6, 872, 1024 }, { 7, 873, 1024 }, { 7, 874, 1024 }, { 8, 875, 1024 }, { 7, 876, 1024 }, { 8, 877, 1024 }, { 8, 878, 1024 }, { 9, 879, 1024 },
{ 6, 880, 1024 }, { 7, 881, 1024 }, { 7, 882, 1024 }, { 8, 883, 1024 }, { 7, 884, 1024 }, { 8, 885, 1024 }, { 8, 886, 1024 }, { 9, 887, 1024 },
{ 7, 888, 1024 }, { 8, 889, 1024 }, { 8, 890, 1024 }, { 9, 891, 1024 }, { 8, 892, 1024 }, { 9, 893, 1024 }, { 9, 894, 1024 }, { 10, 895, 1024 },
{ 4, 896, 1024 }, { 5, 897, 1024 }, { 5, 898, 1024 }, { 6, 899, 1024 }, { 5, 900, 1024 }, { 6, 901, 1024 }, { 6, 902, 1024 }, { 7, 903, 1024 },
{ 5, 904, 1024 }, { 6, 905, 1024 }, { 6, 906, 1024 }, { 7, 907, 1024 }, { 6, 908, 1024 }, { 7, 909, 1024 }, { 7, 910, 1024 }, { 8, 911, 1024 },
{ 5, 912, 1024 }, { 6, 913, 1024 }, { 6, 914, 1024 }, { 7, 915, 1024 }, { 6, 916, 1024 }, { 7, 917, 1024 }, { 7, 918, 1024 }, { 8, 919, 1024 },
{ 6, 920, 1024 }, { 7, 921, 1024 }, { 7, 922, 1024 }, { 8, 923, 1024 }, { 7, 924, 1024 }, { 8, 925, 1024 }, { 8, 926, 1024 }, { 9, 927, 1024 },
{ 5, 928, 1024 }, { 6, 929, 1024 }, { 6, 930, 1024 }, { 7, 931, 1024 }, { 6, 932, 1024 }, { 7, 933, 1024 }, { 7, 934, 1024 }, { 8, 935, 1024 },
{ 6, 936, 1024 }, { 7, 937, 1024 }, { 7, 938, 1024 }, { 8, 939, 1024 }, { 7, 940, 1024 }, { 8, 941, 1024 }, { 8, 942, 1024 }, { 9, 943, 1024 },
{ 6, 944, 1024 }, { 7, 945, 1024 }, { 7, 946, 1024 }, { 8, 947, 1024 }, { 7, 948, 1024 }, { 8, 949, 1024 }, { 8, 950, 1024 }, { 9, 951, 1024 },
{ 7, 952, 1024 }, { 8, 953, 1024 }, { 8, 954, 1024 }, { 9, 955, 1024 }, { 8, 956, 1024 }, { 9, 957, 1024 }, { 9, 958, 1024 }, { 10, 959, 1024 },
{ 5, 960, 1024 }, { 6, 961, 1024 }, { 6, 962, 1024 }, { 7, 963, 1024 }, { 6, 964, 1024 }, { 7, 965, 1024 }, { 7, 966, 1024 }, { 8, 967, 1024 },
{ 6, 968, 1024 }, { 7, 969, 1024 }, { 7, 970, 1024 }, { 8, 971, 1024 }, { 7, 972, 1024 }, { 8, 973, 1024 }, { 8, 974, 1024 }, { 9, 975, 1024 },
{ 6, 976, 1024 }, { 7, 977, 1024 }, { 7, 978, 1024 }, { 8, 979, 1024 }, { 7, 980, 1024 }, { 8, 981, 1024 }, { 8, 982, 1024 }, { 9, 983, 1024 },
{ 7, 984, 1024 }, { 8, 985, 1024 }, { 8, 986, 1024 }, { 9, 987, 1024 }, { 8, 988, 1024 }, { 9, 989, 1024 }, { 9, 990, 1024 }, { 10, 991, 1024 },
{ 6, 992, 1024 }, { 7, 993, 1024 }, { 7, 994, 1024 }, { 8, 995, 1024 }, { 7, 996, 1024 }, { 8, 997, 1024 }, { 8, 998, 1024 }, { 9, 999, 1024 },
{ 7, 1000, 1024 }, { 8, 1001, 1024 }, { 8, 1002, 1024 }, { 9, 1003, 1024 }, { 8, 1004, 1024 }, { 9, 1005, 1024 }, { 9, 1006, 1024 }, { 10, 1007, 1024 },
{ 7, 1008, 1024 }, { 8, 1009, 1024 }, { 8, 1010, 1024 }, { 9, 1011, 1024 }, { 8, 1012, 1024 }, { 9, 1013, 1024 }, { 9, 1014, 1024 }, { 10, 1015, 1024 },
{ 8, 1016, 1024 }, { 9, 1017, 1024 }, { 9, 1018, 1024 }, { 10, 1019, 1024 }, { 9, 1020, 1024 }, { 10, 1021, 1024 }, { 10, 1022, 1024 }, { 11, 1023, 1024 },
#if FP_LUT > 11
{ 1, 0, 0 }, { 2, 1, 2048 }, { 2, 2, 2048 }, { 3, 3, 2048 }, { 2, 4, 2048 }, { 3, 5, 2048 }, { 3, 6, 2048 }, { 4, 7, 2048 },
{ 2, 8, 2048 }, { 3, 9, 2048 }, { 3, 10, 2048 }, { 4, 11, 2048 }, { 3, 12, 2048 }, { 4, 13, 2048 }, { 4, 14, 2048 }, { 5, 15, 2048 },
{ 2, 16, 2048 }, { 3, 17, 2048 }, { 3, 18, 2048 }, { 4, 19, 2048 }, { 3, 20, 2048 }, { 4, 21, 2048 }, { 4, 22, 2048 }, { 5, 23, 2048 },
{ 3, 24, 2048 }, { 4, 25, 2048 }, { 4, 26, 2048 }, { 5, 27, 2048 }, { 4, 28, 2048 }, { 5, 29, 2048 }, { 5, 30, 2048 }, { 6, 31, 2048 },
{ 2, 32, 2048 }, { 3, 33, 2048 }, { 3, 34, 2048 }, { 4, 35, 2048 }, { 3, 36, 2048 }, { 4, 37, 2048 }, { 4, 38, 2048 }, { 5, 39, 2048 },
{ 3, 40, 2048 }, { 4, 41, 2048 }, { 4, 42, 2048 }, { 5, 43, 2048 }, { 4, 44, 2048 }, { 5, 45, 2048 }, { 5, 46, 2048 }, { 6, 47, 2048 },
{ 3, 48, 2048 }, { 4, 49, 2048 }, { 4, 50, 2048 }, { 5, 51, 2048 }, { 4, 52, 2048 }, { 5, 53, 2048 }, { 5, 54, 2048 }, { 6, 55, 2048 },
{ 4, 56, 2048 }, { 5, 57, 2048 }, { 5, 58, 2048 }, { 6, 59, 2048 }, { 5, 60, 2048 }, { 6, 61, 2048 }, { 6, 62, 2048 }, { 7, 63, 2048 },
{ 2, 64, 2048 }, { 3, 65, 2048 }, { 3, 66, 2048 }, { 4, 67, 2048 }, { 3, 68, 2048 }, { 4, 69, 2048 }, { 4, 70, 2048 }, { 5, 71, 2048 },
{ 3, 72, 2048 }, { 4, 73, 2048 }, { 4, 74, 2048 }, { 5, 75, 2048 }, { 4, 76, 2048 }, { 5, 77, 2048 }, { 5, 78, 2048 }, { 6, 79, 2048 },
{ 3, 80, 2048 }, { 4, 81, 2048 }, { 4, 82, 2048 }, { 5, 83, 2048 }, { 4, 84, 2048 }, { 5, 85, 2048 }, { 5, 86, 2048 }, { 6, 87, 2048 },
{ 4, 88, 2048 }, { 5, 89, 2048 }, { 5, 90, 2048 }, { 6, 91, 2048 }, { 5, 92, 2048 }, { 6, 93, 2048 }, { 6, 94, 2048 }, { 7, 95, 2048 },
{ 3, 96, 2048 }, { 4, 97, 2048 }, { 4, 98, 2048 }, { 5, 99, 2048 }, { 4, 100, 2048 }, { 5, 101, 2048 }, { 5, 102, 2048 }, { 6, 103, 2048 },
{ 4, 104, 2048 }, { 5, 105, 2048 }, { 5, 106, 2048 }, { 6, 107, 2048 }, { 5, 108, 2048 }, { 6, 109, 2048 }, { 6, 110, 2048 }, { 7, 111, 2048 },
{ 4, 112, 2048 }, { 5, 113, 2048 }, { 5, 114, 2048 }, { 6, 115, 2048 }, { 5, 116, 2048 }, { 6, 117, 2048 }, { 6, 118, 2048 }, { 7, 119, 2048 },
{ 5, 120, 2048 }, { 6, 121, 2048 }, { 6, 122, 2048 }, { 7, 123, 2048 }, { 6, 124, 2048 }, { 7, 125, 2048 }, { 7, 126, 2048 }, { 8, 127, 2048 },
{ 2, 128, 2048 }, { 3, 129, 2048 }, { 3, 130, 2048 }, { 4, 131, 2048 }, { 3, 132, 2048 }, { 4, 133, 2048 }, { 4, 134, 2048 }, { 5, 135, 2048 },
{ 3, 136, 2048 }, { 4, 137, 2048 }, { 4, 138, 2048 }, { 5, 139, 2048 }, { 4, 140, 2048 }, { 5, 141, 2048 }, { 5, 142, 2048 }, { 6, 143, 2048 },
{ 3, 144, 2048 }, { 4, 145, 2048 }, { 4, 146, 2048 }, { 5, 147, 2048 }, { 4, 148, 2048 }, { 5, 149, 2048 }, { 5, 150, 2048 }, { 6, 151, 2048 },
{ 4, 152, 2048 }, { 5, 153, 2048 }, { 5, 154, 2048 }, { 6, 155, 2048 }, { 5, 156, 2048 }, { 6, 157, 2048 }, { 6, 158, 2048 }, { 7, 159, 2048 },
{ 3, 160, 2048 }, { 4, 161, 2048 }, { 4, 162, 2048 }, { 5, 163, 2048 }, { 4, 164, 2048 }, { 5, 165, 2048 }, { 5, 166, 2048 }, { 6, 167, 2048 },
{ 4, 168, 2048 }, { 5, 169, 2048 }, { 5, 170, 2048 }, { 6, 171, 2048 }, { 5, 172, 2048 }, { 6, 173, 2048 }, { 6, 174, 2048 }, { 7, 175, 2048 },
{ 4, 176, 2048 }, { 5, 177, 2048 }, { 5, 178, 2048 }, { 6, 179, 2048 }, { 5, 180, 2048 }, { 6, 181, 2048 }, { 6, 182, 2048 }, { 7, 183, 2048 },
{ 5, 184, 2048 }, { 6, 185, 2048 }, { 6, 186, 2048 }, { 7, 187, 2048 }, { 6, 188, 2048 }, { 7, 189, 2048 }, { 7, 190, 2048 }, { 8, 191, 2048 },
{ 3, 192, 2048 }, { 4, 193, 2048 }, { 4, 194, 2048 }, { 5, 195, 2048 }, { 4, 196, 2048 }, { 5, 197, 2048 }, { 5, 198, 2048 }, { 6, 199, 2048 },
{ 4, 200, 2048 }, { 5, 201, 2048 }, { 5, 202, 2048 }, { 6, 203, 2048 }, { 5, 204, 2048 }, { 6, 205, 2048 }, { 6, 206, 2048 }, { 7, 207, 2048 },
{ 4, 208, 2048 }, { 5, 209, 2048 }, { 5, 210, 2048 }, { 6, 211, 2048 }, { 5, 212, 2048 }, { 6, 213, 2048 }, { 6, 214, 2048 }, { 7, 215, 2048 },
{ 5, 216, 2048 }, { 6, 217, 2048 }, { 6, 218, 2048 }, { 7, 219, 2048 }, { 6, 220, 2048 }, { 7, 221, 2048 }, { 7, 222, 2048 }, { 8, 223, 2048 },
{ 4, 224, 2048 }, { 5, 225, 2048 }, { 5, 226, 2048 }, { 6, 227, 2048 }, { 5, 228, 2048 }, { 6, 229, 2048 }, { 6, 230, 2048 }, { 7, 231, 2048 },
{ 5, 232, 2048 }, { 6, 233, 2048 }, { 6, 234, 2048 }, { 7, 235, 2048 }, { 6, 236, 2048 }, { 7, 237, 2048 }, { 7, 238, 2048 }, { 8, 239, 2048 },
{ 5, 240, 2048 }, { 6, 241, 2048 }, { 6, 242, 2048 }, { 7, 243, 2048 }, { 6, 244, 2048 }, { 7, 245, 2048 }, { 7, 246, 2048 }, { 8, 247, 2048 },
{ 6, 248, 2048 }, { 7, 249, 2048 }, { 7, 250, 2048 }, { 8, 251, 2048 }, { 7, 252, 2048 }, { 8, 253, 2048 }, { 8, 254, 2048 }, { 9, 255, 2048 },
{ 2, 256, 2048 }, { 3, 257, 2048 }, { 3, 258, 2048 }, { 4, 259, 2048 }, { 3, 260, 2048 }, { 4, 261, 2048 }, { 4, 262, 2048 }, { 5, 263, 2048 },
{ 3, 264, 2048 }, { 4, 265, 2048 }, { 4, 266, 2048 }, { 5, 267, 2048 }, { 4, 268, 2048 }, { 5, 269, 2048 }, { 5, 270, 2048 }, { 6, 271, 2048 },
{ 3, 272, 2048 }, { 4, 273, 2048 }, { 4, 274, 2048 }, { 5, 275, 2048 }, { 4, 276, 2048 }, { 5, 277, 2048 }, { 5, 278, 2048 }, { 6, 279, 2048 },
{ 4, 280, 2048 }, { 5, 281, 2048 }, { 5, 282, 2048 }, { 6, 283, 2048 }, { 5, 284, 2048 }, { 6, 285, 2048 }, { 6, 286, 2048 }, { 7, 287, 2048 },
{ 3, 288, 2048 }, { 4, 289, 2048 }, { 4, 290, 2048 }, { 5, 291, 2048 }, { 4, 292, 2048 }, { 5, 293, 2048 }, { 5, 294, 2048 }, { 6, 295, 2048 },
{ 4, 296, 2048 }, { 5, 297, 2048 }, { 5, 298, 2048 }, { 6, 299, 2048 }, { 5, 300, 2048 }, { 6, 301, 2048 }, { 6, 302, 2048 }, { 7, 303, 2048 },
{ 4, 304, 2048 }, { 5, 305, 2048 }, { 5, 306, 2048 }, { 6, 307, 2048 }, { 5, 308, 2048 }, { 6, 309, 2048 }, { 6, 310, 2048 }, { 7, 311, 2048 },
{ 5, 312, 2048 }, { 6, 313, 2048 }, { 6, 314, 2048 }, { 7, 315, 2048 }, { 6, 316, 2048 }, { 7, 317, 2048 }, { 7, 318, 2048 }, { 8, 319, 2048 },
{ 3, 320, 2048 }, { 4, 321, 2048 }, { 4, 322, 2048 }, { 5, 323, 2048 }, { 4, 324, 2048 }, { 5, 325, 2048 }, { 5, 326, 2048 }, { 6, 327, 2048 },
{ 4, 328, 2048 }, { 5, 329, 2048 }, { 5, 330, 2048 }, { 6, 331, 2048 }, { 5, 332, 2048 }, { 6, 333, 2048 }, { 6, 334, 2048 }, { 7, 335, 2048 },
{ 4, 336, 2048 }, { 5, 337, 2048 }, { 5, 338, 2048 }, { 6, 339, 2048 }, { 5, 340, 2048 }, { 6, 341, 2048 }, { 6, 342, 2048 }, { 7, 343, 2048 },
{ 5, 344, 2048 }, { 6, 345, 2048 }, { 6, 346, 2048 }, { 7, 347, 2048 }, { 6, 348, 2048 }, { 7, 349, 2048 }, { 7, 350, 2048 }, { 8, 351, 2048 },
{ 4, 352, 2048 }, { 5, 353, 2048 }, { 5, 354, 2048 }, { 6, 355, 2048 }, { 5, 356, 2048 }, { 6, 357, 2048 }, { 6, 358, 2048 }, { 7, 359, 2048 },
{ 5, 360, 2048 }, { 6, 361, 2048 }, { 6, 362, 2048 }, { 7, 363, 2048 }, { 6, 364, 2048 }, { 7, 365, 2048 }, { 7, 366, 2048 }, { 8, 367, 2048 },
{ 5, 368, 2048 }, { 6, 369, 2048 }, { 6, 370, 2048 }, { 7, 371, 2048 }, { 6, 372, 2048 }, { 7, 373, 2048 }, { 7, 374, 2048 }, { 8, 375, 2048 },
{ 6, 376, 2048 }, { 7, 377, 2048 }, { 7, 378, 2048 }, { 8, 379, 2048 }, { 7, 380, 2048 }, { 8, 381, 2048 }, { 8, 382, 2048 }, { 9, 383, 2048 },
{ 3, 384, 2048 }, { 4, 385, 2048 }, { 4, 386, 2048 }, { 5, 387, 2048 }, { 4, 388, 2048 }, { 5, 389, 2048 }, { 5, 390, 2048 }, { 6, 391, 2048 },
{ 4, 392, 2048 }, { 5, 393, 2048 }, { 5, 394, 2048 }, { 6, 395, 2048 }, { 5, 396, 2048 }, { 6, 397, 2048 }, { 6, 398, 2048 }, { 7, 399, 2048 },
{ 4, 400, 2048 }, { 5, 401, 2048 }, { 5, 402, 2048 }, { 6, 403, 2048 }, { 5, 404, 2048 }, { 6, 405, 2048 }, { 6, 406, 2048 }, { 7, 407, 2048 },
{ 5, 408, 2048 }, { 6, 409, 2048 }, { 6, 410, 2048 }, { 7, 411, 2048 }, { 6, 412, 2048 }, { 7, 413, 2048 }, { 7, 414, 2048 }, { 8, 415, 2048 },
{ 4, 416, 2048 }, { 5, 417, 2048 }, { 5, 418, 2048 }, { 6, 419, 2048 }, { 5, 420, 2048 }, { 6, 421, 2048 }, { 6, 422, 2048 }, { 7, 423, 2048 },
{ 5, 424, 2048 }, { 6, 425, 2048 }, { 6, 426, 2048 }, { 7, 427, 2048 }, { 6, 428, 2048 }, { 7, 429, 2048 }, { 7, 430, 2048 }, { 8, 431, 2048 },
{ 5, 432, 2048 }, { 6, 433, 2048 }, { 6, 434, 2048 }, { 7, 435, 2048 }, { 6, 436, 2048 }, { 7, 437, 2048 }, { 7, 438, 2048 }, { 8, 439, 2048 },
{ 6, 440, 2048 }, { 7, 441, 2048 }, { 7, 442, 2048 }, { 8, 443, 2048 }, { 7, 444, 2048 }, { 8, 445, 2048 }, { 8, 446, 2048 }, { 9, 447, 2048 },
{ 4, 448, 2048 }, { 5, 449, 2048 }, { 5, 450, 2048 }, { 6, 451, 2048 }, { 5, 452, 2048 }, { 6, 453, 2048 }, { 6, 454, 2048 }, { 7, 455, 2048 },
{ 5, 456, 2048 }, { 6, 457, 2048 }, { 6, 458, 2048 }, { 7, 459, 2048 }, { 6, 460, 2048 }, { 7, 461, 2048 }, { 7, 462, 2048 }, { 8, 463, 2048 },
{ 5, 464, 2048 }, { 6, 465, 2048 }, { 6, 466, 2048 }, { 7, 467, 2048 }, { 6, 468, 2048 }, { 7, 469, 2048 }, { 7, 470, 2048 }, { 8, 471, 2048 },
{ 6, 472, 2048 }, { 7, 473, 2048 }, { 7, 474, 2048 }, { 8, 475, 2048 }, { 7, 476, 2048 }, { 8, 477, 2048 }, { 8, 478, 2048 }, { 9, 479, 2048 },
{ 5, 480, 2048 }, { 6, 481, 2048 }, { 6, 482, 2048 }, { 7, 483, 2048 }, { 6, 484, 2048 }, { 7, 485, 2048 }, { 7, 486, 2048 }, { 8, 487, 2048 },
{ 6, 488, 2048 }, { 7, 489, 2048 }, { 7, 490, 2048 }, { 8, 491, 2048 }, { 7, 492, 2048 }, { 8, 493, 2048 }, { 8, 494, 2048 }, { 9, 495, 2048 },
{ 6, 496, 2048 }, { 7, 497, 2048 }, { 7, 498, 2048 }, { 8, 499, 2048 }, { 7, 500, 2048 }, { 8, 501, 2048 }, { 8, 502, 2048 }, { 9, 503, 2048 },
{ 7, 504, 2048 }, { 8, 505, 2048 }, { 8, 506, 2048 }, { 9, 507, 2048 }, { 8, 508, 2048 }, { 9, 509, 2048 }, { 9, 510, 2048 }, { 10, 511, 2048 },
{ 2, 512, 2048 }, { 3, 513, 2048 }, { 3, 514, 2048 }, { 4, 515, 2048 }, { 3, 516, 2048 }, { 4, 517, 2048 }, { 4, 518, 2048 }, { 5, 519, 2048 },
{ 3, 520, 2048 }, { 4, 521, 2048 }, { 4, 522, 2048 }, { 5, 523, 2048 }, { 4, 524, 2048 }, { 5, 525, 2048 }, { 5, 526, 2048 }, { 6, 527, 2048 },
{ 3, 528, 2048 }, { 4, 529, 2048 }, { 4, 530, 2048 }, { 5, 531, 2048 }, { 4, 532, 2048 }, { 5, 533, 2048 }, { 5, 534, 2048 }, { 6, 535, 2048 },
{ 4, 536, 2048 }, { 5, 537, 2048 }, { 5, 538, 2048 }, { 6, 539, 2048 }, { 5, 540, 2048 }, { 6, 541, 2048 }, { 6, 542, 2048 }, { 7, 543, 2048 },
{ 3, 544, 2048 }, { 4, 545, 2048 }, { 4, 546, 2048 }, { 5, 547, 2048 }, { 4, 548, 2048 }, { 5, 549, 2048 }, { 5, 550, 2048 }, { 6, 551, 2048 },
{ 4, 552, 2048 }, { 5, 553, 2048 }, { 5, 554, 2048 }, { 6, 555, 2048 }, { 5, 556, 2048 }, { 6, 557, 2048 }, { 6, 558, 2048 }, { 7, 559, 2048 },
{ 4, 560, 2048 }, { 5, 561, 2048 }, { 5, 562, 2048 }, { 6, 563, 2048 }, { 5, 564, 2048 }, { 6, 565, 2048 }, { 6, 566, 2048 }, { 7, 567, 2048 },
{ 5, 568, 2048 }, { 6, 569, 2048 }, { 6, 570, 2048 }, { 7, 571, 2048 }, { 6, 572, 2048 }, { 7, 573, 2048 }, { 7, 574, 2048 }, { 8, 575, 2048 },
{ 3, 576, 2048 }, { 4, 577, 2048 }, { 4, 578, 2048 }, { 5, 579, 2048 }, { 4, 580, 2048 }, { 5, 581, 2048 }, { 5, 582, 2048 }, { 6, 583, 2048 },
{ 4, 584, 2048 }, { 5, 585, 2048 }, { 5, 586, 2048 }, { 6, 587, 2048 }, { 5, 588, 2048 }, { 6, 589, 2048 }, { 6, 590, 2048 }, { 7, 591, 2048 },
{ 4, 592, 2048 }, { 5, 593, 2048 }, { 5, 594, 2048 }, { 6, 595, 2048 }, { 5, 596, 2048 }, { 6, 597, 2048 }, { 6, 598, 2048 }, { 7, 599, 2048 },
{ 5, 600, 2048 }, { 6, 601, 2048 }, { 6, 602, 2048 }, { 7, 603, 2048 }, { 6, 604, 2048 }, { 7, 605, 2048 }, { 7, 606, 2048 }, { 8, 607, 2048 },
{ 4, 608, 2048 }, { 5, 609, 2048 }, { 5, 610, 2048 }, { 6, 611, 2048 }, { 5, 612, 2048 }, { 6, 613, 2048 }, { 6, 614, 2048 }, { 7, 615, 2048 },
{ 5, 616, 2048 }, { 6, 617, 2048 }, { 6, 618, 2048 }, { 7, 619, 2048 }, { 6, 620, 2048 }, { 7, 621, 2048 }, { 7, 622, 2048 }, { 8, 623, 2048 },
{ 5, 624, 2048 }, { 6, 625, 2048 }, { 6, 626, 2048 }, { 7, 627, 2048 }, { 6, 628, 2048 }, { 7, 629, 2048 }, { 7, 630, 2048 }, { 8, 631, 2048 },
{ 6, 632, 2048 }, { 7, 633, 2048 }, { 7, 634, 2048 }, { 8, 635, 2048 }, { 7, 636, 2048 }, { 8, 637, 2048 }, { 8, 638, 2048 }, { 9, 639, 2048 },
{ 3, 640, 2048 }, { 4, 641, 2048 }, { 4, 642, 2048 }, { 5, 643, 2048 }, { 4, 644, 2048 }, { 5, 645, 2048 }, { 5, 646, 2048 }, { 6, 647, 2048 },
{ 4, 648, 2048 }, { 5, 649, 2048 }, { 5, 650, 2048 }, { 6, 651, 2048 }, { 5, 652, 2048 }, { 6, 653, 2048 }, { 6, 654, 2048 }, { 7, 655, 2048 },
{ 4, 656, 2048 }, { 5, 657, 2048 }, { 5, 658, 2048 }, { 6, 659, 2048 }, { 5, 660, 2048 }, { 6, 661, 2048 }, { 6, 662, 2048 }, { 7, 663, 2048 },
{ 5, 664, 2048 }, { 6, 665, 2048 }, { 6, 666, 2048 }, { 7, 667, 2048 }, { 6, 668, 2048 }, { 7, 669, 2048 }, { 7, 670, 2048 }, { 8, 671, 2048 },
{ 4, 672, 2048 }, { 5, 673, 2048 }, { 5, 674, 2048 }, { 6, 675, 2048 }, { 5, 676, 2048 }, { 6, 677, 2048 }, { 6, 678, 2048 }, { 7, 679, 2048 },
{ 5, 680, 2048 }, { 6, 681, 2048 }, { 6, 682, 2048 }, { 7, 683, 2048 }, { 6, 684, 2048 }, { 7, 685, 2048 }, { 7, 686, 2048 }, { 8, 687, 2048 },
{ 5, 688, 2048 }, { 6, 689, 2048 }, { 6, 690, 2048 }, { 7, 691, 2048 }, { 6, 692, 2048 }, { 7, 693, 2048 }, { 7, 694, 2048 }, { 8, 695, 2048 },
{ 6, 696, 2048 }, { 7, 697, 2048 }, { 7, 698, 2048 }, { 8, 699, 2048 }, { 7, 700, 2048 }, { 8, 701, 2048 }, { 8, 702, 2048 }, { 9, 703, 2048 },
{ 4, 704, 2048 }, { 5, 705, 2048 }, { 5, 706, 2048 }, { 6, 707, 2048 }, { 5, 708, 2048 }, { 6, 709, 2048 }, { 6, 710, 2048 }, { 7, 711, 2048 },
{ 5, 712, 2048 }, { 6, 713, 2048 }, { 6, 714, 2048 }, { 7, 715, 2048 }, { 6, 716, 2048 }, { 7, 717, 2048 }, { 7, 718, 2048 }, { 8, 719, 2048 },
{ 5, 720, 2048 }, { 6, 721, 2048 }, { 6, 722, 2048 }, { 7, 723, 2048 }, { 6, 724, 2048 }, { 7, 725, 2048 }, { 7, 726, 2048 }, { 8, 727, 2048 },
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{ 5, 1584, 2048 }, { 6, 1585, 2048 }, { 6, 1586, 2048 }, { 7, 1587, 2048 }, { 6, 1588, 2048 }, { 7, 1589, 2048 }, { 7, 1590, 2048 }, { 8, 1591, 2048 },
{ 6, 1592, 2048 }, { 7, 1593, 2048 }, { 7, 1594, 2048 }, { 8, 1595, 2048 }, { 7, 1596, 2048 }, { 8, 1597, 2048 }, { 8, 1598, 2048 }, { 9, 1599, 2048 },
{ 4, 1600, 2048 }, { 5, 1601, 2048 }, { 5, 1602, 2048 }, { 6, 1603, 2048 }, { 5, 1604, 2048 }, { 6, 1605, 2048 }, { 6, 1606, 2048 }, { 7, 1607, 2048 },
{ 5, 1608, 2048 }, { 6, 1609, 2048 }, { 6, 1610, 2048 }, { 7, 1611, 2048 }, { 6, 1612, 2048 }, { 7, 1613, 2048 }, { 7, 1614, 2048 }, { 8, 1615, 2048 },
{ 5, 1616, 2048 }, { 6, 1617, 2048 }, { 6, 1618, 2048 }, { 7, 1619, 2048 }, { 6, 1620, 2048 }, { 7, 1621, 2048 }, { 7, 1622, 2048 }, { 8, 1623, 2048 },
{ 6, 1624, 2048 }, { 7, 1625, 2048 }, { 7, 1626, 2048 }, { 8, 1627, 2048 }, { 7, 1628, 2048 }, { 8, 1629, 2048 }, { 8, 1630, 2048 }, { 9, 1631, 2048 },
{ 5, 1632, 2048 }, { 6, 1633, 2048 }, { 6, 1634, 2048 }, { 7, 1635, 2048 }, { 6, 1636, 2048 }, { 7, 1637, 2048 }, { 7, 1638, 2048 }, { 8, 1639, 2048 },
{ 6, 1640, 2048 }, { 7, 1641, 2048 }, { 7, 1642, 2048 }, { 8, 1643, 2048 }, { 7, 1644, 2048 }, { 8, 1645, 2048 }, { 8, 1646, 2048 }, { 9, 1647, 2048 },
{ 6, 1648, 2048 }, { 7, 1649, 2048 }, { 7, 1650, 2048 }, { 8, 1651, 2048 }, { 7, 1652, 2048 }, { 8, 1653, 2048 }, { 8, 1654, 2048 }, { 9, 1655, 2048 },
{ 7, 1656, 2048 }, { 8, 1657, 2048 }, { 8, 1658, 2048 }, { 9, 1659, 2048 }, { 8, 1660, 2048 }, { 9, 1661, 2048 }, { 9, 1662, 2048 }, { 10, 1663, 2048 },
{ 4, 1664, 2048 }, { 5, 1665, 2048 }, { 5, 1666, 2048 }, { 6, 1667, 2048 }, { 5, 1668, 2048 }, { 6, 1669, 2048 }, { 6, 1670, 2048 }, { 7, 1671, 2048 },
{ 5, 1672, 2048 }, { 6, 1673, 2048 }, { 6, 1674, 2048 }, { 7, 1675, 2048 }, { 6, 1676, 2048 }, { 7, 1677, 2048 }, { 7, 1678, 2048 }, { 8, 1679, 2048 },
{ 5, 1680, 2048 }, { 6, 1681, 2048 }, { 6, 1682, 2048 }, { 7, 1683, 2048 }, { 6, 1684, 2048 }, { 7, 1685, 2048 }, { 7, 1686, 2048 }, { 8, 1687, 2048 },
{ 6, 1688, 2048 }, { 7, 1689, 2048 }, { 7, 1690, 2048 }, { 8, 1691, 2048 }, { 7, 1692, 2048 }, { 8, 1693, 2048 }, { 8, 1694, 2048 }, { 9, 1695, 2048 },
{ 5, 1696, 2048 }, { 6, 1697, 2048 }, { 6, 1698, 2048 }, { 7, 1699, 2048 }, { 6, 1700, 2048 }, { 7, 1701, 2048 }, { 7, 1702, 2048 }, { 8, 1703, 2048 },
{ 6, 1704, 2048 }, { 7, 1705, 2048 }, { 7, 1706, 2048 }, { 8, 1707, 2048 }, { 7, 1708, 2048 }, { 8, 1709, 2048 }, { 8, 1710, 2048 }, { 9, 1711, 2048 },
{ 6, 1712, 2048 }, { 7, 1713, 2048 }, { 7, 1714, 2048 }, { 8, 1715, 2048 }, { 7, 1716, 2048 }, { 8, 1717, 2048 }, { 8, 1718, 2048 }, { 9, 1719, 2048 },
{ 7, 1720, 2048 }, { 8, 1721, 2048 }, { 8, 1722, 2048 }, { 9, 1723, 2048 }, { 8, 1724, 2048 }, { 9, 1725, 2048 }, { 9, 1726, 2048 }, { 10, 1727, 2048 },
{ 5, 1728, 2048 }, { 6, 1729, 2048 }, { 6, 1730, 2048 }, { 7, 1731, 2048 }, { 6, 1732, 2048 }, { 7, 1733, 2048 }, { 7, 1734, 2048 }, { 8, 1735, 2048 },
{ 6, 1736, 2048 }, { 7, 1737, 2048 }, { 7, 1738, 2048 }, { 8, 1739, 2048 }, { 7, 1740, 2048 }, { 8, 1741, 2048 }, { 8, 1742, 2048 }, { 9, 1743, 2048 },
{ 6, 1744, 2048 }, { 7, 1745, 2048 }, { 7, 1746, 2048 }, { 8, 1747, 2048 }, { 7, 1748, 2048 }, { 8, 1749, 2048 }, { 8, 1750, 2048 }, { 9, 1751, 2048 },
{ 7, 1752, 2048 }, { 8, 1753, 2048 }, { 8, 1754, 2048 }, { 9, 1755, 2048 }, { 8, 1756, 2048 }, { 9, 1757, 2048 }, { 9, 1758, 2048 }, { 10, 1759, 2048 },
{ 6, 1760, 2048 }, { 7, 1761, 2048 }, { 7, 1762, 2048 }, { 8, 1763, 2048 }, { 7, 1764, 2048 }, { 8, 1765, 2048 }, { 8, 1766, 2048 }, { 9, 1767, 2048 },
{ 7, 1768, 2048 }, { 8, 1769, 2048 }, { 8, 1770, 2048 }, { 9, 1771, 2048 }, { 8, 1772, 2048 }, { 9, 1773, 2048 }, { 9, 1774, 2048 }, { 10, 1775, 2048 },
{ 7, 1776, 2048 }, { 8, 1777, 2048 }, { 8, 1778, 2048 }, { 9, 1779, 2048 }, { 8, 1780, 2048 }, { 9, 1781, 2048 }, { 9, 1782, 2048 }, { 10, 1783, 2048 },
{ 8, 1784, 2048 }, { 9, 1785, 2048 }, { 9, 1786, 2048 }, { 10, 1787, 2048 }, { 9, 1788, 2048 }, { 10, 1789, 2048 }, { 10, 1790, 2048 }, { 11, 1791, 2048 },
{ 4, 1792, 2048 }, { 5, 1793, 2048 }, { 5, 1794, 2048 }, { 6, 1795, 2048 }, { 5, 1796, 2048 }, { 6, 1797, 2048 }, { 6, 1798, 2048 }, { 7, 1799, 2048 },
{ 5, 1800, 2048 }, { 6, 1801, 2048 }, { 6, 1802, 2048 }, { 7, 1803, 2048 }, { 6, 1804, 2048 }, { 7, 1805, 2048 }, { 7, 1806, 2048 }, { 8, 1807, 2048 },
{ 5, 1808, 2048 }, { 6, 1809, 2048 }, { 6, 1810, 2048 }, { 7, 1811, 2048 }, { 6, 1812, 2048 }, { 7, 1813, 2048 }, { 7, 1814, 2048 }, { 8, 1815, 2048 },
{ 6, 1816, 2048 }, { 7, 1817, 2048 }, { 7, 1818, 2048 }, { 8, 1819, 2048 }, { 7, 1820, 2048 }, { 8, 1821, 2048 }, { 8, 1822, 2048 }, { 9, 1823, 2048 },
{ 5, 1824, 2048 }, { 6, 1825, 2048 }, { 6, 1826, 2048 }, { 7, 1827, 2048 }, { 6, 1828, 2048 }, { 7, 1829, 2048 }, { 7, 1830, 2048 }, { 8, 1831, 2048 },
{ 6, 1832, 2048 }, { 7, 1833, 2048 }, { 7, 1834, 2048 }, { 8, 1835, 2048 }, { 7, 1836, 2048 }, { 8, 1837, 2048 }, { 8, 1838, 2048 }, { 9, 1839, 2048 },
{ 6, 1840, 2048 }, { 7, 1841, 2048 }, { 7, 1842, 2048 }, { 8, 1843, 2048 }, { 7, 1844, 2048 }, { 8, 1845, 2048 }, { 8, 1846, 2048 }, { 9, 1847, 2048 },
{ 7, 1848, 2048 }, { 8, 1849, 2048 }, { 8, 1850, 2048 }, { 9, 1851, 2048 }, { 8, 1852, 2048 }, { 9, 1853, 2048 }, { 9, 1854, 2048 }, { 10, 1855, 2048 },
{ 5, 1856, 2048 }, { 6, 1857, 2048 }, { 6, 1858, 2048 }, { 7, 1859, 2048 }, { 6, 1860, 2048 }, { 7, 1861, 2048 }, { 7, 1862, 2048 }, { 8, 1863, 2048 },
{ 6, 1864, 2048 }, { 7, 1865, 2048 }, { 7, 1866, 2048 }, { 8, 1867, 2048 }, { 7, 1868, 2048 }, { 8, 1869, 2048 }, { 8, 1870, 2048 }, { 9, 1871, 2048 },
{ 6, 1872, 2048 }, { 7, 1873, 2048 }, { 7, 1874, 2048 }, { 8, 1875, 2048 }, { 7, 1876, 2048 }, { 8, 1877, 2048 }, { 8, 1878, 2048 }, { 9, 1879, 2048 },
{ 7, 1880, 2048 }, { 8, 1881, 2048 }, { 8, 1882, 2048 }, { 9, 1883, 2048 }, { 8, 1884, 2048 }, { 9, 1885, 2048 }, { 9, 1886, 2048 }, { 10, 1887, 2048 },
{ 6, 1888, 2048 }, { 7, 1889, 2048 }, { 7, 1890, 2048 }, { 8, 1891, 2048 }, { 7, 1892, 2048 }, { 8, 1893, 2048 }, { 8, 1894, 2048 }, { 9, 1895, 2048 },
{ 7, 1896, 2048 }, { 8, 1897, 2048 }, { 8, 1898, 2048 }, { 9, 1899, 2048 }, { 8, 1900, 2048 }, { 9, 1901, 2048 }, { 9, 1902, 2048 }, { 10, 1903, 2048 },
{ 7, 1904, 2048 }, { 8, 1905, 2048 }, { 8, 1906, 2048 }, { 9, 1907, 2048 }, { 8, 1908, 2048 }, { 9, 1909, 2048 }, { 9, 1910, 2048 }, { 10, 1911, 2048 },
{ 8, 1912, 2048 }, { 9, 1913, 2048 }, { 9, 1914, 2048 }, { 10, 1915, 2048 }, { 9, 1916, 2048 }, { 10, 1917, 2048 }, { 10, 1918, 2048 }, { 11, 1919, 2048 },
{ 5, 1920, 2048 }, { 6, 1921, 2048 }, { 6, 1922, 2048 }, { 7, 1923, 2048 }, { 6, 1924, 2048 }, { 7, 1925, 2048 }, { 7, 1926, 2048 }, { 8, 1927, 2048 },
{ 6, 1928, 2048 }, { 7, 1929, 2048 }, { 7, 1930, 2048 }, { 8, 1931, 2048 }, { 7, 1932, 2048 }, { 8, 1933, 2048 }, { 8, 1934, 2048 }, { 9, 1935, 2048 },
{ 6, 1936, 2048 }, { 7, 1937, 2048 }, { 7, 1938, 2048 }, { 8, 1939, 2048 }, { 7, 1940, 2048 }, { 8, 1941, 2048 }, { 8, 1942, 2048 }, { 9, 1943, 2048 },
{ 7, 1944, 2048 }, { 8, 1945, 2048 }, { 8, 1946, 2048 }, { 9, 1947, 2048 }, { 8, 1948, 2048 }, { 9, 1949, 2048 }, { 9, 1950, 2048 }, { 10, 1951, 2048 },
{ 6, 1952, 2048 }, { 7, 1953, 2048 }, { 7, 1954, 2048 }, { 8, 1955, 2048 }, { 7, 1956, 2048 }, { 8, 1957, 2048 }, { 8, 1958, 2048 }, { 9, 1959, 2048 },
{ 7, 1960, 2048 }, { 8, 1961, 2048 }, { 8, 1962, 2048 }, { 9, 1963, 2048 }, { 8, 1964, 2048 }, { 9, 1965, 2048 }, { 9, 1966, 2048 }, { 10, 1967, 2048 },
{ 7, 1968, 2048 }, { 8, 1969, 2048 }, { 8, 1970, 2048 }, { 9, 1971, 2048 }, { 8, 1972, 2048 }, { 9, 1973, 2048 }, { 9, 1974, 2048 }, { 10, 1975, 2048 },
{ 8, 1976, 2048 }, { 9, 1977, 2048 }, { 9, 1978, 2048 }, { 10, 1979, 2048 }, { 9, 1980, 2048 }, { 10, 1981, 2048 }, { 10, 1982, 2048 }, { 11, 1983, 2048 },
{ 6, 1984, 2048 }, { 7, 1985, 2048 }, { 7, 1986, 2048 }, { 8, 1987, 2048 }, { 7, 1988, 2048 }, { 8, 1989, 2048 }, { 8, 1990, 2048 }, { 9, 1991, 2048 },
{ 7, 1992, 2048 }, { 8, 1993, 2048 }, { 8, 1994, 2048 }, { 9, 1995, 2048 }, { 8, 1996, 2048 }, { 9, 1997, 2048 }, { 9, 1998, 2048 }, { 10, 1999, 2048 },
{ 7, 2000, 2048 }, { 8, 2001, 2048 }, { 8, 2002, 2048 }, { 9, 2003, 2048 }, { 8, 2004, 2048 }, { 9, 2005, 2048 }, { 9, 2006, 2048 }, { 10, 2007, 2048 },
{ 8, 2008, 2048 }, { 9, 2009, 2048 }, { 9, 2010, 2048 }, { 10, 2011, 2048 }, { 9, 2012, 2048 }, { 10, 2013, 2048 }, { 10, 2014, 2048 }, { 11, 2015, 2048 },
{ 7, 2016, 2048 }, { 8, 2017, 2048 }, { 8, 2018, 2048 }, { 9, 2019, 2048 }, { 8, 2020, 2048 }, { 9, 2021, 2048 }, { 9, 2022, 2048 }, { 10, 2023, 2048 },
{ 8, 2024, 2048 }, { 9, 2025, 2048 }, { 9, 2026, 2048 }, { 10, 2027, 2048 }, { 9, 2028, 2048 }, { 10, 2029, 2048 }, { 10, 2030, 2048 }, { 11, 2031, 2048 },
{ 8, 2032, 2048 }, { 9, 2033, 2048 }, { 9, 2034, 2048 }, { 10, 2035, 2048 }, { 9, 2036, 2048 }, { 10, 2037, 2048 }, { 10, 2038, 2048 }, { 11, 2039, 2048 },
{ 9, 2040, 2048 }, { 10, 2041, 2048 }, { 10, 2042, 2048 }, { 11, 2043, 2048 }, { 10, 2044, 2048 }, { 11, 2045, 2048 }, { 11, 2046, 2048 }, { 12, 2047, 2048 },
#endif
#endif
#endif
#endif
#endif
#endif
};
/* find a hole and free as required */
static int find_hole(void)
{
int x, y, z;
for (z = 0, y = INT_MAX, x = 0; x < FP_ENTRIES; x++) {
if (fp_cache[x].lru_count < y) {
z = x;
y = fp_cache[x].lru_count;
}
}
/* decrease all */
for (x = 0; x < FP_ENTRIES; x++) {
if (fp_cache[x].lru_count > 3) {
--(fp_cache[x].lru_count);
}
}
/* free entry z */
if (fp_cache[z].g) {
ltc_ecc_del_point(fp_cache[z].g);
fp_cache[z].g = NULL;
for (x = 0; x < (1<<FP_LUT); x++) {
ltc_ecc_del_point(fp_cache[z].LUT[x]);
fp_cache[z].LUT[x] = NULL;
}
fp_cache[z].lru_count = 0;
}
return z;
}
static int find_base(ecc_point *g)
{
int x;
for (x = 0; x < FP_ENTRIES; x++) {
if (fp_cache[x].g != NULL &&
mp_cmp(fp_cache[x].g->x, g->x) == LTC_MP_EQ &&
mp_cmp(fp_cache[x].g->y, g->y) == LTC_MP_EQ &&
mp_cmp(fp_cache[x].g->z, g->z) == LTC_MP_EQ) {
break;
}
}
if (x == FP_ENTRIES) {
x = -1;
}
return x;
}
static int add_entry(int idx, ecc_point *g)
{
int x, y;
/* allocate base and LUT */
fp_cache[idx].g = ltc_ecc_new_point();
if (fp_cache[idx].g == NULL) {
return CRYPT_MEM;
}
/* copy x and y */
if ((mp_copy(g->x, fp_cache[idx].g->x) != CRYPT_OK) ||
(mp_copy(g->y, fp_cache[idx].g->y) != CRYPT_OK) ||
(mp_copy(g->z, fp_cache[idx].g->z) != CRYPT_OK)) {
ltc_ecc_del_point(fp_cache[idx].g);
fp_cache[idx].g = NULL;
return CRYPT_MEM;
}
for (x = 0; x < (1<<FP_LUT); x++) {
fp_cache[idx].LUT[x] = ltc_ecc_new_point();
if (fp_cache[idx].LUT[x] == NULL) {
for (y = 0; y < x; y++) {
ltc_ecc_del_point(fp_cache[idx].LUT[y]);
fp_cache[idx].LUT[y] = NULL;
}
ltc_ecc_del_point(fp_cache[idx].g);
fp_cache[idx].g = NULL;
fp_cache[idx].lru_count = 0;
return CRYPT_MEM;
}
}
fp_cache[idx].lru_count = 0;
return CRYPT_OK;
}
/* build the LUT by spacing the bits of the input by #modulus/FP_LUT bits apart
*
* The algorithm builds patterns in increasing bit order by first making all
* single bit input patterns, then all two bit input patterns and so on
*/
static int build_lut(int idx, void *modulus, void *mp, void *mu)
{
unsigned x, y, err, bitlen, lut_gap;
/* sanity check to make sure lut_order table is of correct size, should compile out to a NOP if true */
if ((sizeof(lut_orders) / sizeof(lut_orders[0])) < (1U<<FP_LUT)) {
err = CRYPT_INVALID_ARG;
goto DONE;
}
/* get bitlen and round up to next multiple of FP_LUT */
bitlen = mp_unsigned_bin_size(modulus) << 3;
x = bitlen % FP_LUT;
if (x) {
bitlen += FP_LUT - x;
}
lut_gap = bitlen / FP_LUT;
/* copy base */
if ((mp_mulmod(fp_cache[idx].g->x, mu, modulus, fp_cache[idx].LUT[1]->x) != CRYPT_OK) ||
(mp_mulmod(fp_cache[idx].g->y, mu, modulus, fp_cache[idx].LUT[1]->y) != CRYPT_OK) ||
(mp_mulmod(fp_cache[idx].g->z, mu, modulus, fp_cache[idx].LUT[1]->z) != CRYPT_OK)) { goto ERR; }
/* make all single bit entries */
for (x = 1; x < FP_LUT; x++) {
if ((mp_copy(fp_cache[idx].LUT[1<<(x-1)]->x, fp_cache[idx].LUT[1<<x]->x) != CRYPT_OK) ||
(mp_copy(fp_cache[idx].LUT[1<<(x-1)]->y, fp_cache[idx].LUT[1<<x]->y) != CRYPT_OK) ||
(mp_copy(fp_cache[idx].LUT[1<<(x-1)]->z, fp_cache[idx].LUT[1<<x]->z) != CRYPT_OK)) { goto ERR; }
/* now double it bitlen/FP_LUT times */
for (y = 0; y < lut_gap; y++) {
if ((err = ltc_mp.ecc_ptdbl(fp_cache[idx].LUT[1<<x], fp_cache[idx].LUT[1<<x], modulus, mp)) != CRYPT_OK) {
goto ERR;
}
}
}
/* now make all entries in increase order of hamming weight */
for (x = 2; x <= FP_LUT; x++) {
for (y = 0; y < (1<<FP_LUT); y++) {
if (lut_orders[y].ham != (int)x) continue;
/* perform the add */
if ((err = ltc_mp.ecc_ptadd(fp_cache[idx].LUT[lut_orders[y].terma], fp_cache[idx].LUT[lut_orders[y].termb],
fp_cache[idx].LUT[y], modulus, mp)) != CRYPT_OK) {
goto ERR;
}
}
}
return CRYPT_OK;
ERR:
err = CRYPT_MEM;
DONE:
for (y = 0; y < (1<<FP_LUT); y++) {
ltc_ecc_del_point(fp_cache[idx].LUT[y]);
fp_cache[idx].LUT[y] = NULL;
}
ltc_ecc_del_point(fp_cache[idx].g);
fp_cache[idx].g = NULL;
fp_cache[idx].lru_count = 0;
return CRYPT_MEM;
}
static int accel_fp_mul(int idx, void *k, ecc_point *R, void *modulus, void *mp, int map)
{
unsigned char kb[128];
int x;
unsigned y, z, err, bitlen, bitpos, lut_gap, first;
void *tk, *order;
/* if it's smaller than modulus we fine */
if (mp_unsigned_bin_size(k) > mp_unsigned_bin_size(modulus)) {
/* find order */
y = mp_unsigned_bin_size(modulus);
for (x = 0; ltc_ecc_sets[x].size; x++) {
if (y <= (unsigned)ltc_ecc_sets[x].size) break;
}
/* back off if we are on the 521 bit curve */
if (y == 66) --x;
if ((err = mp_init(&order)) != CRYPT_OK) {
return err;
}
if ((err = mp_read_radix(order, ltc_ecc_sets[x].order, 16)) != CRYPT_OK) {
mp_clear(&order);
return err;
}
/* k must be less than modulus */
if (mp_cmp(k, order) != LTC_MP_LT) {
if ((err = mp_init(&tk)) != CRYPT_OK) {
mp_clear(order);
return err;
}
if ((err = mp_mod(k, order, tk)) != CRYPT_OK) {
mp_clear(tk);
mp_clear(order);
return err;
}
} else {
tk = k;
}
mp_clear(order);
} else {
tk = k;
}
/* get bitlen and round up to next multiple of FP_LUT */
bitlen = mp_unsigned_bin_size(modulus) << 3;
x = bitlen % FP_LUT;
if (x) {
bitlen += FP_LUT - x;
}
lut_gap = bitlen / FP_LUT;
/* get the k value */
if (mp_unsigned_bin_size(tk) > (sizeof(kb) - 2)) {
if (tk != k) {
mp_clear(tk);
}
return CRYPT_BUFFER_OVERFLOW;
}
/* store k */
zeromem(kb, sizeof(kb));
if ((err = mp_to_unsigned_bin(tk, kb)) != CRYPT_OK) {
if (tk != k) {
mp_clear(tk);
}
return err;
}
/* let's reverse kb so it's little endian */
x = 0;
y = mp_unsigned_bin_size(tk) - 1;
if (tk != k) {
mp_clear(tk);
}
while ((unsigned)x < y) {
z = kb[x]; kb[x] = kb[y]; kb[y] = z;
++x; --y;
}
/* at this point we can start, yipee */
first = 1;
for (x = lut_gap-1; x >= 0; x--) {
/* extract FP_LUT bits from kb spread out by lut_gap bits and offset by x bits from the start */
bitpos = x;
for (y = z = 0; y < FP_LUT; y++) {
z |= ((kb[bitpos>>3] >> (bitpos&7)) & 1) << y;
bitpos += lut_gap; /* it's y*lut_gap + x, but here we can avoid the mult in each loop */
}
/* double if not first */
if (!first) {
if ((err = ltc_mp.ecc_ptdbl(R, R, modulus, mp)) != CRYPT_OK) {
return err;
}
}
/* add if not first, otherwise copy */
if (!first && z) {
if ((err = ltc_mp.ecc_ptadd(R, fp_cache[idx].LUT[z], R, modulus, mp)) != CRYPT_OK) {
return err;
}
} else if (z) {
if ((mp_copy(fp_cache[idx].LUT[z]->x, R->x) != CRYPT_OK) ||
(mp_copy(fp_cache[idx].LUT[z]->y, R->y) != CRYPT_OK) ||
(mp_copy(fp_cache[idx].LUT[z]->z, R->z) != CRYPT_OK)) { return CRYPT_MEM; }
first = 0;
}
}
z = 0;
zeromem(kb, sizeof(kb));
/* map R back from projective space */
if (map) {
err = ltc_ecc_map(R, modulus, mp);
} else {
err = CRYPT_OK;
}
return err;
}
int ltc_ecc_fp_mulmod(void *k, ecc_point *G, ecc_point *R, void *modulus, int map)
{
int idx, err;
void *mp, *mu;
mp = NULL;
mu = NULL;
LTC_MUTEX_LOCK(&ltc_ecc_fp_lock);
/* find point */
idx = find_base(G);
/* no entry? */
if (idx == -1) {
/* find hole and add it */
idx = find_hole();
if ((err = add_entry(idx, G)) != CRYPT_OK) {
goto LBL_ERR;
}
}
/* increment LRU */
++(fp_cache[idx].lru_count);
/* if it's 2 build the LUT, if it's higher just use the LUT */
if (fp_cache[idx].lru_count == 2) {
/* compute mp */
if ((err = mp_montgomery_setup(modulus, &mp)) != CRYPT_OK) { goto LBL_ERR; }
/* compute mu */
if ((err = mp_init(&mu)) != CRYPT_OK) {
goto LBL_ERR;
}
if ((err = mp_montgomery_normalization(mu, modulus)) != CRYPT_OK) {
goto LBL_ERR;
}
/* build the LUT */
if ((err = build_lut(idx, modulus, mp, mu)) != CRYPT_OK) {
goto LBL_ERR;;
}
}
if (fp_cache[idx].lru_count >= 2) {
if (mp == NULL) {
/* compute mp */
if ((err = mp_montgomery_setup(modulus, &mp)) != CRYPT_OK) { goto LBL_ERR; }
}
err = accel_fp_mul(idx, k, R, modulus, mp, map);
} else {
err = ltc_ecc_mulmod(k, G, R, modulus, map);
}
LBL_ERR:
LTC_MUTEX_UNLOCK(&ltc_ecc_fp_lock);
if (mp != NULL) {
mp_montgomery_free(mp);
}
if (mu != NULL) {
mp_clear(mu);
}
return err;
}
void ltc_ecc_fp_free(void)
{
int x, y;
LTC_MUTEX_LOCK(&ltc_ecc_fp_lock);
for (x = 0; x < FP_ENTRIES; x++) {
if (fp_cache[x].g != NULL) {
for (y = 0; y < (1<<FP_LUT); y++) {
ltc_ecc_del_point(fp_cache[x].LUT[y]);
fp_cache[x].LUT[y] = NULL;
}
ltc_ecc_del_point(fp_cache[x].g);
fp_cache[x].g = NULL;
fp_cache[x].lru_count = 0;
}
}
LTC_MUTEX_UNLOCK(&ltc_ecc_fp_lock);
}
#endif
/* $Source$ */
/* $Revision$ */
/* $Date$ */

38
src/math/gmp_desc.c
View File

@ -17,32 +17,6 @@
#include <stdio.h>
#include <gmp.h>
static const struct {
int gmp_code, ltc_code;
} gmp_to_ltc_codes[] = {
{ GMP_ERROR_NONE, CRYPT_OK},
{ GMP_ERROR_ALLOCATE, CRYPT_MEM},
{ GMP_ERROR_DIVISION_BY_ZERO, CRYPT_INVALID_ARG},
{ GMP_ERROR_UNSUPPORTED_ARGUMENT, CRYPT_INVALID_ARG},
};
/**
Convert a GMP error to a LTC error (Possibly the most powerful function ever! Oh wait... no)
@param err The error to convert
@return The equivalent LTC error code or CRYPT_ERROR if none found
*/
static int gmp_to_ltc_error(int err)
{
int x;
for (x = 0; x < (int)(sizeof(gmp_to_ltc_codes)/sizeof(gmp_to_ltc_codes[0])); x++) {
if (err == gmp_to_ltc_codes[x].gmp_code) {
return gmp_to_ltc_codes[x].ltc_code;
}
}
return CRYPT_ERROR;
}
static int init(void **a)
{
LTC_ARGCHK(a != NULL);
@ -147,6 +121,13 @@ static int count_bits(void *a)
return mpz_sizeinbase(a, 2);
}
static int count_lsb_bits(void *a)
{
LTC_ARGCHK(a != NULL);
return mpz_scan1(a, 0);
}
static int twoexpt(void *a, int n)
{
LTC_ARGCHK(a != NULL);
@ -415,6 +396,7 @@ const ltc_math_descriptor gmp_desc = {
&compare,
&compare_d,
&count_bits,
&count_lsb_bits,
&twoexpt,
&read_radix,
@ -448,7 +430,11 @@ const ltc_math_descriptor gmp_desc = {
&isprime,
#ifdef MECC
#ifdef MECC_FP
&ltc_ecc_fp_mulmod,
#else
&ltc_ecc_mulmod,
#endif /* MECC_FP */
&ltc_ecc_projective_add_point,
&ltc_ecc_projective_dbl_point,
&ltc_ecc_map,

12
src/math/ltm_desc.c
View File

@ -149,6 +149,13 @@ static int count_bits(void *a)
return mp_count_bits(a);
}
static int count_lsb_bits(void *a)
{
LTC_ARGCHK(a != NULL);
return mp_cnt_lsb(a);
}
static int twoexpt(void *a, int n)
{
LTC_ARGCHK(a != NULL);
@ -396,6 +403,7 @@ const ltc_math_descriptor ltm_desc = {
&compare,
&compare_d,
&count_bits,
&count_lsb_bits,
&twoexpt,
&read_radix,
@ -429,7 +437,11 @@ const ltc_math_descriptor ltm_desc = {
&isprime,
#ifdef MECC
#ifdef MECC_FP
&ltc_ecc_fp_mulmod,
#else
&ltc_ecc_mulmod,
#endif
&ltc_ecc_projective_add_point,
&ltc_ecc_projective_dbl_point,
&ltc_ecc_map,

11
src/math/tfm_desc.c
View File

@ -148,6 +148,12 @@ static int count_bits(void *a)
return fp_count_bits(a);
}
static int count_lsb_bits(void *a)
{
LTC_ARGCHK(a != NULL);
return fp_cnt_lsb(a);
}
static int twoexpt(void *a, int n)
{
LTC_ARGCHK(a != NULL);
@ -681,6 +687,7 @@ const ltc_math_descriptor tfm_desc = {
&compare,
&compare_d,
&count_bits,
&count_lsb_bits,
&twoexpt,
&read_radix,
@ -714,7 +721,11 @@ const ltc_math_descriptor tfm_desc = {
&isprime,
#ifdef MECC
#ifdef MECC_FP
&ltc_ecc_fp_mulmod,
#else
&ltc_ecc_mulmod,
#endif /* MECC_FP */
#ifdef MECC_ACCEL
&tfm_ecc_projective_add_point,
&tfm_ecc_projective_dbl_point,

4
src/misc/crypt/crypt.c
View File

@ -330,7 +330,9 @@ const char *crypt_build_settings =
#if defined(LTC_EASY)
" (easy) "
#endif
#if defined(MECC_FP)
" MECC_FP "
#endif
"\n"
"\n\n\n"
;

47
src/pk/asn1/der/boolean/der_decode_boolean.c Normal file
View File

@ -0,0 +1,47 @@
/* LibTomCrypt, modular cryptographic library -- Tom St Denis
*
* LibTomCrypt is a library that provides various cryptographic
* algorithms in a highly modular and flexible manner.
*
* The library is free for all purposes without any express
* guarantee it works.
*
* Tom St Denis, tomstdenis@gmail.com, http://libtomcrypt.com
*/
#include "tomcrypt.h"
/**
@file der_decode_boolean.c
ASN.1 DER, decode a BOOLEAN, Tom St Denis
*/
#ifdef LTC_DER
/**
Read a BOOLEAN
@param in The destination for the DER encoded BOOLEAN
@param inlen The size of the DER BOOLEAN
@param out [out] The boolean to decode
@return CRYPT_OK if successful
*/
int der_decode_boolean(const unsigned char *in, unsigned long inlen,
int *out)
{
LTC_ARGCHK(in != NULL);
LTC_ARGCHK(out != NULL);
if (inlen != 3 || in[0] != 0x01 || in[1] != 0x01 || (in[2] != 0x00 && in[2] != 0xFF)) {
return CRYPT_INVALID_ARG;
}
*out = (in[2]==0xFF) ? 1 : 0;
return CRYPT_OK;
}
#endif
/* $Source$ */
/* $Revision$ */
/* $Date$ */

50
src/pk/asn1/der/boolean/der_encode_boolean.c Normal file
View File

@ -0,0 +1,50 @@
/* LibTomCrypt, modular cryptographic library -- Tom St Denis
*
* LibTomCrypt is a library that provides various cryptographic
* algorithms in a highly modular and flexible manner.
*
* The library is free for all purposes without any express
* guarantee it works.
*
* Tom St Denis, tomstdenis@gmail.com, http://libtomcrypt.com
*/
#include "tomcrypt.h"
/**
@file der_encode_boolean.c
ASN.1 DER, encode a BOOLEAN, Tom St Denis
*/
#ifdef LTC_DER
/**
Store a BOOLEAN
@param in The boolean to encode
@param out [out] The destination for the DER encoded BOOLEAN
@param outlen [in/out] The max size and resulting size of the DER BOOLEAN
@return CRYPT_OK if successful
*/
int der_encode_boolean(int in,
unsigned char *out, unsigned long *outlen)
{
LTC_ARGCHK(outlen != NULL);
LTC_ARGCHK(out != NULL);
if (*outlen < 3) {
return CRYPT_BUFFER_OVERFLOW;
}
*outlen = 3;
out[0] = 0x01;
out[1] = 0x01;
out[2] = in ? 0xFF : 0x00;
return CRYPT_OK;
}
#endif
/* $Source$ */
/* $Revision$ */
/* $Date$ */

35
src/pk/asn1/der/boolean/der_length_boolean.c Normal file
View File

@ -0,0 +1,35 @@
/* LibTomCrypt, modular cryptographic library -- Tom St Denis
*
* LibTomCrypt is a library that provides various cryptographic
* algorithms in a highly modular and flexible manner.
*
* The library is free for all purposes without any express
* guarantee it works.
*
* Tom St Denis, tomstdenis@gmail.com, http://libtomcrypt.com
*/
#include "tomcrypt.h"
/**
@file der_length_boolean.c
ASN.1 DER, get length of a BOOLEAN, Tom St Denis
*/
#ifdef LTC_DER
/**
Gets length of DER encoding of a BOOLEAN
@param outlen [out] The length of the DER encoding
@return CRYPT_OK if successful
*/
int der_length_boolean(unsigned long *outlen)
{
LTC_ARGCHK(outlen != NULL);
*outlen = 3;
return CRYPT_OK;
}
#endif
/* $Source$ */
/* $Revision$ */
/* $Date$ */

4
src/pk/asn1/der/integer/der_encode_integer.c
View File

@ -59,7 +59,7 @@ int der_encode_integer(void *num, unsigned char *out, unsigned long *outlen)
y = mp_count_bits(num);
y = y + (8 - (y & 7));
y = y >> 3;
if (((mp_cnt_lsb(num)+1)==mp_count_bits(num)) && ((mp_count_bits(num)&7)==0)) --y;
}
/* now store initial data */
@ -105,11 +105,11 @@ int der_encode_integer(void *num, unsigned char *out, unsigned long *outlen)
/* 2^roundup and subtract */
y = mp_count_bits(num);
y = y + (8 - (y & 7));
if (((mp_cnt_lsb(num)+1)==mp_count_bits(num)) && ((mp_count_bits(num)&7)==0)) y -= 8;
if (mp_2expt(tmp, y) != CRYPT_OK || mp_add(tmp, num, tmp) != CRYPT_OK) {
mp_clear(tmp);
return CRYPT_MEM;
}
if ((err = mp_to_unsigned_bin(tmp, out)) != CRYPT_OK) {
mp_clear(tmp);
return err;

1
src/pk/asn1/der/integer/der_length_integer.c
View File

@ -49,6 +49,7 @@ int der_length_integer(void *num, unsigned long *outlen)
leading_zero = 0;
z = mp_count_bits(num);
z = z + (8 - (z & 7));
if (((mp_cnt_lsb(num)+1)==mp_count_bits(num)) && ((mp_count_bits(num)&7)==0)) --z;
len = z = z >> 3;
}

18
src/pk/asn1/der/object_identifier/der_decode_object_identifier.c
View File

@ -67,14 +67,8 @@ int der_decode_object_identifier(const unsigned char *in, unsigned long inle
return CRYPT_INVALID_PACKET;
}
/* decode word1 and word2 */
--len;
t = in[x++];
words[0] = t/40;
words[1] = t%40;
/* decode rest */
y = 2;
/* decode words */
y = 0;
t = 0;
while (len--) {
t = (t << 7) | (in[x] & 0x7F);
@ -83,7 +77,13 @@ int der_decode_object_identifier(const unsigned char *in, unsigned long inle
if (y >= *outlen) {
return CRYPT_BUFFER_OVERFLOW;
}
words[y++] = t;
if (y == 0) {
words[0] = t / 40;
words[1] = t % 40;
y = 2;
} else {
words[y++] = t;
}
t = 0;
}
}

25
src/pk/asn1/der/object_identifier/der_encode_object_identifier.c
View File

@ -27,7 +27,7 @@
int der_encode_object_identifier(unsigned long *words, unsigned long nwords,
unsigned char *out, unsigned long *outlen)
{
unsigned long i, x, y, z, t, mask;
unsigned long i, x, y, z, t, mask, wordbuf;
int err;
LTC_ARGCHK(words != NULL);
@ -43,10 +43,14 @@ int der_encode_object_identifier(unsigned long *words, unsigned long nwords,
}
/* compute length to store OID data */
z = 1;
for (y = 2; y < nwords; y++) {
t = der_object_identifier_bits(words[y]);
z += t/7 + ((t%7) ? 1 : 0);
z = 0;
wordbuf = words[0] * 40 + words[1];
for (y = 1; y < nwords; y++) {
t = der_object_identifier_bits(wordbuf);
z += t/7 + ((t%7) ? 1 : 0) + (wordbuf == 0 ? 1 : 0);
if (y < nwords - 1) {
wordbuf = words[y + 1];
}
}
/* store header + length */
@ -66,11 +70,10 @@ int der_encode_object_identifier(unsigned long *words, unsigned long nwords,
}
/* store first byte */
out[x++] = words[0] * 40 + words[1];
for (i = 2; i < nwords; i++) {
wordbuf = words[0] * 40 + words[1];
for (i = 1; i < nwords; i++) {
/* store 7 bit words in little endian */
t = words[i] & 0xFFFFFFFF;
t = wordbuf & 0xFFFFFFFF;
if (t) {
y = x;
mask = 0;
@ -90,6 +93,10 @@ int der_encode_object_identifier(unsigned long *words, unsigned long nwords,
/* zero word */
out[x++] = 0x00;
}
if (i < nwords - 1) {
wordbuf = words[i + 1];
}
}
*outlen = x;

21
src/pk/asn1/der/object_identifier/der_length_object_identifier.c
View File

@ -39,7 +39,7 @@ unsigned long der_object_identifier_bits(unsigned long x)
*/
int der_length_object_identifier(unsigned long *words, unsigned long nwords, unsigned long *outlen)
{
unsigned long y, z, t;
unsigned long y, z, t, wordbuf;
LTC_ARGCHK(words != NULL);
LTC_ARGCHK(outlen != NULL);
@ -50,16 +50,21 @@ int der_length_object_identifier(unsigned long *words, unsigned long nwords, uns
return CRYPT_INVALID_ARG;
}
/* word1 = 0,1,2 and word2 0..39 */
if (words[0] > 2 || words[1] > 39) {
/* word1 = 0,1,2,3 and word2 0..39 */
if (words[0] > 3 || (words[0] < 2 && words[1] > 39)) {
return CRYPT_INVALID_ARG;
}
/* leading byte of first two words */
z = 1;
for (y = 2; y < nwords; y++) {
t = der_object_identifier_bits(words[y]);
z += t/7 + ((t%7) ? 1 : 0);
/* leading word is the first two */
z = 0;
wordbuf = words[0] * 40 + words[1];
for (y = 1; y < nwords; y++) {
t = der_object_identifier_bits(wordbuf);
z += t/7 + ((t%7) ? 1 : 0) + (wordbuf == 0 ? 1 : 0);
if (y < nwords - 1) {
/* grab next word */
wordbuf = words[y+1];
}
}
/* now depending on the length our length encoding changes */

10
src/pk/asn1/der/sequence/der_decode_sequence_ex.c
View File

@ -94,6 +94,16 @@ int der_decode_sequence_ex(const unsigned char *in, unsigned long inlen,
}
switch (type) {
case LTC_ASN1_BOOLEAN:
z = inlen;
if ((err = der_decode_boolean(in + x, z, ((int *)data))) != CRYPT_OK) {
goto LBL_ERR;
}
if ((err = der_length_boolean(&z)) != CRYPT_OK) {
goto LBL_ERR;
}
break;
case LTC_ASN1_INTEGER:
z = inlen;
if ((err = der_decode_integer(in + x, z, data)) != CRYPT_OK) {

14
src/pk/asn1/der/sequence/der_decode_sequence_flexi.c
View File

@ -104,6 +104,20 @@ int der_decode_sequence_flexi(const unsigned char *in, unsigned long *inlen, ltc
/* now switch on type */
switch (type) {
case 0x01: /* BOOLEAN */
l->type = LTC_ASN1_BOOLEAN;
l->size = 1;
l->data = XCALLOC(1, sizeof(int));
if ((err = der_decode_boolean(in, *inlen, l->data)) != CRYPT_OK) {
goto error;
}
if ((err = der_length_boolean(&len)) != CRYPT_OK) {
goto error;
}
break;
case 0x02: /* INTEGER */
/* init field */
l->type = LTC_ASN1_INTEGER;

2
src/pk/asn1/der/sequence/der_decode_sequence_multi.c
View File

@ -49,6 +49,7 @@ int der_decode_sequence_multi(const unsigned char *in, unsigned long inlen, ...)
}
switch (type) {
case LTC_ASN1_BOOLEAN:
case LTC_ASN1_INTEGER:
case LTC_ASN1_SHORT_INTEGER:
case LTC_ASN1_BIT_STRING:
@ -95,6 +96,7 @@ int der_decode_sequence_multi(const unsigned char *in, unsigned long inlen, ...)
}
switch (type) {
case LTC_ASN1_BOOLEAN:
case LTC_ASN1_INTEGER:
case LTC_ASN1_SHORT_INTEGER:
case LTC_ASN1_BIT_STRING:

16
src/pk/asn1/der/sequence/der_encode_sequence_ex.c
View File

@ -51,6 +51,13 @@ int der_encode_sequence_ex(ltc_asn1_list *list, unsigned long inlen,
}
switch (type) {
case LTC_ASN1_BOOLEAN:
if ((err = der_length_boolean(&x)) != CRYPT_OK) {
goto LBL_ERR;
}
y += x;
break;
case LTC_ASN1_INTEGER:
if ((err = der_length_integer(data, &x)) != CRYPT_OK) {
goto LBL_ERR;
@ -182,6 +189,15 @@ int der_encode_sequence_ex(ltc_asn1_list *list, unsigned long inlen,
}
switch (type) {
case LTC_ASN1_BOOLEAN:
z = *outlen;
if ((err = der_encode_boolean(*((int *)data), out + x, &z)) != CRYPT_OK) {
goto LBL_ERR;
}
x += z;
*outlen -= z;
break;
case LTC_ASN1_INTEGER:
z = *outlen;
if ((err = der_encode_integer(data, out + x, &z)) != CRYPT_OK) {

2
src/pk/asn1/der/sequence/der_encode_sequence_multi.c
View File

@ -50,6 +50,7 @@ int der_encode_sequence_multi(unsigned char *out, unsigned long *outlen, ...)
}
switch (type) {
case LTC_ASN1_BOOLEAN:
case LTC_ASN1_INTEGER:
case LTC_ASN1_SHORT_INTEGER:
case LTC_ASN1_BIT_STRING:
@ -95,6 +96,7 @@ int der_encode_sequence_multi(unsigned char *out, unsigned long *outlen, ...)
}
switch (type) {
case LTC_ASN1_BOOLEAN:
case LTC_ASN1_INTEGER:
case LTC_ASN1_SHORT_INTEGER:
case LTC_ASN1_BIT_STRING:

7
src/pk/asn1/der/sequence/der_length_sequence.c
View File

@ -46,6 +46,13 @@ int der_length_sequence(ltc_asn1_list *list, unsigned long inlen,
}
switch (type) {
case LTC_ASN1_BOOLEAN:
if ((err = der_length_boolean(&x)) != CRYPT_OK) {
goto LBL_ERR;
}
y += x;
break;
case LTC_ASN1_INTEGER:
if ((err = der_length_integer(data, &x)) != CRYPT_OK) {
goto LBL_ERR;

1
src/pk/asn1/der/set/der_encode_set.c
View File

@ -21,6 +21,7 @@
static int ltc_to_asn1(int v)
{
switch (v) {
case LTC_ASN1_BOOLEAN: return 0x01;
case LTC_ASN1_INTEGER:
case LTC_ASN1_SHORT_INTEGER: return 0x02;
case LTC_ASN1_BIT_STRING: return 0x03;

2
src/pk/ecc/ltc_ecc_projective_add_point.c
View File

@ -21,7 +21,7 @@
ECC Crypto, Tom St Denis
*/
#if defined(MECC) && !defined(MECC_ACCEL)
#if defined(MECC) && (!defined(MECC_ACCEL) || defined(LTM_DESC))
/**
Add two ECC points

2
src/pk/ecc/ltc_ecc_projective_dbl_point.c
View File

@ -21,7 +21,7 @@
ECC Crypto, Tom St Denis
*/
#if defined(MECC) && !defined(MECC_ACCEL)
#if defined(MECC) && (!defined(MECC_ACCEL) || defined(LTM_DESC))
/**
Double an ECC point

2
testprof/der_tests.c
View File

@ -1,5 +1,7 @@
#include <tomcrypt_test.h>
#if defined(GMP_DESC) || defined(USE_GMP)
#include <gmp.h>
#endif
#ifndef LTC_DER

6
testprof/ecc_test.c
View File

@ -15,7 +15,7 @@ static int sizes[] = {
#ifdef ECC384
48,
#endif
#ifdef ECC512
#ifdef ECC521
65
#endif
};
@ -27,6 +27,10 @@ int ecc_tests (void)
int stat, stat2;
ecc_key usera, userb, pubKey, privKey;
DO(ecc_test ());
DO(ecc_test ());
DO(ecc_test ());
DO(ecc_test ());
DO(ecc_test ());
for (s = 0; s < (sizeof(sizes)/sizeof(sizes[0])); s++) {