#include "jpake.h" #include <openssl/crypto.h> #include <openssl/sha.h> #include <openssl/err.h> #include <memory.h> /* * 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 { char *name; /* Must be unique */ char *peer_name; BIGNUM *p; BIGNUM *g; BIGNUM *q; BIGNUM *gxc; /* Alice's g^{x3} or Bob's g^{x1} */ BIGNUM *gxd; /* Alice's g^{x4} or Bob's g^{x2} */ } JPAKE_CTX_PUBLIC; struct JPAKE_CTX { JPAKE_CTX_PUBLIC p; BIGNUM *secret; /* The shared secret */ BN_CTX *ctx; BIGNUM *xa; /* Alice's x1 or Bob's x3 */ BIGNUM *xb; /* Alice's x2 or Bob's x4 */ BIGNUM *key; /* The calculated (shared) key */ }; static void JPAKE_ZKP_init(JPAKE_ZKP *zkp) { zkp->gr = BN_new(); zkp->b = BN_new(); } static void JPAKE_ZKP_release(JPAKE_ZKP *zkp) { BN_free(zkp->b); BN_free(zkp->gr); } /* Two birds with one stone - make the global name as expected */ #define JPAKE_STEP_PART_init JPAKE_STEP2_init #define JPAKE_STEP_PART_release JPAKE_STEP2_release void JPAKE_STEP_PART_init(JPAKE_STEP_PART *p) { p->gx = BN_new(); JPAKE_ZKP_init(&p->zkpx); } void JPAKE_STEP_PART_release(JPAKE_STEP_PART *p) { JPAKE_ZKP_release(&p->zkpx); BN_free(p->gx); } void JPAKE_STEP1_init(JPAKE_STEP1 *s1) { JPAKE_STEP_PART_init(&s1->p1); JPAKE_STEP_PART_init(&s1->p2); } void JPAKE_STEP1_release(JPAKE_STEP1 *s1) { JPAKE_STEP_PART_release(&s1->p2); JPAKE_STEP_PART_release(&s1->p1); } static void JPAKE_CTX_init(JPAKE_CTX *ctx, const char *name, const char *peer_name, const BIGNUM *p, const BIGNUM *g, const BIGNUM *q, const BIGNUM *secret) { ctx->p.name = OPENSSL_strdup(name); ctx->p.peer_name = OPENSSL_strdup(peer_name); ctx->p.p = BN_dup(p); ctx->p.g = BN_dup(g); ctx->p.q = BN_dup(q); ctx->secret = BN_dup(secret); ctx->p.gxc = BN_new(); ctx->p.gxd = BN_new(); ctx->xa = BN_new(); ctx->xb = BN_new(); ctx->key = BN_new(); ctx->ctx = BN_CTX_new(); } static void JPAKE_CTX_release(JPAKE_CTX *ctx) { BN_CTX_free(ctx->ctx); BN_clear_free(ctx->key); BN_clear_free(ctx->xb); BN_clear_free(ctx->xa); BN_free(ctx->p.gxd); BN_free(ctx->p.gxc); BN_clear_free(ctx->secret); BN_free(ctx->p.q); BN_free(ctx->p.g); BN_free(ctx->p.p); OPENSSL_free(ctx->p.peer_name); OPENSSL_free(ctx->p.name); memset(ctx, '\0', sizeof *ctx); } JPAKE_CTX *JPAKE_CTX_new(const char *name, const char *peer_name, const BIGNUM *p, const BIGNUM *g, const BIGNUM *q, const BIGNUM *secret) { JPAKE_CTX *ctx = OPENSSL_malloc(sizeof *ctx); JPAKE_CTX_init(ctx, name, peer_name, p, g, q, secret); return ctx; } void JPAKE_CTX_free(JPAKE_CTX *ctx) { JPAKE_CTX_release(ctx); OPENSSL_free(ctx); } static void hashlength(SHA_CTX *sha, size_t l) { unsigned char b[2]; OPENSSL_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 = OPENSSL_malloc(l); hashlength(sha, l); BN_bn2bin(bn, bin); SHA1_Update(sha, bin, l); OPENSSL_free(bin); } /* h=hash(g, g^r, g^x, name) */ static void zkp_hash(BIGNUM *h, const BIGNUM *zkpg, const JPAKE_STEP_PART *p, const char *proof_name) { 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, zkpg); OPENSSL_assert(!BN_is_zero(p->zkpx.gr)); hashbn(&sha, p->zkpx.gr); hashbn(&sha, p->gx); hashstring(&sha, proof_name); SHA1_Final(md, &sha); BN_bin2bn(md, SHA_DIGEST_LENGTH, h); } /* * Prove knowledge of x * Note that p->gx has already been calculated */ static void generate_zkp(JPAKE_STEP_PART *p, const BIGNUM *x, const BIGNUM *zkpg, JPAKE_CTX *ctx) { BIGNUM *r = 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, ctx->p.q); /* g^r */ BN_mod_exp(p->zkpx.gr, zkpg, r, ctx->p.p, ctx->ctx); /* h=hash... */ zkp_hash(h, zkpg, p, ctx->p.name); /* b = r - x*h */ BN_mod_mul(t, x, h, ctx->p.q, ctx->ctx); BN_mod_sub(p->zkpx.b, r, t, ctx->p.q, ctx->ctx); /* cleanup */ BN_free(t); BN_free(h); BN_free(r); } static int verify_zkp(const JPAKE_STEP_PART *p, const BIGNUM *zkpg, JPAKE_CTX *ctx) { BIGNUM *h = BN_new(); BIGNUM *t1 = BN_new(); BIGNUM *t2 = BN_new(); BIGNUM *t3 = BN_new(); int ret = 0; zkp_hash(h, zkpg, p, ctx->p.peer_name); /* t1 = g^b */ BN_mod_exp(t1, zkpg, p->zkpx.b, ctx->p.p, ctx->ctx); /* t2 = (g^x)^h = g^{hx} */ BN_mod_exp(t2, p->gx, h, ctx->p.p, ctx->ctx); /* t3 = t1 * t2 = g^{hx} * g^b = g^{hx+b} = g^r (allegedly) */ BN_mod_mul(t3, t1, t2, ctx->p.p, ctx->ctx); /* verify t3 == g^r */ if(BN_cmp(t3, p->zkpx.gr) == 0) ret = 1; else JPAKEerr(JPAKE_F_VERIFY_ZKP, JPAKE_R_ZKP_VERIFY_FAILED); /* cleanup */ BN_free(t3); BN_free(t2); BN_free(t1); BN_free(h); return ret; } static void generate_step_part(JPAKE_STEP_PART *p, const BIGNUM *x, const BIGNUM *g, JPAKE_CTX *ctx) { BN_mod_exp(p->gx, g, x, ctx->p.p, ctx->ctx); generate_zkp(p, x, g, ctx); } /* Generate each party's random numbers. xa is in [0, q), xb is in [1, q). */ static void genrand(JPAKE_CTX *ctx) { BIGNUM *qm1; /* xa in [0, q) */ BN_rand_range(ctx->xa, ctx->p.q); /* q-1 */ qm1 = BN_new(); BN_copy(qm1, ctx->p.q); BN_sub_word(qm1, 1); /* ... and xb in [0, q-1) */ BN_rand_range(ctx->xb, qm1); /* [1, q) */ BN_add_word(ctx->xb, 1); /* cleanup */ BN_free(qm1); } int JPAKE_STEP1_generate(JPAKE_STEP1 *send, JPAKE_CTX *ctx) { genrand(ctx); generate_step_part(&send->p1, ctx->xa, ctx->p.g, ctx); generate_step_part(&send->p2, ctx->xb, ctx->p.g, ctx); return 1; } /* g^x is a legal value */ static int is_legal(const BIGNUM *gx, const JPAKE_CTX *ctx) { BIGNUM *t; int res; if(BN_is_negative(gx) || BN_is_zero(gx) || BN_cmp(gx, ctx->p.p) >= 0) return 0; t = BN_new(); BN_mod_exp(t, gx, ctx->p.q, ctx->p.p, ctx->ctx); res = BN_is_one(t); BN_free(t); return res; } int JPAKE_STEP1_process(JPAKE_CTX *ctx, const JPAKE_STEP1 *received) { if(!is_legal(received->p1.gx, ctx)) { JPAKEerr(JPAKE_F_JPAKE_STEP1_PROCESS, JPAKE_R_G_TO_THE_X3_IS_NOT_LEGAL); return 0; } if(!is_legal(received->p2.gx, ctx)) { JPAKEerr(JPAKE_F_JPAKE_STEP1_PROCESS, JPAKE_R_G_TO_THE_X4_IS_NOT_LEGAL); return 0; } /* verify their ZKP(xc) */ if(!verify_zkp(&received->p1, ctx->p.g, ctx)) { JPAKEerr(JPAKE_F_JPAKE_STEP1_PROCESS, JPAKE_R_VERIFY_X3_FAILED); return 0; } /* verify their ZKP(xd) */ if(!verify_zkp(&received->p2, ctx->p.g, ctx)) { JPAKEerr(JPAKE_F_JPAKE_STEP1_PROCESS, JPAKE_R_VERIFY_X4_FAILED); return 0; } /* g^xd != 1 */ if(BN_is_one(received->p2.gx)) { JPAKEerr(JPAKE_F_JPAKE_STEP1_PROCESS, JPAKE_R_G_TO_THE_X4_IS_ONE); return 0; } /* Save the bits we need for later */ BN_copy(ctx->p.gxc, received->p1.gx); BN_copy(ctx->p.gxd, received->p2.gx); return 1; } int JPAKE_STEP2_generate(JPAKE_STEP2 *send, JPAKE_CTX *ctx) { BIGNUM *t1 = BN_new(); BIGNUM *t2 = BN_new(); /* * X = g^{(xa + xc + xd) * xb * s} * t1 = g^xa */ BN_mod_exp(t1, ctx->p.g, ctx->xa, ctx->p.p, ctx->ctx); /* t2 = t1 * g^{xc} = g^{xa} * g^{xc} = g^{xa + xc} */ BN_mod_mul(t2, t1, ctx->p.gxc, ctx->p.p, ctx->ctx); /* t1 = t2 * g^{xd} = g^{xa + xc + xd} */ BN_mod_mul(t1, t2, ctx->p.gxd, ctx->p.p, ctx->ctx); /* t2 = xb * s */ BN_mod_mul(t2, ctx->xb, ctx->secret, ctx->p.q, ctx->ctx); /* * 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} * X = t1^{t2} = t1^{xb * s} = g^{(xa + xc + xd) * xb * s} */ generate_step_part(send, t2, t1, ctx); /* cleanup */ BN_free(t1); BN_free(t2); return 1; } /* gx = g^{xc + xa + xb} * xd * s */ static int compute_key(JPAKE_CTX *ctx, const BIGNUM *gx) { BIGNUM *t1 = BN_new(); BIGNUM *t2 = BN_new(); BIGNUM *t3 = BN_new(); /* * K = (gx/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, ctx->p.gxd, ctx->xb, ctx->p.p, ctx->ctx); /* t2 = -s = q-s */ BN_sub(t2, ctx->p.q, ctx->secret); /* t3 = t1^t2 = g^{-xb * xd * s} */ BN_mod_exp(t3, t1, t2, ctx->p.p, ctx->ctx); /* t1 = gx * t3 = X/g^{xb * xd * s} */ BN_mod_mul(t1, gx, t3, ctx->p.p, ctx->ctx); /* K = t1^{xb} */ BN_mod_exp(ctx->key, t1, ctx->xb, ctx->p.p, ctx->ctx); /* cleanup */ BN_free(t3); BN_free(t2); BN_free(t1); return 1; } int JPAKE_STEP2_process(JPAKE_CTX *ctx, const JPAKE_STEP2 *received) { BIGNUM *t1 = BN_new(); BIGNUM *t2 = BN_new(); int ret = 0; /* * g' = g^{xc + xa + xb} [from our POV] * t1 = xa + xb */ BN_mod_add(t1, ctx->xa, ctx->xb, ctx->p.q, ctx->ctx); /* t2 = g^{t1} = g^{xa+xb} */ BN_mod_exp(t2, ctx->p.g, t1, ctx->p.p, ctx->ctx); /* t1 = g^{xc} * t2 = g^{xc + xa + xb} */ BN_mod_mul(t1, ctx->p.gxc, t2, ctx->p.p, ctx->ctx); if(verify_zkp(received, t1, ctx)) ret = 1; else JPAKEerr(JPAKE_F_JPAKE_STEP2_PROCESS, JPAKE_R_VERIFY_B_FAILED); compute_key(ctx, received->gx); /* cleanup */ BN_free(t2); BN_free(t1); return ret; } static void quickhashbn(unsigned char *md, const BIGNUM *bn) { SHA_CTX sha; SHA1_Init(&sha); hashbn(&sha, bn); SHA1_Final(md, &sha); } void JPAKE_STEP3A_init(JPAKE_STEP3A *s3a) {} int JPAKE_STEP3A_generate(JPAKE_STEP3A *send, JPAKE_CTX *ctx) { quickhashbn(send->hhk, ctx->key); SHA1(send->hhk, sizeof send->hhk, send->hhk); return 1; } int JPAKE_STEP3A_process(JPAKE_CTX *ctx, const JPAKE_STEP3A *received) { unsigned char hhk[SHA_DIGEST_LENGTH]; quickhashbn(hhk, ctx->key); SHA1(hhk, sizeof hhk, hhk); if(memcmp(hhk, received->hhk, sizeof hhk)) { JPAKEerr(JPAKE_F_JPAKE_STEP3A_PROCESS, JPAKE_R_HASH_OF_HASH_OF_KEY_MISMATCH); return 0; } return 1; } void JPAKE_STEP3A_release(JPAKE_STEP3A *s3a) {} void JPAKE_STEP3B_init(JPAKE_STEP3B *s3b) {} int JPAKE_STEP3B_generate(JPAKE_STEP3B *send, JPAKE_CTX *ctx) { quickhashbn(send->hk, ctx->key); return 1; } int JPAKE_STEP3B_process(JPAKE_CTX *ctx, const JPAKE_STEP3B *received) { unsigned char hk[SHA_DIGEST_LENGTH]; quickhashbn(hk, ctx->key); if(memcmp(hk, received->hk, sizeof hk)) { JPAKEerr(JPAKE_F_JPAKE_STEP3B_PROCESS, JPAKE_R_HASH_OF_KEY_MISMATCH); return 0; } return 1; } void JPAKE_STEP3B_release(JPAKE_STEP3B *s3b) {} const BIGNUM *JPAKE_get_shared_key(JPAKE_CTX *ctx) { return ctx->key; }