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
{
- const char *name; // Must be unique
- int base; // 1 for Alice, 3 for Bob. Only used for printing stuff.
+ 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
- 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)
} JPakeUser;
// Generate each party's random numbers. xa is in [0, q), xb is in [1, q).
BN_free(qm1);
// Show
- printf("x%d", user->base);
+ printf("x%d", user->p.base);
showbn("", user->xa);
- printf("x%d", user->base+1);
+ printf("x%d", user->p.base+1);
showbn("", user->xb);
}
// h=hash(g, g^r, g^x, name)
static void zkpHash(BIGNUM *h, const JPakeZKP *zkp, const BIGNUM *gx,
- const JPakeUser *from, const JPakeParameters *params)
+ const JPakeUserPublic *from, const JPakeParameters *params)
{
unsigned char md[SHA_DIGEST_LENGTH];
SHA_CTX sha;
BN_mod_exp(gx, zkpg, x, params->p, params->ctx);
// h=hash...
- zkpHash(h, zkp, gx, us, params);
+ zkpHash(h, zkp, gx, &us->p, params);
// b = r - x*h
BN_mod_mul(t, x, h, params->q, params->ctx);
BN_free(r);
}
-static int VerifyZKP(const JPakeZKP *zkp, BIGNUM *x, const JPakeUser *them,
- const BIGNUM *zkpg, const JPakeParameters *params,
- int n, const char *suffix)
+static int VerifyZKP(const JPakeZKP *zkp, BIGNUM *x,
+ const JPakeUserPublic *them, const BIGNUM *zkpg,
+ const JPakeParameters *params, int n, const char *suffix)
{
BIGNUM *h = BN_new();
BIGNUM *t1 = BN_new();
CreateZKP(&s1->zkpx, x, us, params->g, params, n, "");
}
-static void sendstep1(const JPakeUser *us, JPakeUser *them,
+static void sendstep1(const JPakeUser *us, JPakeUserPublic *them,
const JPakeParameters *params)
{
- printf("\n%s sends %s:\n\n", us->name, them->name);
+ 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->base);
+ 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->base+1);
+ sendstep1_substep(&them->s1d, us->xb, us, params, us->p.base+1);
}
-static int verifystep1(const JPakeUser *us, const JPakeUser *them,
+static int verifystep1(const JPakeUser *us, const JPakeUserPublic *them,
const JPakeParameters *params)
{
- printf("\n%s verifies %s:\n\n", us->name, them->name);
+ printf("\n%s verifies %s:\n\n", us->p.name, them->name);
// verify their ZKP(xc)
- if(!VerifyZKP(&us->s1c.zkpx, us->s1c.gx, them, params->g, params,
+ 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->s1d.zkpx, us->s1d.gx, them, params->g, params,
+ 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->s1d.gx))
+ if(BN_is_one(us->p.s1d.gx))
{
puts("FAIL");
return 0;
return 1;
}
-static void sendstep2(const JPakeUser *us, JPakeUser *them,
+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->name, them->name);
+ 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->s1c.gx, params->p, params->ctx);
+ 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->s1d.gx, params->p, params->ctx);
+ 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}
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->base, them->base,
- them->base+1, us->base+1);
+ 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)
//
// g' = g^{xa + xc + xd}
//
- // as the generator, which means B is g'^{xb * s}
- CreateZKP(&them->s2.zkpxbs, t2, us, t1, params, us->base+1, " * s");
+ // 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 JPakeUser *them,
+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->name, them->name);
+ printf("\n%s verifies %s:\n\n", us->p.name, them->name);
// g' = g^{xc + xa + xb} [from our POV]
// t1 = xa + xb
// 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->s1c.gx, t2, params->p, params->ctx);
+ BN_mod_mul(t1, us->p.s1c.gx, t2, params->p, params->ctx);
- if(VerifyZKP(&us->s2.zkpxbs, us->s2.X, them, t1, params, them->base+1,
+ if(VerifyZKP(&us->p.s2.zkpxbs, us->p.s2.X, them, t1, params, them->base+1,
" * s"))
ret = 1;
BIGNUM *t2 = BN_new();
BIGNUM *t3 = BN_new();
- printf("\n%s calculates the shared key:\n\n", us->name);
+ 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}
// [which is the same regardless of who calculates it]
// t1 = (g^{xd})^{xb} = g^{xb * xd}
- BN_mod_exp(t1, us->s1d.gx, us->xb, params->p, params->ctx);
+ 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->s2.X, t3, params->p, params->ctx);
+ 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);
JPakeParameters params;
JPakeUser alice, bob;
- alice.name = "Alice";
- alice.base = 1;
- bob.name = "Bob";
- bob.base = 3;
+ alice.p.name = "Alice";
+ alice.p.base = 1;
+ bob.p.name = "Bob";
+ bob.p.base = 3;
JPakeParametersInit(¶ms);
genrand(&bob, ¶ms);
// Now send stuff to each other...
- sendstep1(&alice, &bob, ¶ms);
- sendstep1(&bob, &alice, ¶ms);
+ sendstep1(&alice, &bob.p, ¶ms);
+ sendstep1(&bob, &alice.p, ¶ms);
// And verify what each other sent
- if(!verifystep1(&alice, &bob, ¶ms))
+ if(!verifystep1(&alice, &bob.p, ¶ms))
return 1;
- if(!verifystep1(&bob, &alice, ¶ms))
+ if(!verifystep1(&bob, &alice.p, ¶ms))
return 2;
// Second send
- sendstep2(&alice, &bob, ¶ms);
- sendstep2(&bob, &alice, ¶ms);
+ sendstep2(&alice, &bob.p, ¶ms);
+ sendstep2(&bob, &alice.p, ¶ms);
// And second verify
- if(!verifystep2(&alice, &bob, ¶ms))
+ if(!verifystep2(&alice, &bob.p, ¶ms))
return 3;
- if(!verifystep2(&bob, &alice, ¶ms))
+ if(!verifystep2(&bob, &alice.p, ¶ms))
return 4;
// Compute common key