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crashtest-r0ket/firmware/basic/ecc.c

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/*
This program implements the ECIES public key encryption scheme based on the
NIST B163 elliptic curve and the XTEA block cipher. The code was written
as an accompaniment for an article published in phrack #63 and is released to
the public domain.
Original author: Phrack Staff
Ported to ARM7TDMI: Jiri Pittner <jiri@pittnerovi.com>
compiled by arm-elf-gcc (GCC) 4.0.1 and tested on LPC2106
*/
#include <stdlib.h>
#include <string.h>
#include <stdio.h>
#include <stdint.h>
#include "ecc.h"
exp_t base_order;
elem_t poly; /* the reduction polynomial */
elem_t coeff_b, base_x, base_y;
static int xrandm=100000000;
static int xrandm1=10000;
static int xrandb1=51723621;
int xmult(int p,int q)
{
int p1,p0,q1,q0;
p1=p/xrandm1; p0=p%xrandm1;
q1=q/xrandm1; q0=q%xrandm1;
return (((p0*q1+p1*q0)%xrandm1)*xrandm1+p0*q0)%xrandm;
}
unsigned char rnd1()
{
static int a=123456789;
a = (xmult(a,xrandb1)+1)%xrandm;
return a & 0xff;
}
#define MACRO(A) do { A; } while(0)
#define MIN(a, b) ((a) < (b) ? (a) : (b))
//compiles to a quite reasonable assembly code
//void INT2CHARS (unsigned char *ptr, uint32_t val)
void INT2CHARS (char *ptr, uint32_t val)
{
*ptr++ =val; val>>=8;
*ptr++ =val; val>>=8;
*ptr++ =val; val>>=8;
*ptr++ =val;
}
//uint32_t CHARS2INT(const unsigned char *ptr)
uint32_t CHARS2INT(const char *ptr)
{
uint32_t r;
ptr+=3;
r=*ptr--; r<<=8;
r|=*ptr--; r<<=8;
r|=*ptr--; r<<=8;
r|=*ptr--;
return r;
}
/* some basic bit-manipulation routines that act on these vectors follow */
#define bitstr_getbit(A, idx) ((A[(idx) / 32] >> ((idx) % 32)) & 1)
#define bitstr_setbit(A, idx) MACRO( A[(idx) / 32] |= 1 << ((idx) % 32) )
#define bitstr_clrbit(A, idx) MACRO( A[(idx) / 32] &= ~(1 << ((idx) % 32)) )
#define bitstr_clear(A) MACRO( memset(A, 0, sizeof(bitstr_t)) )
#define bitstr_copy(A, B) MACRO( memcpy(A, B, sizeof(bitstr_t)) )
#define bitstr_swap(A, B) MACRO( bitstr_t h; \
bitstr_copy(h, A); bitstr_copy(A, B); bitstr_copy(B, h) )
#define bitstr_is_equal(A, B) (! memcmp(A, B, sizeof(bitstr_t)))
int bitstr_is_clear(const bitstr_t x)
{
int i;
for(i = 0; i < NUMWORDS && ! *x++; i++);
return i == NUMWORDS;
}
/* return the number of the highest one-bit + 1 */
int bitstr_sizeinbits(const bitstr_t x)
{
int i;
uint32_t mask;
for(x += NUMWORDS, i = 32 * NUMWORDS; i > 0 && ! *--x; i -= 32);
if (i)
for(mask = ((uint32_t) 1) << 31; ! (*x & mask); mask >>= 1, i--);
return i;
}
/* left-shift by 'count' digits */
void bitstr_lshift(bitstr_t A, const bitstr_t B, int count)
{
int i, offs = 4 * (count / 32);
memmove((void*)A + offs, B, sizeof(bitstr_t) - offs);
memset(A, 0, offs);
if (count %= 32) {
for(i = NUMWORDS - 1; i > 0; i--)
A[i] = (A[i] << count) | (A[i - 1] >> (32 - count));
A[0] <<= count;
}
}
/* (raw) import from a byte array */
void bitstr_import(bitstr_t x, const char *s)
{
int i;
for(x += NUMWORDS, i = 0; i < NUMWORDS; i++, s += 4)
*--x = CHARS2INT(s);
}
/* (raw) export to a byte array */
void bitstr_export(char *s, const bitstr_t x)
{
int i;
for(x += NUMWORDS, i = 0; i < NUMWORDS; i++, s += 4)
INT2CHARS(s, *--x);
}
/* export as hex string (null-terminated!) */
void bitstr_to_hex(char *s, const bitstr_t x)
{
int i;
for(x += NUMWORDS, i = 0; i < NUMWORDS; i++, s += 8)
siprintf(s, "%08lx", *--x);
}
uint8_t letter2bin (const char c)
{
return c>'9' ? c+10-(c>='a'?'a':'A') : c-'0';
}
uint8_t octet2bin(const char* octet)
{
return (letter2bin(octet[0])<<4) | letter2bin(octet[1]);
}
void bin2letter(char *c, uint8_t b)
{
*c = b<10? '0'+b : 'A'+b-10;
}
void bin2octet(char *octet, uint8_t bin)
{
bin2letter(octet,bin>>4);
bin2letter(octet+1,bin&0x0f);
}
uint32_t getword32(const char *s)
{
//little endian
union {uint32_t i; uint8_t c[sizeof(uint32_t)];} r;
r.c[3]=octet2bin(s);
r.c[2]=octet2bin(s+2);
r.c[1]=octet2bin(s+4);
r.c[0]=octet2bin(s+6);
return r.i;
}
/* import from a hex string */
int bitstr_parse(bitstr_t x, const char *s)
{
int len = strlen(s);
//if ((s[len = strspn(s, "0123456789abcdefABCDEF")]) ||
// (len > NUMWORDS * 8))
// return -1;
bitstr_clear(x);
x += len / 8;
if (len % 8) {
*x=getword32(s);
*x >>= 32 - 4 * (len % 8);
s += len % 8;
len &= ~7;
}
for(; *s; s += 8)
*--x = getword32(s);
return len;
}
int bitstr_parse_export(char *exp, const char *s)
{
bitstr_t x;
if( bitstr_parse(x, s) != -1 ){
bitstr_export(exp, x);
return 0;
}
return -1;
}
/******************************************************************************/
#define field_set1(A) MACRO( A[0] = 1; memset(A + 1, 0, sizeof(elem_t) - 4) )
int field_is1(const elem_t x)
{
int i;
if (*x++ != 1) return 0;
for(i = 1; i < NUMWORDS && ! *x++; i++);
return i == NUMWORDS;
}
void field_add(elem_t z, const elem_t x, const elem_t y) /* field addition */
{
int i;
for(i = 0; i < NUMWORDS; i++)
*z++ = *x++ ^ *y++;
}
#define field_add1(A) MACRO( A[0] ^= 1 )
/* field multiplication */
void field_mult(elem_t z, const elem_t x, const elem_t y)
{
elem_t b;
int i, j;
/* assert(z != y); */
bitstr_copy(b, x);
if (bitstr_getbit(y, 0))
bitstr_copy(z, x);
else
bitstr_clear(z);
for(i = 1; i < DEGREE; i++) {
for(j = NUMWORDS - 1; j > 0; j--)
b[j] = (b[j] << 1) | (b[j - 1] >> 31);
b[0] <<= 1;
if (bitstr_getbit(b, DEGREE))
field_add(b, b, poly);
if (bitstr_getbit(y, i))
field_add(z, z, b);
}
}
void field_invert(elem_t z, const elem_t x) /* field inversion */
{
elem_t u, v, g, h;
int i;
bitstr_copy(u, x);
bitstr_copy(v, poly);
bitstr_clear(g);
field_set1(z);
while (! field_is1(u)) {
i = bitstr_sizeinbits(u) - bitstr_sizeinbits(v);
if (i < 0) {
bitstr_swap(u, v); bitstr_swap(g, z); i = -i;
}
bitstr_lshift(h, v, i);
field_add(u, u, h);
bitstr_lshift(h, g, i);
field_add(z, z, h);
}
}
/******************************************************************************/
/* The following routines do the ECC arithmetic. Elliptic curve points
are represented by pairs (x,y) of elem_t. It is assumed that curve
coefficient 'a' is equal to 1 (this is the case for all NIST binary
curves). Coefficient 'b' is given in 'coeff_b'. '(base_x, base_y)'
is a point that generates a large prime order group. */
#define point_is_zero(x, y) (bitstr_is_clear(x) && bitstr_is_clear(y))
#define point_set_zero(x, y) MACRO( bitstr_clear(x); bitstr_clear(y) )
#define point_copy(x1, y1, x2, y2) MACRO( bitstr_copy(x1, x2); \
bitstr_copy(y1, y2) )
/* check if y^2 + x*y = x^3 + *x^2 + coeff_b holds */
int is_point_on_curve(const elem_t x, const elem_t y)
{
elem_t a, b;
if (point_is_zero(x, y))
return 1;
field_mult(a, x, x);
field_mult(b, a, x);
field_add(a, a, b);
field_add(a, a, coeff_b);
field_mult(b, y, y);
field_add(a, a, b);
field_mult(b, x, y);
return bitstr_is_equal(a, b);
}
void point_double(elem_t x, elem_t y) /* double the point (x,y) */
{
if (! bitstr_is_clear(x)) {
elem_t a;
field_invert(a, x);
field_mult(a, a, y);
field_add(a, a, x);
field_mult(y, x, x);
field_mult(x, a, a);
field_add1(a);
field_add(x, x, a);
field_mult(a, a, x);
field_add(y, y, a);
}
else
bitstr_clear(y);
}
/* add two points together (x1, y1) := (x1, y1) + (x2, y2) */
void point_add(elem_t x1, elem_t y1, const elem_t x2, const elem_t y2)
{
if (! point_is_zero(x2, y2)) {
if (point_is_zero(x1, y1))
point_copy(x1, y1, x2, y2);
else {
if (bitstr_is_equal(x1, x2)) {
if (bitstr_is_equal(y1, y2))
point_double(x1, y1);
else
point_set_zero(x1, y1);
}
else {
elem_t a, b, c, d;
field_add(a, y1, y2);
field_add(b, x1, x2);
field_invert(c, b);
field_mult(c, c, a);
field_mult(d, c, c);
field_add(d, d, c);
field_add(d, d, b);
field_add1(d);
field_add(x1, x1, d);
field_mult(a, x1, c);
field_add(a, a, d);
field_add(y1, y1, a);
bitstr_copy(x1, d);
}
}
}
}
/******************************************************************************/
/* point multiplication via double-and-add algorithm */
void point_mult(elem_t x, elem_t y, const exp_t exp)
{
elem_t X, Y;
int i;
point_set_zero(X, Y);
for(i = bitstr_sizeinbits(exp) - 1; i >= 0; i--) {
point_double(X, Y);
if (bitstr_getbit(exp, i))
point_add(X, Y, x, y);
}
point_copy(x, y, X, Y);
}
/* draw a random value 'exp' with 1 <= exp < n */
//@@@ Make a HARDWARE randomness generator with ARM, at the moment just a simple pseudorandom replacement
void get_random_exponent(exp_t exp)
{
char buf[4 * NUMWORDS];
int r ;
do {
for(r=0; r<4 * NUMWORDS; ++r)
{
buf[r]= rnd1();
}
bitstr_import(exp, buf);
for(r = bitstr_sizeinbits(base_order) - 1; r < NUMWORDS * 32; r++)
bitstr_clrbit(exp, r);
} while(bitstr_is_clear(exp));
}
/******************************************************************************/
void XTEA_init_key(uint32_t *k, const char *key)
{
k[0] = CHARS2INT(key + 0); k[1] = CHARS2INT(key + 4);
k[2] = CHARS2INT(key + 8); k[3] = CHARS2INT(key + 12);
}
/* the XTEA block cipher */
void XTEA_encipher_block(char *data, const uint32_t *k)
{
uint32_t sum = 0, delta = 0x9e3779b9, y, z;
int i;
y = CHARS2INT(data); z = CHARS2INT(data + 4);
for(i = 0; i < 32; i++) {
y += ((z << 4 ^ z >> 5) + z) ^ (sum + k[sum & 3]);
sum += delta;
z += ((y << 4 ^ y >> 5) + y) ^ (sum + k[(sum >> 11) & 3]);
}
INT2CHARS(data, y); INT2CHARS(data + 4, z);
}
/* encrypt in CTR mode */
void XTEA_ctr_crypt(char *data, int size, const char *key)
{
uint32_t k[4], ctr = 0;
int len, i;
char buf[8];
XTEA_init_key(k, key);
while(size) {
INT2CHARS(buf, 0); INT2CHARS(buf + 4, ctr++);
XTEA_encipher_block(buf, k);
len = MIN(8, size);
for(i = 0; i < len; i++)
*data++ ^= buf[i];
size -= len;
}
}
/* calculate the CBC MAC */
void XTEA_cbcmac(char *mac, const char *data, int size, const char *key)
{
uint32_t k[4];
int len, i;
XTEA_init_key(k, key);
INT2CHARS(mac, 0L);
INT2CHARS(mac + 4, size);
XTEA_encipher_block(mac, k);
while(size) {
len = MIN(8, size);
for(i = 0; i < len; i++)
mac[i] ^= *data++;
XTEA_encipher_block(mac, k);
size -= len;
}
}
/* modified(!) Davies-Meyer construction.*/
void XTEA_davies_meyer(char *out, const char *in, int ilen)
{
uint32_t k[4];
char buf[8];
int i;
memset(out, 0, 8);
while(ilen--) {
XTEA_init_key(k, in);
memcpy(buf, out, 8);
XTEA_encipher_block(buf, k);
for(i = 0; i < 8; i++)
out[i] ^= buf[i];
in += 16;
}
}
/******************************************************************************/
#if 0
void ECIES_generate_key_pair(void) /* generate a public/private key pair */
{
char buf[8 * NUMWORDS + 1]; *bufptr = buf + NUMWORDS * 8 - (DEGREE + 3) / 4;
elem_t x, y;
exp_t k;
get_random_exponent(k);
point_copy(x, y, base_x, base_y);
point_mult(x, y, k);
/*
uart0Puts("Here is your new public/private key pair:\n");
bitstr_to_hex(buf, x); uart0Puts("Public key: "); uart0Puts(bufptr); uart0Putch(':');
bitstr_to_hex(buf, y); uart0Puts(bufptr);
bitstr_to_hex(buf, k); uart0Puts("\nPrivate key: "); uart0Puts(bufptr); uart0Putch('\n');
*/
}
#endif
/* check that a given elem_t-pair is a valid point on the curve != 'o' */
int ECIES_embedded_public_key_validation(const elem_t Px, const elem_t Py)
{
return (bitstr_sizeinbits(Px) > DEGREE) || (bitstr_sizeinbits(Py) > DEGREE) ||
point_is_zero(Px, Py) || ! is_point_on_curve(Px, Py) ? -1 : 1;
}
/* same thing, but check also that (Px,Py) generates a group of order n */
int ECIES_public_key_validation(const char *Px, const char *Py)
{
elem_t x, y;
if ((bitstr_parse(x, Px) < 0) || (bitstr_parse(y, Py) < 0))
return -1;
if (ECIES_embedded_public_key_validation(x, y) < 0)
return -1;
point_mult(x, y, base_order);
return point_is_zero(x, y) ? 1 : -1;
}
void ECIES_kdf(char *k1, char *k2, const elem_t Zx, /* a non-standard KDF */
const elem_t Rx, const elem_t Ry)
{
int bufsize = (3 * (4 * NUMWORDS) + 1 + 15) & ~15;
char buf[bufsize];
memset(buf, 0, bufsize);
bitstr_export(buf, Zx);
bitstr_export(buf + 4 * NUMWORDS, Rx);
bitstr_export(buf + 8 * NUMWORDS, Ry);
buf[12 * NUMWORDS] = 0; XTEA_davies_meyer(k1, buf, bufsize / 16);
buf[12 * NUMWORDS] = 1; XTEA_davies_meyer(k1 + 8, buf, bufsize / 16);
buf[12 * NUMWORDS] = 2; XTEA_davies_meyer(k2, buf, bufsize / 16);
buf[12 * NUMWORDS] = 3; XTEA_davies_meyer(k2 + 8, buf, bufsize / 16);
}
void ECIES_encyptkeygen(uint8_t *px, uint8_t *py,
uint8_t k1[16], uint8_t k2[16], uint8_t *Rx_exp, uint8_t *Ry_exp)
{
elem_t Rx, Ry, Zx, Zy;
exp_t k;
do {
get_random_exponent(k);
bitstr_import(Zx, (char*)px);
bitstr_import(Zy, (char*)py);
point_mult(Zx, Zy, k);
point_double(Zx, Zy); /* cofactor h = 2 on B163 */
} while(point_is_zero(Zx, Zy));
point_copy(Rx, Ry, base_x, base_y);
point_mult(Rx, Ry, k);
ECIES_kdf((char *)k1,(char *) k2, Zx, Rx, Ry);
bitstr_export((char*)Rx_exp, Rx);
bitstr_export((char*)Ry_exp, Ry);
}
int ECIES_decryptkeygen(uint8_t *rx, uint8_t *ry,
uint8_t k1[16], uint8_t k2[16], const char *privkey)
{
elem_t Rx, Ry, Zx, Zy;
exp_t d;
bitstr_import(Rx, (char*)rx);
bitstr_import(Ry, (char*)ry);
if (ECIES_embedded_public_key_validation(Rx, Ry) < 0)
return -1;
bitstr_parse(d, privkey);
point_copy(Zx, Zy, Rx, Ry);
point_mult(Zx, Zy, d);
point_double(Zx, Zy); /* cofactor h = 2 on B163 */
if (point_is_zero(Zx, Zy))
return -1;
ECIES_kdf((char*)k1,(char*) k2, Zx, Rx, Ry);
return 0;
}
void ECIES_setup(void)
{
bitstr_parse(poly, "800000000000000000000000000000000000000c9");
bitstr_parse(coeff_b, "20a601907b8c953ca1481eb10512f78744a3205fd");
bitstr_parse(base_x, "3f0eba16286a2d57ea0991168d4994637e8343e36");
bitstr_parse(base_y, "0d51fbc6c71a0094fa2cdd545b11c5c0c797324f1");
bitstr_parse(base_order, "40000000000000000000292fe77e70c12a4234c33");
}
#define ECIES_OVERHEAD (8 * NUMWORDS + 8)
/* ECIES encryption; the resulting cipher text message will be
(len + ECIES_OVERHEAD) bytes long */
void ECIES_encryption(char *msg, const char *text, int len,
const char *Px, const char *Py)
{
elem_t Rx, Ry, Zx, Zy;
char k1[16], k2[16];
exp_t k;
//memset(msg,0,len+ECIES_OVERHEAD); //in the case buffer was not clean
do {
get_random_exponent(k);
bitstr_parse(Zx, Px);
bitstr_parse(Zy, Py);
point_mult(Zx, Zy, k);
point_double(Zx, Zy); /* cofactor h = 2 on B163 */
} while(point_is_zero(Zx, Zy));
point_copy(Rx, Ry, base_x, base_y);
point_mult(Rx, Ry, k);
ECIES_kdf(k1, k2, Zx, Rx, Ry);
bitstr_export(msg, Rx);
bitstr_export(msg + 4 * NUMWORDS, Ry);
memcpy(msg + 8 * NUMWORDS, text, len);
XTEA_ctr_crypt(msg + 8 * NUMWORDS, len, k1);
XTEA_cbcmac(msg + 8 * NUMWORDS + len, msg + 8 * NUMWORDS, len, k2);
}
/* ECIES decryption */
int ECIES_decryption(char *text, const char *msg, int len,
const char *privkey)
{
elem_t Rx, Ry, Zx, Zy;
char k1[16], k2[16], mac[8];
exp_t d;
bitstr_import(Rx, msg);
bitstr_import(Ry, msg + 4 * NUMWORDS);
if (ECIES_embedded_public_key_validation(Rx, Ry) < 0)
return -1;
bitstr_parse(d, privkey);
point_copy(Zx, Zy, Rx, Ry);
point_mult(Zx, Zy, d);
point_double(Zx, Zy); /* cofactor h = 2 on B163 */
if (point_is_zero(Zx, Zy))
return -1;
ECIES_kdf(k1, k2, Zx, Rx, Ry);
XTEA_cbcmac(mac, msg + 8 * NUMWORDS, len, k2);
if (memcmp(mac, msg + 8 * NUMWORDS + len, 8))
return -1;
memcpy(text, msg + 8 * NUMWORDS, len);
XTEA_ctr_crypt(text, len, k1);
return 1;
}
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