952 lines
24 KiB
C
952 lines
24 KiB
C
/* C version of ake4mnta.cpp
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*
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Example for embedded implementation.
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Should build immediately with standard mirdef.h file on a PC. For example using MS C
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cl /O2 ake4mnta.c ms32.lib
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To simulate performance on a PC of an 8-bit computer use
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#define MR_LITTLE_ENDIAN
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#define MIRACL 8
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#define mr_utype char
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#define MR_IBITS 32
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#define MR_LBITS 32
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#define mr_unsign32 unsigned int
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#define mr_dltype short
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#define MR_STATIC 20
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#define MR_ALWAYS_BINARY
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#define MR_STRIPPED_DOWN
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#define MR_GENERIC_MT
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#define MAXBASE ((mr_small)1<<(MIRACL-1))
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#define MR_COMBA 20
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#define MR_NOASM
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#define MR_BITSINCHAR 8
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#define MR_NOSUPPORT_COMPRESSION
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rem Compile MIRACL modules
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mex 20 c mrcomba
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cl /c /O2 /W3 mrzzn2.c
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cl /c /O2 /W3 mrcore.c
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cl /c /O2 /W3 mrarth0.c
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cl /c /O2 /W3 mrarth1.c
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cl /c /O2 /W3 mrarth2.c
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cl /c /O2 /W3 mrxgcd.c
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cl /c /O2 /W3 mrbits.c
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cl /c /O2 /W3 mrmonty.c
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cl /c /O2 /W3 mrcomba.c
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cl /c /O2 /W3 mrcurve.c
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cl /c /O2 /W3 mrio1.c
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cl /c /O2 /W3 mrpower.c
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rem
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rem Create library 'miracl.lib'
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del miracl.lib
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lib /OUT:miracl.lib mrxgcd.obj mrarth2.obj mrio1.obj mrcomba.obj
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lib /OUT:miracl.lib miracl.lib mrmonty.obj mrarth1.obj mrarth0.obj mrcore.obj
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lib /OUT:miracl.lib miracl.lib mrcurve.obj mrbits.obj mrzzn2.obj mrpower.obj
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del mr*.obj
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cl /O2 ake4mnta.c miracl.lib
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For Atmel AVR (atmega128) use
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#define MR_LITTLE_ENDIAN
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#define MIRACL 8
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#define mr_utype char
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#define MR_IBITS 16
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#define MR_LBITS 32
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#define mr_unsign32 unsigned long
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#define mr_dltype int
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#define mr_qltype long
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#define MR_STATIC 20
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#define MR_ALWAYS_BINARY
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#define MR_STRIPPED_DOWN
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#define MR_GENERIC_MT
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#define MAXBASE ((mr_small)1<<(MIRACL-1))
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#define MR_COMBA 20
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#define MR_NOASM
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#define MR_BITSINCHAR 8
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#define MR_NO_STANDARD_IO
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#define MR_NO_FILE_IO
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#define MR_NOSUPPORT_COMPRESSION
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#define MR_AVR
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This last line must be added manually - config.c will not do it automatically
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and execute
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mex 20 avr4 mrcomba
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On an ARM use a header like
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#define MR_LITTLE_ENDIAN
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#define MIRACL 32
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#define mr_utype int
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#define MR_IBITS 32
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#define MR_LBITS 32
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#define mr_unsign32 unsigned int
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#define mr_dltype long long
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#define MR_STATIC 5
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#define MR_ALWAYS_BINARY
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#define MR_STRIPPED_DOWN
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#define MR_GENERIC_MT
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#define MAXBASE ((mr_small)1<<(MIRACL-1))
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#define MR_COMBA 5
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#define MR_BITSINCHAR 8
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#define MR_NOSUPPORT_COMPRESSION
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and possible
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#define MR_NO_STANDARD_IO
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#define MR_NO_FILE_IO
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and execute
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mex 5 arm mrcomba
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Speeded up using ideas from
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"Efficient Computation of Tate Pairing in Projective Coordinate over General Characteristic Fields"
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by Sanjit Chatterjee1, Palash Sarkar1 and Rana Barua1
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*/
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#include <stdio.h>
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#include <stdlib.h>
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#include "miracl.h"
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#ifdef MR_COUNT_OPS
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int fpm2,fpi2,fpc,fpa,fpx;
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#endif
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/* Fix the contents of k4mnt.ecs */
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/* ROM contains details of a k=4 MNT pairing-friendly curve. In this case p is 160-bits, and
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=5 mod 8. The pairing friendly prime-order group is of order (p+1-t)/34 */
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#define CF 34
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#if MIRACL==32
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#define WORDS 5
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#define NPW 8 /* Nibbles per Word */
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#define ROMSZ 30
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static const mr_small romp[]={
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0x76A5755D,0x245769E6,0xF33DC5F3,0x42C82027,0xE3F367D5,
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0x866BA034,0x14DB64EB,0xDF4CF677,0xE45200C4,0xDABC0397,
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0x58290FC5,0x0BD4BB42,0x0EAEF730,0xA014F1E3,0x6B455E0,
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0xC1315D34,0x92168B16,0xF191,0x0,0x0,
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0xB79C2B47,0x10BEC9C5,0xE0BF4D14,0x67B5A4AC,0xB3657D09,
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0xC1315D33,0x92168B16,0xF191,0x0,0x0};
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/* Points - in n-residue form */
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#define PROMSZ 30
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static const mr_small Prom[]={
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0x1E6EA84F,0xE7CE6B23,0x7B6AC239,0x805022A9,0x260BF17B,
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0x90898C7E,0x9D8C9BC9,0xD482E11C,0x2D4D3F68,0x1D1DA150,
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0xC8501310,0x524DD4A,0x3DED1AE2,0x3094317B,0x9DB2C44C,
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0x23E533B2,0xC8BD73FB,0xF3D25667,0x1CEE805C,0x24EDB45C,
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0x21E3CEBD,0x625F7B2E,0xF924576E,0x35FCAA2,0x67DE6249,
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0xF780367B,0x43AD112B,0xD9F11765,0xF0BA13D1,0x1F0355FE};
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#endif
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#if MIRACL==8
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#define WORDS 20
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#define NPW 2 /* Nibbles per Word */
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#define ROMSZ 120
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#ifdef MR_AVR
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__attribute__((__progmem__))
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#endif
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static const mr_small romp[]={
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0x5D,0x75,0xA5,0x76,0xE6,0x69,0x57,0x24,0xF3,0xC5,0x3D,0xF3,0x27,0x20,0xC8,0x42,0xD5,0x67,0xF3,0xE3,
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0x34,0xA0,0x6B,0x86,0xEB,0x64,0xDB,0x14,0x77,0xF6,0x4C,0xDF,0xC4,0x00,0x52,0xE4,0x97,0x03,0xBC,0xDA,
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0xC5,0x0F,0x29,0x58,0x42,0xBB,0xD4,0x0B,0x30,0xF7,0xAE,0x0E,0xE3,0xF1,0x14,0xA0,0xE0,0x55,0xB4,0x06,
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0x34,0x5D,0x31,0xC1,0x16,0x8B,0x16,0x92,0x91,0xF1,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,
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0x47,0x2B,0x9C,0xB7,0xC5,0xC9,0xBE,0x10,0x14,0x4D,0xBF,0xE0,0xAC,0xA4,0xB5,0x67,0x09,0x7D,0x65,0xB3,
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0x33,0x5D,0x31,0xC1,0x16,0x8B,0x16,0x92,0x91,0xF1,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00};
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#define PROMSZ 120
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#ifdef MR_AVR
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__attribute__((__progmem__))
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#endif
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static const mr_small Prom[]={
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0x4F,0xA8,0x6E,0x1E,0x23,0x6B,0xCE,0xE7,0x39,0xC2,0x6A,0x7B,0xA9,0x22,0x50,0x80,0x7B,0xF1,0xB,0x26,
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0x7E,0x8C,0x89,0x90,0xC9,0x9B,0x8C,0x9D,0x1C,0xE1,0x82,0xD4,0x68,0x3F,0x4D,0x2D,0x50,0xA1,0x1D,0x1D,
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0x10,0x13,0x50,0xC8,0x4A,0xDD,0x24,0x5,0xE2,0x1A,0xED,0x3D,0x7B,0x31,0x94,0x30,0x4C,0xC4,0xB2,0x9D,
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0xB2,0x33,0xE5,0x23,0xFB,0x73,0xBD,0xC8,0x67,0x56,0xD2,0xF3,0x5C,0x80,0xEE,0x1C,0x5C,0xB4,0xED,0x24,
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0xBD,0xCE,0xE3,0x21,0x2E,0x7B,0x5F,0x62,0x6E,0x57,0x24,0xF9,0xA2,0xCA,0x5F,0x3,0x49,0x62,0xDE,0x67,
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0x7B,0x36,0x80,0xF7,0x2B,0x11,0xAD,0x43,0x65,0x17,0xF1,0xD9,0xD1,0x13,0xBA,0xF0,0xFE,0x55,0x3,0x1F};
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#endif
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/* Fp4 support functions */
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typedef struct
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{
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zzn2 x;
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zzn2 y;
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BOOL unitary;
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} zzn4;
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#ifndef MR_NO_STANDARD_IO
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void zzn2_out(_MIPD_ char *p,zzn2 *x)
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{
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printf(p); printf("\n");
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redc(_MIPP_ x->a,x->a);
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redc(_MIPP_ x->b,x->b);
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otnum(_MIPP_ x->a,stdout);
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otnum(_MIPP_ x->b,stdout);
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nres(_MIPP_ x->a,x->a);
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nres(_MIPP_ x->b,x->b);
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}
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#endif
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/* Irreducible over zzn2 is x^2+n */
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/* zzn4 is towered on top of this with irreducible X^2+sqrt(n) p=5 mod 8, or X^2+(1+sqrt(n)) p=3,7 mod 8 */
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/* same as txx(.) function in C++ */
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void zzn2_times_irp(_MIPD_ zzn2 *u)
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{
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zzn2 t;
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switch (mr_mip->pmod8)
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{
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case 5: /* times sqrt(n) */
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zzn2_timesi(_MIPP_ u);
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break;
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case 3: /* times 1+sqrt(n) */
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case 7:
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t.a=mr_mip->w5;
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t.b=mr_mip->w6;
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zzn2_copy(u,&t);
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zzn2_timesi(_MIPP_ &t);
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zzn2_add(_MIPP_ u,&t,u);
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break;
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default:
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break;
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}
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}
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void zzn4_copy(zzn4 *u,zzn4 *w)
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{
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if (u==w) return;
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zzn2_copy(&(u->x),&(w->x));
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zzn2_copy(&(u->y),&(w->y));
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w->unitary=u->unitary;
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}
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void zzn4_from_int(_MIPD_ int i,zzn4 *w)
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{
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zzn2_from_int(_MIPP_ i,&(w->x));
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zzn2_zero(&(w->y));
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if (i==1) w->unitary=TRUE;
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else w->unitary=FALSE;
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}
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void zzn4_conj(_MIPD_ zzn4 *u,zzn4 *w)
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{
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zzn4_copy(u,w);
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zzn2_negate(_MIPP_ &(w->y),&(w->y));
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}
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void zzn4_mul(_MIPD_ zzn4 *u,zzn4 *v,zzn4 *w)
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{
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zzn2 t1,t2,t3;
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t1.a=mr_mip->w3;
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t1.b=mr_mip->w4;
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t2.a=mr_mip->w8;
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t2.b=mr_mip->w9;
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if (u==v)
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{
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if (u->unitary)
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{ /* this is faster.. - see Lenstra & Stam */
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zzn4_copy(u,w);
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zzn2_mul(_MIPP_ &(w->y),&(w->y),&t1);
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zzn2_add(_MIPP_ &(w->y),&(w->x),&(w->y));
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zzn2_mul(_MIPP_ &(w->y),&(w->y),&(w->y));
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zzn2_sub(_MIPP_ &(w->y),&t1,&(w->y));
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zzn2_timesi(_MIPP_ &t1);
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zzn2_copy(&t1,&(w->x));
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zzn2_sub(_MIPP_ &(w->y),&(w->x),&(w->y));
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zzn2_add(_MIPP_ &(w->x),&(w->x),&(w->x));
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zzn2_sadd(_MIPP_ &(w->x),mr_mip->one,&(w->x));
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zzn2_ssub(_MIPP_ &(w->y),mr_mip->one,&(w->y));
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}
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else
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{
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zzn4_copy(u,w);
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zzn2_copy(&(w->y),&t2); // t2=b;
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zzn2_add(_MIPP_ &(w->x),&t2,&t1); // t1=a+b
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zzn2_times_irp(_MIPP_ &t2); // t2=txx(b);
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zzn2_add(_MIPP_ &t2,&(w->x),&t2); // t2=a+txx(b)
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zzn2_mul(_MIPP_ &(w->y),&(w->x),&(w->y)); // b*=a
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zzn2_mul(_MIPP_ &t1,&t2,&(w->x)); // a=t1*t2
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zzn2_copy(&(w->y),&t2); //t2=b
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zzn2_sub(_MIPP_ &(w->x),&t2,&(w->x)); //a-=b
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zzn2_times_irp(_MIPP_ &t2); // t2=txx(b)
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zzn2_sub(_MIPP_ &(w->x),&t2,&(w->x)); // a-=txx(b);
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zzn2_add(_MIPP_ &(w->y),&(w->y),&(w->y)); // b+=b;
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}
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}
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else
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{
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t3.a=mr_mip->w10;
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t3.b=mr_mip->w11;
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zzn2_copy(&(u->x),&t1);
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zzn2_copy(&(u->y),&t2);
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zzn2_mul(_MIPP_ &t1,&(v->x),&t1);
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zzn2_mul(_MIPP_ &t2,&(v->y),&t2);
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zzn2_copy(&(v->x),&t3);
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zzn2_add(_MIPP_ &t3,&(v->y),&t3);
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zzn2_add(_MIPP_ &(u->y),&(u->x),&(w->y));
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zzn2_mul(_MIPP_ &(w->y),&t3,&(w->y));
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zzn2_sub(_MIPP_ &(w->y),&t1,&(w->y));
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zzn2_sub(_MIPP_ &(w->y),&t2,&(w->y));
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zzn2_copy(&t1,&(w->x));
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zzn2_times_irp(_MIPP_ &t2);
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zzn2_add(_MIPP_ &(w->x),&t2,&(w->x));
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if (u->unitary && v->unitary) w->unitary=TRUE;
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else w->unitary=FALSE;
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}
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}
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/* zzn4 powering of unitary elements */
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void zzn4_powu(_MIPD_ zzn4 *x,big k,zzn4 *u)
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{
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zzn4 t[5],u2;
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big k3;
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int i,j,n,nb,nbw,nzs;
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#ifndef MR_STATIC
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char *mem=memalloc(_MIPP_ 25);
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#else
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char mem[MR_BIG_RESERVE(25)];
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memset(mem,0,MR_BIG_RESERVE(25));
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#endif
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if (size(k)==0)
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{
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zzn4_from_int(_MIPP_ 1,u);
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return;
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}
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zzn4_copy(x,u);
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if (size(k)==1) return;
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for (j=i=0;i<5;i++)
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{
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t[i].x.a=mirvar_mem(_MIPP_ mem,j++);
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t[i].x.b=mirvar_mem(_MIPP_ mem,j++);
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t[i].y.a=mirvar_mem(_MIPP_ mem,j++);
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t[i].y.b=mirvar_mem(_MIPP_ mem,j++);
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t[i].unitary=FALSE;
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}
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u2.x.a=mirvar_mem(_MIPP_ mem,j++);
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u2.x.b=mirvar_mem(_MIPP_ mem,j++);
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u2.y.a=mirvar_mem(_MIPP_ mem,j++);
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u2.y.b=mirvar_mem(_MIPP_ mem,j++);
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u2.unitary=FALSE;
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k3=mirvar_mem(_MIPP_ mem,j);
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premult(_MIPP_ k,3,k3);
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zzn4_mul(_MIPP_ u,u,&u2);
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zzn4_copy(u,&t[0]);
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for (i=1;i<=4;i++)
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zzn4_mul(_MIPP_ &u2,&t[i-1],&t[i]);
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nb=logb2(_MIPP_ k3);
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for (i=nb-2;i>=1;)
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{
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n=mr_naf_window(_MIPP_ k,k3,i,&nbw,&nzs,5);
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for (j=0;j<nbw;j++) zzn4_mul(_MIPP_ u,u,u);
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if (n>0) zzn4_mul(_MIPP_ u,&t[n/2],u);
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if (n<0)
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{
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zzn4_conj(_MIPP_ &t[-n/2],&u2);
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zzn4_mul(_MIPP_ u,&u2,u);
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}
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i-=nbw;
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if (nzs)
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{
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for (j=0;j<nzs;j++) zzn4_mul(_MIPP_ u,u,u);
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i-=nzs;
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}
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}
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#ifndef MR_STATIC
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memkill(_MIPP_ mem,25);
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#else
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memset(mem,0,MR_BIG_RESERVE(25));
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#endif
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}
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/* Lucas-style ladder exponentiation of traces */
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void zzn2_powl(_MIPD_ zzn2 *x,big e,zzn2 *w)
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{
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int i,s;
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|
zzn2 t1,t3,t4;
|
|
t1.a=mr_mip->w7;
|
|
t1.b=mr_mip->w8;
|
|
t3.a=mr_mip->w10;
|
|
t3.b=mr_mip->w11;
|
|
t4.a=mr_mip->w13;
|
|
t4.b=mr_mip->w14;
|
|
|
|
zzn2_from_int(_MIPP_ 1,&t1);
|
|
|
|
s=size(e);
|
|
if (s==0)
|
|
{
|
|
zzn2_copy(&t1,w);
|
|
return;
|
|
}
|
|
zzn2_copy(x,w);
|
|
if (s==1 || s==(-1)) return;
|
|
|
|
i=logb2(_MIPP_ e)-1;
|
|
|
|
zzn2_copy(w,&t3);
|
|
zzn2_mul(_MIPP_ w,w,&t4);
|
|
zzn2_add(_MIPP_ &t4,&t4,&t4);
|
|
zzn2_sub(_MIPP_ &t4,&t1,&t4);
|
|
|
|
while (i--)
|
|
{
|
|
if (mr_testbit(_MIPP_ e,i))
|
|
{
|
|
zzn2_mul(_MIPP_ &t3,&t4,&t3);
|
|
zzn2_add(_MIPP_ &t3,&t3,&t3);
|
|
zzn2_sub(_MIPP_ &t3,w,&t3);
|
|
zzn2_mul(_MIPP_ &t4,&t4,&t4);
|
|
zzn2_add(_MIPP_ &t4,&t4,&t4);
|
|
zzn2_sub(_MIPP_ &t4,&t1,&t4);
|
|
}
|
|
else
|
|
{
|
|
zzn2_mul(_MIPP_ &t4,&t3,&t4);
|
|
zzn2_add(_MIPP_ &t4,&t4,&t4);
|
|
zzn2_sub(_MIPP_ &t4,w,&t4);
|
|
zzn2_mul(_MIPP_ &t3,&t3,&t3);
|
|
zzn2_add(_MIPP_ &t3,&t3,&t3);
|
|
zzn2_sub(_MIPP_ &t3,&t1,&t3);
|
|
}
|
|
}
|
|
zzn2_copy(&t3,w);
|
|
}
|
|
|
|
void zzn4_powq(_MIPD_ big fr,zzn4 *w)
|
|
{
|
|
zzn2_conj(_MIPP_ &(w->x),&(w->x));
|
|
zzn2_conj(_MIPP_ &(w->y),&(w->y));
|
|
nres(_MIPP_ fr,mr_mip->w1);
|
|
zzn2_smul(_MIPP_ &(w->y),mr_mip->w1,&(w->y));
|
|
}
|
|
|
|
void zzn4_inv(_MIPD_ zzn4 *u)
|
|
{
|
|
zzn2 t1,t2;
|
|
if (u->unitary)
|
|
{
|
|
zzn4_conj(_MIPP_ u,u);
|
|
return;
|
|
}
|
|
t1.a=mr_mip->w8;
|
|
t1.b=mr_mip->w9;
|
|
t2.a=mr_mip->w3;
|
|
t2.b=mr_mip->w4;
|
|
zzn2_mul(_MIPP_ &(u->x),&(u->x),&t1);
|
|
zzn2_mul(_MIPP_ &(u->y),&(u->y),&t2);
|
|
zzn2_times_irp(_MIPP_ &t2);
|
|
zzn2_sub(_MIPP_ &t1,&t2,&t1);
|
|
zzn2_inv(_MIPP_ &t1);
|
|
zzn2_mul(_MIPP_ &(u->x),&t1,&(u->x));
|
|
zzn2_negate(_MIPP_ &t1,&t1);
|
|
zzn2_mul(_MIPP_ &(u->y),&t1,&(u->y));
|
|
}
|
|
|
|
/* Original from A. Devegili. Thanks Augusto! Projective point addition */
|
|
|
|
BOOL ecurve_fp2_add(_MIPD_ zzn2 *Zx, zzn2 *Zy, zzn2 *Zz, zzn2 *x, zzn2 *y, zzn2 *z, zzn2 *lam,zzn2 *ex1,zzn2 *ex2)
|
|
{
|
|
BOOL doubling,normed;
|
|
zzn2 Xzz, Yzzz, xZZ, yZZZ, zz, ZZ;
|
|
zzn2 t1, t2, t3, x3;
|
|
#ifndef MR_STATIC
|
|
char *mem = memalloc(_MIPP_ 20);
|
|
#else
|
|
char mem[MR_BIG_RESERVE(20)];
|
|
memset(mem, 0, MR_BIG_RESERVE(20));
|
|
#endif
|
|
|
|
Xzz.a = mirvar_mem(_MIPP_ mem, 0);
|
|
Xzz.b = mirvar_mem(_MIPP_ mem, 1);
|
|
Yzzz.a = mirvar_mem(_MIPP_ mem, 2);
|
|
Yzzz.b = mirvar_mem(_MIPP_ mem, 3);
|
|
xZZ.a = mirvar_mem(_MIPP_ mem, 4);
|
|
xZZ.b = mirvar_mem(_MIPP_ mem, 5);
|
|
yZZZ.a = mirvar_mem(_MIPP_ mem, 6);
|
|
yZZZ.b = mirvar_mem(_MIPP_ mem, 7);
|
|
zz.a = mirvar_mem(_MIPP_ mem, 8);
|
|
zz.b = mirvar_mem(_MIPP_ mem, 9);
|
|
ZZ.a = mirvar_mem(_MIPP_ mem, 10);
|
|
ZZ.b = mirvar_mem(_MIPP_ mem, 11);
|
|
t1.a = mirvar_mem(_MIPP_ mem, 12);
|
|
t1.b = mirvar_mem(_MIPP_ mem, 13);
|
|
t2.a = mirvar_mem(_MIPP_ mem, 14);
|
|
t2.b = mirvar_mem(_MIPP_ mem, 15);
|
|
t3.a = mirvar_mem(_MIPP_ mem, 16);
|
|
t3.b = mirvar_mem(_MIPP_ mem, 17);
|
|
x3.a = mirvar_mem(_MIPP_ mem, 18);
|
|
x3.b = mirvar_mem(_MIPP_ mem, 19);
|
|
|
|
doubling=FALSE;
|
|
if (z==Zz) doubling=TRUE;
|
|
|
|
if (!doubling)
|
|
{ // maybe we are really doubling? Or P-=P?
|
|
if (!zzn2_isunity(_MIPP_ Zz))
|
|
{
|
|
zzn2_mul(_MIPP_ Zz, Zz, &ZZ); // ZZ = Zz^2
|
|
zzn2_mul(_MIPP_ x, &ZZ, &xZZ); // xZZ = x * Zz^2
|
|
zzn2_mul(_MIPP_ &ZZ, Zz, &yZZZ); // yZZZ = Zz^3
|
|
zzn2_mul(_MIPP_ &yZZZ, y, &yZZZ); // yZZZ = y * Zz^3
|
|
normed=FALSE;
|
|
}
|
|
else
|
|
{
|
|
zzn2_copy(x,&xZZ);
|
|
zzn2_copy(y,&yZZZ);
|
|
normed=TRUE;
|
|
}
|
|
if (!zzn2_isunity(_MIPP_ z))
|
|
{
|
|
zzn2_mul(_MIPP_ z, z, &zz); // zz = z^2
|
|
zzn2_mul(_MIPP_ Zx, &zz, &Xzz); // Xzz = Zx * z^2
|
|
zzn2_mul(_MIPP_ &zz, z, &Yzzz); // Yzzz = z^3
|
|
zzn2_mul(_MIPP_ &Yzzz, Zy, &Yzzz); // Yzzz = Zy * z^3
|
|
}
|
|
else
|
|
{
|
|
zzn2_copy(Zx,&Xzz);
|
|
zzn2_copy(Zy,&Yzzz);
|
|
}
|
|
|
|
if (zzn2_compare(&Xzz,&xZZ))
|
|
{
|
|
if (!zzn2_compare(&Yzzz,&yZZZ) || zzn2_iszero(y))
|
|
{
|
|
zzn2_zero(x);
|
|
zzn2_zero(y);
|
|
zzn2_zero(z);
|
|
zzn2_from_int(_MIPP_ 1,lam);
|
|
#ifndef MR_STATIC
|
|
memkill(_MIPP_ mem, 20);
|
|
#else
|
|
memset(mem, 0, MR_BIG_RESERVE(20));
|
|
#endif
|
|
return doubling;
|
|
}
|
|
else
|
|
doubling=TRUE;
|
|
}
|
|
}
|
|
|
|
if (!doubling)
|
|
{ // point addition
|
|
zzn2_sub(_MIPP_ &xZZ, &Xzz, &t1); // t1 = Xzz - xZZ
|
|
zzn2_sub(_MIPP_ &yZZZ, &Yzzz, lam); // lam = yZZZ - yZZZ
|
|
zzn2_mul(_MIPP_ z,&t1,z);
|
|
if (!normed) zzn2_mul(_MIPP_ z,&ZZ,z);
|
|
|
|
zzn2_mul(_MIPP_ &t1,&t1,&t2);
|
|
zzn2_add(_MIPP_ &xZZ,&Xzz,&t3);
|
|
zzn2_mul(_MIPP_ &t3,&t2,&t3);
|
|
zzn2_mul(_MIPP_ lam, lam, &x3); // x3 = lam^2
|
|
zzn2_sub(_MIPP_ &x3,&t3,&x3);
|
|
zzn2_sub(_MIPP_ &t3,&x3,&t3);
|
|
zzn2_sub(_MIPP_ &t3,&x3,&t3);
|
|
|
|
zzn2_mul(_MIPP_ &t3,lam,&t3);
|
|
zzn2_mul(_MIPP_ &t2,&t1,&t2);
|
|
zzn2_add(_MIPP_ &yZZZ,&Yzzz,&t1);
|
|
zzn2_mul(_MIPP_ &t1,&t2,&t1);
|
|
zzn2_sub(_MIPP_ &t3,&t1,y);
|
|
zzn2_div2(_MIPP_ y);
|
|
zzn2_copy(&x3,x);
|
|
}
|
|
else
|
|
{ // point doubling
|
|
zzn2_mul(_MIPP_ y, y, &t2); // t2 = y^2
|
|
|
|
/* its on the twist so A=6! */
|
|
|
|
zzn2_mul(_MIPP_ z,z,ex2);
|
|
zzn2_mul(_MIPP_ x,x,lam);
|
|
zzn2_mul(_MIPP_ ex2,ex2,&t1);
|
|
zzn2_add(_MIPP_ &t1,&t1,&t1);
|
|
zzn2_add(_MIPP_ lam,&t1,lam);
|
|
zzn2_copy(lam,&t1);
|
|
zzn2_add(_MIPP_ lam,lam,lam);
|
|
zzn2_add(_MIPP_ lam,&t1,lam);
|
|
|
|
zzn2_mul(_MIPP_ x, &t2, &t1); // t1 = x * y^2
|
|
zzn2_add(_MIPP_ &t1, &t1, &t1); // t1 = 2(x*y^2)
|
|
zzn2_add(_MIPP_ &t1, &t1, &t1); // t1 = 4(x*y^2)
|
|
|
|
// x = lam^2 - t1 - t1
|
|
zzn2_mul(_MIPP_ lam, lam, x); // x = lam^2
|
|
zzn2_sub(_MIPP_ x, &t1, x); // x = lam^2 - t1
|
|
zzn2_sub(_MIPP_ x, &t1, x); // x = lam^2 - 2t1
|
|
|
|
zzn2_mul(_MIPP_ z, y , z); // z = yz
|
|
zzn2_add(_MIPP_ z, z, z); // z = 2yz
|
|
|
|
// 8 * y^2
|
|
zzn2_add(_MIPP_ &t2, &t2, &t2); // t2 = 2y^2
|
|
zzn2_copy(&t2,ex1);
|
|
zzn2_mul(_MIPP_ &t2, &t2, &t2); // t2 = 4y^2
|
|
zzn2_add(_MIPP_ &t2, &t2, &t2); // t2 = 8y^2
|
|
|
|
// y = lam*(t - x) - y^2
|
|
zzn2_sub(_MIPP_ &t1, x, y); // y = t1 - x
|
|
zzn2_mul(_MIPP_ y, lam, y); // y = lam(t1 - x)
|
|
zzn2_sub(_MIPP_ y, &t2, y); // y = lam(t1 - x) * y^2
|
|
}
|
|
|
|
#ifndef MR_STATIC
|
|
memkill(_MIPP_ mem, 20);
|
|
#else
|
|
memset(mem, 0, MR_BIG_RESERVE(20));
|
|
#endif
|
|
return doubling;
|
|
}
|
|
|
|
void g(_MIPD_ zzn2 *Ax,zzn2 *Ay,zzn2 *Az,zzn2 *Bx,zzn2 *By,zzn2 *Bz,big Px,big Py,zzn4 *w)
|
|
{
|
|
BOOL Doubling;
|
|
zzn2 lam,extra1,extra2,Kx,nn,dd;
|
|
|
|
#ifndef MR_STATIC
|
|
char *mem = memalloc(_MIPP_ 12);
|
|
#else
|
|
char mem[MR_BIG_RESERVE(12)];
|
|
memset(mem, 0, MR_BIG_RESERVE(12));
|
|
#endif
|
|
lam.a=mirvar_mem(_MIPP_ mem,0);
|
|
lam.b=mirvar_mem(_MIPP_ mem,1);
|
|
extra1.a=mirvar_mem(_MIPP_ mem,2);
|
|
extra1.b=mirvar_mem(_MIPP_ mem,3);
|
|
extra2.a=mirvar_mem(_MIPP_ mem,4);
|
|
extra2.b=mirvar_mem(_MIPP_ mem,5);
|
|
Kx.a=mirvar_mem(_MIPP_ mem,6);
|
|
Kx.b=mirvar_mem(_MIPP_ mem,7);
|
|
nn.a=mirvar_mem(_MIPP_ mem,8);
|
|
nn.b=mirvar_mem(_MIPP_ mem,9);
|
|
dd.a=mirvar_mem(_MIPP_ mem,10);
|
|
dd.b=mirvar_mem(_MIPP_ mem,11);
|
|
|
|
zzn2_copy(Ax,&Kx);
|
|
|
|
Doubling=ecurve_fp2_add(_MIPP_ Bx,By,Bz,Ax,Ay,Az,&lam,&extra1,&extra2);
|
|
|
|
/* Get extra information from the point addition, for use in the line functions */
|
|
|
|
if (!Doubling)
|
|
{
|
|
zzn2_smul(_MIPP_ Az,Py,&nn);
|
|
zzn2_timesi(_MIPP_ &nn);
|
|
zzn2_copy(Bx,&dd);
|
|
zzn2_timesi(_MIPP_ &dd);
|
|
zzn2_sadd(_MIPP_ &dd,Px,&dd);
|
|
zzn2_mul(_MIPP_ &lam,&dd,&lam);
|
|
zzn2_copy(By,&dd);
|
|
zzn2_timesi(_MIPP_ &dd);
|
|
zzn2_mul(_MIPP_ &dd,Az,&dd);
|
|
zzn2_sub(_MIPP_ &lam,&dd,&dd);
|
|
}
|
|
else
|
|
{
|
|
zzn2_smul(_MIPP_ &extra2,Py,&nn);
|
|
zzn2_mul(_MIPP_ &nn,Az,&nn);
|
|
zzn2_timesi(_MIPP_ &nn);
|
|
zzn2_timesi(_MIPP_ &Kx);
|
|
zzn2_smul(_MIPP_ &extra2,Px,&dd);
|
|
zzn2_add(_MIPP_ &dd,&Kx,&dd);
|
|
zzn2_mul(_MIPP_ &lam,&dd,&lam);
|
|
zzn2_timesi(_MIPP_ &extra1);
|
|
zzn2_sub(_MIPP_ &lam,&extra1,&dd);
|
|
|
|
}
|
|
zzn2_copy(&nn,&(w->x));
|
|
zzn2_copy(&dd,&(w->y));
|
|
|
|
#ifndef MR_STATIC
|
|
memkill(_MIPP_ mem,12);
|
|
#else
|
|
memset(mem,0,MR_BIG_RESERVE(12));
|
|
#endif
|
|
return;
|
|
}
|
|
|
|
void fast_tate_pairing(_MIPD_ zzn2 *Qx,zzn2 *Qy,epoint *P,big T,big fr,big delta,zzn4 *w,zzn4* res)
|
|
{
|
|
int i,j,nb;
|
|
zzn2 Ax,Ay,Az,Qz;
|
|
zzn Px,Py;
|
|
|
|
#ifndef MR_STATIC
|
|
char *mem=memalloc(_MIPP_ 10);
|
|
#else
|
|
char mem[MR_BIG_RESERVE(10)];
|
|
memset(mem,0,MR_BIG_RESERVE(10));
|
|
#endif
|
|
|
|
#ifdef MR_COUNT_OPS
|
|
fpa=fpc=fpx=0;
|
|
#endif
|
|
|
|
Ax.a=mirvar_mem(_MIPP_ mem,0);
|
|
Ax.b=mirvar_mem(_MIPP_ mem,1);
|
|
Ay.a=mirvar_mem(_MIPP_ mem,2);
|
|
Ay.b=mirvar_mem(_MIPP_ mem,3);
|
|
Az.a=mirvar_mem(_MIPP_ mem,4);
|
|
Az.b=mirvar_mem(_MIPP_ mem,5);
|
|
Qz.a=mirvar_mem(_MIPP_ mem,6);
|
|
Qz.b=mirvar_mem(_MIPP_ mem,7);
|
|
Px=mirvar_mem(_MIPP_ mem,8);
|
|
Py=mirvar_mem(_MIPP_ mem,9);
|
|
|
|
copy(P->X,Px);
|
|
copy(P->Y,Py);
|
|
|
|
nres_modadd(_MIPP_ Px,Px,Px); /* removes a factor of 2 from g() */
|
|
nres_modadd(_MIPP_ Py,Py,Py);
|
|
|
|
zzn2_from_int(_MIPP_ 1,&Qz);
|
|
zzn2_copy(Qx,&Ax);
|
|
zzn2_copy(Qy,&Ay);
|
|
zzn2_copy(&Qz,&Az);
|
|
|
|
zzn4_from_int(_MIPP_ 1,res);
|
|
|
|
/* Simple Miller loop */
|
|
nb=logb2(_MIPP_ T);
|
|
for (i=nb-2;i>=0;i--)
|
|
{
|
|
zzn4_mul(_MIPP_ res,res,res);
|
|
g(_MIPP_ &Ax,&Ay,&Az,&Ax,&Ay,&Az,Px,Py,w);
|
|
zzn4_mul(_MIPP_ res,w,res);
|
|
if (mr_testbit(_MIPP_ T,i))
|
|
{
|
|
g(_MIPP_ &Ax,&Ay,&Az,Qx,Qy,&Qz,Px,Py,w);
|
|
zzn4_mul(_MIPP_ res,w,res);
|
|
}
|
|
}
|
|
|
|
#ifdef MR_COUNT_OPS
|
|
printf("Millers loop Cost\n");
|
|
printf("fpc= %d\n",fpc);
|
|
printf("fpa= %d\n",fpa);
|
|
printf("fpx= %d\n",fpx);
|
|
|
|
fpa=fpc=fpx=0;
|
|
#endif
|
|
|
|
zzn4_copy(res,w);
|
|
zzn4_powq(_MIPP_ fr,w); zzn4_powq(_MIPP_ fr,w);
|
|
zzn4_inv(_MIPP_ res);
|
|
zzn4_mul(_MIPP_ res,w,res); /* ^(p*p-1) */
|
|
|
|
res->unitary=TRUE;
|
|
|
|
zzn4_mul(_MIPP_ res,res,res);
|
|
zzn4_copy(res,w);
|
|
zzn4_mul(_MIPP_ res,res,res);
|
|
zzn4_mul(_MIPP_ res,res,res);
|
|
zzn4_mul(_MIPP_ res,res,res);
|
|
zzn4_mul(_MIPP_ res,res,res);
|
|
zzn4_mul(_MIPP_ res,w,res); /* res=powu(res,CF) for CF=34 */
|
|
|
|
#ifndef MR_STATIC
|
|
memkill(_MIPP_ mem,10);
|
|
#else
|
|
memset(mem,0,MR_BIG_RESERVE(10));
|
|
#endif
|
|
}
|
|
|
|
void ecap(_MIPD_ zzn2 *Qx,zzn2 *Qy,epoint *P,big T,big fr,big delta,zzn2* r)
|
|
{
|
|
zzn4 res,w;
|
|
#ifndef MR_STATIC
|
|
char *mem=memalloc(_MIPP_ 8);
|
|
#else
|
|
char mem[MR_BIG_RESERVE(8)];
|
|
memset(mem,0,MR_BIG_RESERVE(8));
|
|
#endif
|
|
res.x.a=mirvar_mem(_MIPP_ mem,0);
|
|
res.x.b=mirvar_mem(_MIPP_ mem,1);
|
|
res.y.a=mirvar_mem(_MIPP_ mem,2);
|
|
res.y.b=mirvar_mem(_MIPP_ mem,3);
|
|
w.x.a=mirvar_mem(_MIPP_ mem,4);
|
|
w.x.b=mirvar_mem(_MIPP_ mem,5);
|
|
w.y.a=mirvar_mem(_MIPP_ mem,6);
|
|
w.y.b=mirvar_mem(_MIPP_ mem,7);
|
|
|
|
res.unitary=FALSE;
|
|
w.unitary=FALSE;
|
|
|
|
epoint_norm(_MIPP_ P);
|
|
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fast_tate_pairing(_MIPP_ Qx,Qy,P,T,fr,delta,&w,&res);
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|
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|
zzn4_copy(&res,&w);
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zzn4_powq(_MIPP_ fr,&res);
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zzn4_powu(_MIPP_ &w,delta,&w);
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zzn4_mul(_MIPP_ &res,&w,&res);
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zzn2_copy(&(res.x),r);
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|
|
|
#ifdef MR_COUNT_OPS
|
|
printf("Final Exponentiation cost\n");
|
|
printf("fpc= %d\n",fpc);
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|
printf("fpa= %d\n",fpa);
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|
printf("fpx= %d\n",fpx);
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|
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|
fpa=fpc=fpx=0;
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|
#endif
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|
|
|
#ifndef MR_STATIC
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|
memkill(_MIPP_ mem,8);
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|
#else
|
|
memset(mem,0,MR_BIG_RESERVE(8));
|
|
#endif
|
|
}
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|
|
|
int main()
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{
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#ifdef MR_GENERIC_MT
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|
miracl instance;
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#endif
|
|
big p,A,B,fr,q,delta,t,T;
|
|
zzn2 res,Qx,Qy;
|
|
epoint *P;
|
|
int i,romptr;
|
|
#ifndef MR_STATIC
|
|
#ifdef MR_GENERIC_MT
|
|
miracl *mr_mip=mirsys(&instance,WORDS*NPW,16);
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|
#else
|
|
miracl *mr_mip=mirsys(WORDS*NPW,16);
|
|
#endif
|
|
char *mem=memalloc(_MIPP_ 14);
|
|
|
|
#else
|
|
#ifdef MR_GENERIC_MT
|
|
miracl *mr_mip=mirsys(&instance,MR_STATIC*NPW,16);
|
|
#else
|
|
miracl *mr_mip=mirsys(MR_STATIC*NPW,16);
|
|
#endif
|
|
char mem[MR_BIG_RESERVE(14)]; /* reserve space on the stack for 14 bigs */
|
|
char mem1[MR_ECP_RESERVE(1)]; /* reserve space on stack for 1 curve points */
|
|
memset(mem,0,MR_BIG_RESERVE(14)); /* clear this memory */
|
|
memset(mem1,0,MR_ECP_RESERVE(1));
|
|
#endif
|
|
p=mirvar_mem(_MIPP_ mem,0);
|
|
A=mirvar_mem(_MIPP_ mem,1);
|
|
B=mirvar_mem(_MIPP_ mem,2);
|
|
T=mirvar_mem(_MIPP_ mem,3);
|
|
q=mirvar_mem(_MIPP_ mem,4);
|
|
fr=mirvar_mem(_MIPP_ mem,5);
|
|
delta=mirvar_mem(_MIPP_ mem,6);
|
|
res.a=mirvar_mem(_MIPP_ mem,7);
|
|
res.b=mirvar_mem(_MIPP_ mem,8);
|
|
t=mirvar_mem(_MIPP_ mem,9);
|
|
Qx.a=mirvar_mem(_MIPP_ mem,10);
|
|
Qx.b=mirvar_mem(_MIPP_ mem,11);
|
|
Qy.a=mirvar_mem(_MIPP_ mem,12);
|
|
Qy.b=mirvar_mem(_MIPP_ mem,13);
|
|
|
|
P=epoint_init_mem(_MIPP_ mem1,0);
|
|
convert(_MIPP_ -3,A);
|
|
|
|
romptr=0;
|
|
init_big_from_rom(p,WORDS,romp,ROMSZ,&romptr);
|
|
init_big_from_rom(B,WORDS,romp,ROMSZ,&romptr);
|
|
init_big_from_rom(q,WORDS,romp,ROMSZ,&romptr);
|
|
init_big_from_rom(delta,WORDS,romp,ROMSZ,&romptr);
|
|
init_big_from_rom(fr,WORDS,romp,ROMSZ,&romptr);
|
|
init_big_from_rom(T,WORDS,romp,ROMSZ,&romptr);
|
|
|
|
#ifndef MR_NO_STANDARD_IO
|
|
printf("ROM size= %d\n",sizeof(romp)+sizeof(Prom));
|
|
printf("sizeof(miracl)= %d\n",sizeof(miracl));
|
|
#endif
|
|
|
|
ecurve_init(_MIPP_ A,B,p,MR_PROJECTIVE);
|
|
|
|
romptr=0;
|
|
init_point_from_rom(P,WORDS,Prom,PROMSZ,&romptr);
|
|
init_big_from_rom(Qx.a,WORDS,Prom,PROMSZ,&romptr);
|
|
init_big_from_rom(Qx.b,WORDS,Prom,PROMSZ,&romptr);
|
|
init_big_from_rom(Qy.a,WORDS,Prom,PROMSZ,&romptr);
|
|
init_big_from_rom(Qy.b,WORDS,Prom,PROMSZ,&romptr);
|
|
#ifdef MR_COUNT_OPS
|
|
fpa=fpc=fpx=0;
|
|
#endif
|
|
|
|
ecap(_MIPP_ &Qx,&Qy,P,T,fr,delta,&res);
|
|
/*
|
|
#ifdef MR_COUNT_OPS
|
|
printf("fpc= %d\n",fpc);
|
|
printf("fpa= %d\n",fpa);
|
|
printf("fpx= %d\n",fpx);
|
|
|
|
fpa=fpc=fpx=0;
|
|
#endif
|
|
*/
|
|
bigbits(_MIPP_ 160,t);
|
|
|
|
zzn2_powl(_MIPP_ &res,t,&res);
|
|
|
|
#ifndef MR_NO_STANDARD_IO
|
|
zzn2_out(_MIPP_ "res= ",&res);
|
|
#endif
|
|
|
|
ecurve_mult(_MIPP_ t,P,P);
|
|
|
|
ecap(_MIPP_ &Qx,&Qy,P,T,fr,delta,&res);
|
|
|
|
#ifndef MR_NO_STANDARD_IO
|
|
zzn2_out(_MIPP_ "res= ",&res);
|
|
#endif
|
|
|
|
#ifndef MR_STATIC
|
|
memkill(_MIPP_ mem,14);
|
|
ecp_memkill(_MIPP_ mem1,1);
|
|
#else
|
|
memset(mem,0,MR_BIG_RESERVE(14)); /* clear this stack memory */
|
|
memset(mem1,0,MR_ECP_RESERVE(1));
|
|
#endif
|
|
return 0;
|
|
}
|
|
|
|
|