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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"
#include "random.h"
elem_t poly = {0x8, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x000000c9};
//bitstr (poly, "8 00000000 00000000 00000000 00000000 000000c9");
elem_t coeff_b = {0x2, 0x0a601907, 0xb8c953ca, 0x1481eb10, 0x512f7874, 0x4a3205fd};
//bitstr (coeff_b," 2 0a601907 b8c953ca 1481eb10 512f7874 4a3205fd");
elem_t base_x = {0x3, 0xf0eba162, 0x86a2d57e, 0xa0991168, 0xd4994637, 0xe8343e36};
// bitstr_parse(base_x, "3f0eba16286a2d57ea0991168d4994637e8343e36");
elem_t base_y = {0x0, 0xd51fbc6c, 0x71a0094f, 0xa2cdd545, 0xb11c5c0c, 0x797324f1};
// bitstr_parse(base_y, "0d51fbc6c71a0094fa2cdd545b11c5c0c797324f1");
elem_t base_order = {0x4, 0x00000000, 0x00000000, 0x000292fe, 0x77e70c12, 0xa4234c33};
//bitstr_parse(base_order, "40000000000000000000292fe77e70c12a4234c33");
static unsigned char rnd1()
{
return getRandom() & 0xFF;
}
//compiles to a quite reasonable assembly code
//void INT2CHARS (unsigned char *ptr, uint32_t val)
static 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)
static 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;
}
static 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 */
static 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 */
static 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 */
static 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 */
static 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!) */
static 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);
}
static uint8_t letter2bin (const char c)
{
return c>'9' ? c+10-(c>='a'?'a':'A') : c-'0';
}
static uint8_t octet2bin(const char* octet)
{
return (letter2bin(octet[0])<<4) | letter2bin(octet[1]);
}
static void bin2letter(char *c, uint8_t b)
{
*c = b<10? '0'+b : 'A'+b-10;
}
static void bin2octet(char *octet, uint8_t bin)
{
bin2letter(octet,bin>>4);
bin2letter(octet+1,bin&0x0f);
}
static 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 */
static 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;
}
/******************************************************************************/
static int field_is1(const elem_t x)
{
int i;
if (*x++ != 1) return 0;
for(i = 1; i < NUMWORDS && ! *x++; i++);
return i == NUMWORDS;
}
static 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 */
static 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);
}
}
static 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. */
/* check if y^2 + x*y = x^3 + *x^2 + coeff_b holds */
static 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);
}
static 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) */
static 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 */
static 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
static 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));
}
/******************************************************************************/
static 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 */
static 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 */
static 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 */
static 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.*/
static 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' */
static 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 */
static 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;
}
static 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;
}
#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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