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openssl/demos/jpake/jpakedemo.c
Ben Laurie 3b668eedda Minor clarity enhancements.
2008-10-26 15:37:31 +00:00

470 lines
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#include "openssl/bn.h"
#include "openssl/sha.h"
#include <assert.h>
#include <string.h>
#include <stdlib.h>
/* Copyright (C) 2008 Ben Laurie (ben@links.org) */
/*
* Implement J-PAKE, as described in
* http://grouper.ieee.org/groups/1363/Research/contributions/hao-ryan-2008.pdf
*
* With hints from http://www.cl.cam.ac.uk/~fh240/software/JPAKE2.java.
*/
static void showbn(const char *name, const BIGNUM *bn)
{
fputs(name, stdout);
fputs(" = ", stdout);
BN_print_fp(stdout, bn);
putc('\n', stdout);
}
typedef struct
{
BN_CTX *ctx; // Perhaps not the best place for this?
BIGNUM *p;
BIGNUM *q;
BIGNUM *g;
} JPakeParameters;
static void JPakeParametersInit(JPakeParameters *params)
{
params->ctx = BN_CTX_new();
// For now use p, q, g from Java sample code. Later, generate them.
params->p = NULL;
BN_hex2bn(&params->p, "fd7f53811d75122952df4a9c2eece4e7f611b7523cef4400c31e3f80b6512669455d402251fb593d8d58fabfc5f5ba30f6cb9b556cd7813b801d346ff26660b76b9950a5a49f9fe8047b1022c24fbba9d7feb7c61bf83b57e7c6a8a6150f04fb83f6d3c51ec3023554135a169132f675f3ae2b61d72aeff22203199dd14801c7");
params->q = NULL;
BN_hex2bn(&params->q, "9760508f15230bccb292b982a2eb840bf0581cf5");
params->g = NULL;
BN_hex2bn(&params->g, "f7e1a085d69b3ddecbbcab5c36b857b97994afbbfa3aea82f9574c0b3d0782675159578ebad4594fe67107108180b449167123e84c281613b7cf09328cc8a6e13c167a8b547c8d28e0a3ae1e2bb3a675916ea37f0bfa213562f1fb627a01243bcca4f1bea8519089a883dfe15ae59f06928b665e807b552564014c3bfecf492a");
showbn("p", params->p);
showbn("q", params->q);
showbn("g", params->g);
}
typedef struct
{
BIGNUM *gr; // g^r (r random)
BIGNUM *b; // b = r - x*h, h=hash(g, g^r, g^x, name)
} JPakeZKP;
typedef struct
{
BIGNUM *gx; // g^x
JPakeZKP zkpx; // ZKP(x)
} JPakeStep1;
typedef struct
{
BIGNUM *X; // g^(xa + xc + xd) * xb * s
JPakeZKP zkpxbs; // ZKP(xb * s)
} JPakeStep2;
typedef struct
{
const char *name; // Must be unique
int base; // 1 for Alice, 3 for Bob. Only used for printing stuff.
JPakeStep1 s1c; // Alice's g^x3, ZKP(x3) or Bob's g^x1, ZKP(x1)
JPakeStep1 s1d; // Alice's g^x4, ZKP(x4) or Bob's g^x2, ZKP(x2)
JPakeStep2 s2; // Alice's A, ZKP(x2 * s) or Bob's B, ZKP(x4 * s)
} JPakeUserPublic;
/*
* The user structure. In the definition, (xa, xb, xc, xd) are Alice's
* (x1, x2, x3, x4) or Bob's (x3, x4, x1, x2). If you see what I mean.
*/
typedef struct
{
JPakeUserPublic p;
BIGNUM *secret; // The shared secret
BIGNUM *key; // The calculated (shared) key
BIGNUM *xa; // Alice's x1 or Bob's x3
BIGNUM *xb; // Alice's x2 or Bob's x4
} JPakeUser;
// Generate each party's random numbers. xa is in [0, q), xb is in [1, q).
static void genrand(JPakeUser *user, const JPakeParameters *params)
{
BIGNUM *qm1;
// xa in [0, q)
user->xa = BN_new();
BN_rand_range(user->xa, params->q);
// q-1
qm1 = BN_new();
BN_copy(qm1, params->q);
BN_sub_word(qm1, 1);
// ... and xb in [0, q-1)
user->xb = BN_new();
BN_rand_range(user->xb, qm1);
// [1, q)
BN_add_word(user->xb, 1);
// cleanup
BN_free(qm1);
// Show
printf("x%d", user->p.base);
showbn("", user->xa);
printf("x%d", user->p.base+1);
showbn("", user->xb);
}
static void hashlength(SHA_CTX *sha, size_t l)
{
unsigned char b[2];
assert(l <= 0xffff);
b[0] = l >> 8;
b[1] = l&0xff;
SHA1_Update(sha, b, 2);
}
static void hashstring(SHA_CTX *sha, const char *string)
{
size_t l = strlen(string);
hashlength(sha, l);
SHA1_Update(sha, string, l);
}
static void hashbn(SHA_CTX *sha, const BIGNUM *bn)
{
size_t l = BN_num_bytes(bn);
unsigned char *bin = alloca(l);
hashlength(sha, l);
BN_bn2bin(bn, bin);
SHA1_Update(sha, bin, l);
}
// h=hash(g, g^r, g^x, name)
static void zkpHash(BIGNUM *h, const JPakeZKP *zkp, const BIGNUM *gx,
const JPakeUserPublic *from, const JPakeParameters *params)
{
unsigned char md[SHA_DIGEST_LENGTH];
SHA_CTX sha;
// XXX: hash should not allow moving of the boundaries - Java code
// is flawed in this respect. Length encoding seems simplest.
SHA1_Init(&sha);
hashbn(&sha, params->g);
hashbn(&sha, zkp->gr);
hashbn(&sha, gx);
hashstring(&sha, from->name);
SHA1_Final(md, &sha);
BN_bin2bn(md, SHA_DIGEST_LENGTH, h);
}
// Prove knowledge of x
// Note that we don't send g^x because, as it happens, we've always
// sent it elsewhere. Also note that because of that, we could avoid
// calculating it here, but we don't, for clarity...
static void CreateZKP(JPakeZKP *zkp, const BIGNUM *x, const JPakeUser *us,
const BIGNUM *zkpg, const JPakeParameters *params,
int n, const char *suffix)
{
BIGNUM *r = BN_new();
BIGNUM *gx = BN_new();
BIGNUM *h = BN_new();
BIGNUM *t = BN_new();
// r in [0,q)
// XXX: Java chooses r in [0, 2^160) - i.e. distribution not uniform
BN_rand_range(r, params->q);
// g^r
zkp->gr = BN_new();
BN_mod_exp(zkp->gr, zkpg, r, params->p, params->ctx);
// g^x
BN_mod_exp(gx, zkpg, x, params->p, params->ctx);
// h=hash...
zkpHash(h, zkp, gx, &us->p, params);
// b = r - x*h
BN_mod_mul(t, x, h, params->q, params->ctx);
zkp->b = BN_new();
BN_mod_sub(zkp->b, r, t, params->q, params->ctx);
// show
printf(" ZKP(x%d%s)\n", n, suffix);
showbn(" zkpg", zkpg);
showbn(" g^x", gx);
showbn(" g^r", zkp->gr);
showbn(" b", zkp->b);
// cleanup
BN_free(t);
BN_free(h);
BN_free(gx);
BN_free(r);
}
static int VerifyZKP(const JPakeZKP *zkp, BIGNUM *gx,
const JPakeUserPublic *them, const BIGNUM *zkpg,
const JPakeParameters *params, int n, const char *suffix)
{
BIGNUM *h = BN_new();
BIGNUM *t1 = BN_new();
BIGNUM *t2 = BN_new();
BIGNUM *t3 = BN_new();
int ret = 0;
zkpHash(h, zkp, gx, them, params);
// t1 = g^b
BN_mod_exp(t1, zkpg, zkp->b, params->p, params->ctx);
// t2 = (g^x)^h = g^{hx}
BN_mod_exp(t2, gx, h, params->p, params->ctx);
// t3 = t1 * t2 = g^{hx} * g^b = g^{hx+b} = g^r (allegedly)
BN_mod_mul(t3, t1, t2, params->p, params->ctx);
printf(" ZKP(x%d%s)\n", n, suffix);
showbn(" zkpg", zkpg);
showbn(" g^r'", t3);
// verify t3 == g^r
if(BN_cmp(t3, zkp->gr) == 0)
ret = 1;
// cleanup
BN_free(t3);
BN_free(t2);
BN_free(t1);
BN_free(h);
if(ret)
puts(" OK");
else
puts(" FAIL");
return ret;
}
static void sendstep1_substep(JPakeStep1 *s1, const BIGNUM *x,
const JPakeUser *us,
const JPakeParameters *params, int n)
{
s1->gx = BN_new();
BN_mod_exp(s1->gx, params->g, x, params->p, params->ctx);
printf(" g^{x%d}", n);
showbn("", s1->gx);
CreateZKP(&s1->zkpx, x, us, params->g, params, n, "");
}
static void sendstep1(const JPakeUser *us, JPakeUserPublic *them,
const JPakeParameters *params)
{
printf("\n%s sends %s:\n\n", us->p.name, them->name);
// from's g^xa (which becomes to's g^xc) and ZKP(xa)
sendstep1_substep(&them->s1c, us->xa, us, params, us->p.base);
// from's g^xb (which becomes to's g^xd) and ZKP(xb)
sendstep1_substep(&them->s1d, us->xb, us, params, us->p.base+1);
}
static int verifystep1(const JPakeUser *us, const JPakeUserPublic *them,
const JPakeParameters *params)
{
printf("\n%s verifies %s:\n\n", us->p.name, them->name);
// verify their ZKP(xc)
if(!VerifyZKP(&us->p.s1c.zkpx, us->p.s1c.gx, them, params->g, params,
them->base, ""))
return 0;
// verify their ZKP(xd)
if(!VerifyZKP(&us->p.s1d.zkpx, us->p.s1d.gx, them, params->g, params,
them->base+1, ""))
return 0;
// g^xd != 1
printf(" g^{x%d} != 1: ", them->base+1);
if(BN_is_one(us->p.s1d.gx))
{
puts("FAIL");
return 0;
}
puts("OK");
return 1;
}
static void sendstep2(const JPakeUser *us, JPakeUserPublic *them,
const JPakeParameters *params)
{
BIGNUM *t1 = BN_new();
BIGNUM *t2 = BN_new();
printf("\n%s sends %s:\n\n", us->p.name, them->name);
// X = g^{(xa + xc + xd) * xb * s}
// t1 = g^xa
BN_mod_exp(t1, params->g, us->xa, params->p, params->ctx);
// t2 = t1 * g^{xc} = g^{xa} * g^{xc} = g^{xa + xc}
BN_mod_mul(t2, t1, us->p.s1c.gx, params->p, params->ctx);
// t1 = t2 * g^{xd} = g^{xa + xc + xd}
BN_mod_mul(t1, t2, us->p.s1d.gx, params->p, params->ctx);
// t2 = xb * s
BN_mod_mul(t2, us->xb, us->secret, params->q, params->ctx);
// X = t1^{t2} = t1^{xb * s} = g^{(xa + xc + xd) * xb * s}
them->s2.X = BN_new();
BN_mod_exp(them->s2.X, t1, t2, params->p, params->ctx);
// Show
printf(" g^{(x%d + x%d + x%d) * x%d * s)", us->p.base, them->base,
them->base+1, us->p.base+1);
showbn("", them->s2.X);
// ZKP(xb * s)
// XXX: this is kinda funky, because we're using
//
// g' = g^{xa + xc + xd}
//
// as the generator, which means X is g'^{xb * s}
CreateZKP(&them->s2.zkpxbs, t2, us, t1, params, us->p.base+1, " * s");
// cleanup
BN_free(t1);
BN_free(t2);
}
static int verifystep2(const JPakeUser *us, const JPakeUserPublic *them,
const JPakeParameters *params)
{
BIGNUM *t1 = BN_new();
BIGNUM *t2 = BN_new();
int ret = 0;
printf("\n%s verifies %s:\n\n", us->p.name, them->name);
// g' = g^{xc + xa + xb} [from our POV]
// t1 = xa + xb
BN_mod_add(t1, us->xa, us->xb, params->q, params->ctx);
// t2 = g^{t1} = g^{xa+xb}
BN_mod_exp(t2, params->g, t1, params->p, params->ctx);
// t1 = g^{xc} * t2 = g^{xc + xa + xb}
BN_mod_mul(t1, us->p.s1c.gx, t2, params->p, params->ctx);
if(VerifyZKP(&us->p.s2.zkpxbs, us->p.s2.X, them, t1, params, them->base+1,
" * s"))
ret = 1;
// cleanup
BN_free(t2);
BN_free(t1);
return ret;
}
static void computekey(JPakeUser *us, const JPakeParameters *params)
{
BIGNUM *t1 = BN_new();
BIGNUM *t2 = BN_new();
BIGNUM *t3 = BN_new();
printf("\n%s calculates the shared key:\n\n", us->p.name);
// K = (X/g^{xb * xd * s})^{xb}
// = (g^{(xc + xa + xb) * xd * s - xb * xd *s})^{xb}
// = (g^{(xa + xc) * xd * s})^{xb}
// = g^{(xa + xc) * xb * xd * s}
// [which is the same regardless of who calculates it]
// t1 = (g^{xd})^{xb} = g^{xb * xd}
BN_mod_exp(t1, us->p.s1d.gx, us->xb, params->p, params->ctx);
// t2 = -s = q-s
BN_sub(t2, params->q, us->secret);
// t3 = t1^t2 = g^{-xb * xd * s}
BN_mod_exp(t3, t1, t2, params->p, params->ctx);
// t1 = X * t3 = X/g^{xb * xd * s}
BN_mod_mul(t1, us->p.s2.X, t3, params->p, params->ctx);
// K = t1^{xb}
us->key = BN_new();
BN_mod_exp(us->key, t1, us->xb, params->p, params->ctx);
// show
showbn(" K", us->key);
// cleanup
BN_free(t3);
BN_free(t2);
BN_free(t1);
}
int main(int argc, char **argv)
{
JPakeParameters params;
JPakeUser alice, bob;
alice.p.name = "Alice";
alice.p.base = 1;
bob.p.name = "Bob";
bob.p.base = 3;
JPakeParametersInit(&params);
// Shared secret
alice.secret = BN_new();
BN_rand(alice.secret, 32, -1, 0);
bob.secret = alice.secret;
showbn("secret", alice.secret);
assert(BN_cmp(alice.secret, params.q) < 0);
// Alice's x1, x2
genrand(&alice, &params);
// Bob's x3, x4
genrand(&bob, &params);
// Now send stuff to each other...
sendstep1(&alice, &bob.p, &params);
sendstep1(&bob, &alice.p, &params);
// And verify what each other sent
if(!verifystep1(&alice, &bob.p, &params))
return 1;
if(!verifystep1(&bob, &alice.p, &params))
return 2;
// Second send
sendstep2(&alice, &bob.p, &params);
sendstep2(&bob, &alice.p, &params);
// And second verify
if(!verifystep2(&alice, &bob.p, &params))
return 3;
if(!verifystep2(&bob, &alice.p, &params))
return 4;
// Compute common key
computekey(&alice, &params);
computekey(&bob, &params);
// Confirm the common key is identical
// XXX: if the two secrets are not the same, everything works up
// to this point, so the only way to detect a failure is by the
// difference in the calculated keys.
// Since we're all the same code, just compare them directly. In a
// real system, Alice sends Bob H(H(K)), Bob checks it, then sends
// back H(K), which Alice checks, or something equivalent.
puts("\nAlice and Bob check keys are the same:");
if(BN_cmp(alice.key, bob.key) == 0)
puts(" OK");
else
{
puts(" FAIL");
return 5;
}
return 0;
}
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