| /* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com) |
| * All rights reserved. |
| * |
| * This package is an SSL implementation written |
| * by Eric Young (eay@cryptsoft.com). |
| * The implementation was written so as to conform with Netscapes SSL. |
| * |
| * This library is free for commercial and non-commercial use as long as |
| * the following conditions are aheared to. The following conditions |
| * apply to all code found in this distribution, be it the RC4, RSA, |
| * lhash, DES, etc., code; not just the SSL code. The SSL documentation |
| * included with this distribution is covered by the same copyright terms |
| * except that the holder is Tim Hudson (tjh@cryptsoft.com). |
| * |
| * Copyright remains Eric Young's, and as such any Copyright notices in |
| * the code are not to be removed. |
| * If this package is used in a product, Eric Young should be given attribution |
| * as the author of the parts of the library used. |
| * This can be in the form of a textual message at program startup or |
| * in documentation (online or textual) provided with the package. |
| * |
| * Redistribution and use in source and binary forms, with or without |
| * modification, are permitted provided that the following conditions |
| * are met: |
| * 1. Redistributions of source code must retain the copyright |
| * notice, this list of conditions and the following disclaimer. |
| * 2. Redistributions in binary form must reproduce the above copyright |
| * notice, this list of conditions and the following disclaimer in the |
| * documentation and/or other materials provided with the distribution. |
| * 3. All advertising materials mentioning features or use of this software |
| * must display the following acknowledgement: |
| * "This product includes cryptographic software written by |
| * Eric Young (eay@cryptsoft.com)" |
| * The word 'cryptographic' can be left out if the rouines from the library |
| * being used are not cryptographic related :-). |
| * 4. If you include any Windows specific code (or a derivative thereof) from |
| * the apps directory (application code) you must include an acknowledgement: |
| * "This product includes software written by Tim Hudson (tjh@cryptsoft.com)" |
| * |
| * THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND |
| * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE |
| * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE |
| * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE |
| * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL |
| * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS |
| * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) |
| * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT |
| * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY |
| * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF |
| * SUCH DAMAGE. |
| * |
| * The licence and distribution terms for any publically available version or |
| * derivative of this code cannot be changed. i.e. this code cannot simply be |
| * copied and put under another distribution licence |
| * [including the GNU Public Licence.] |
| * |
| * The DSS routines are based on patches supplied by |
| * Steven Schoch <schoch@sheba.arc.nasa.gov>. */ |
| |
| #include <openssl/dsa.h> |
| |
| #include <string.h> |
| |
| #include <openssl/bn.h> |
| #include <openssl/digest.h> |
| #include <openssl/err.h> |
| #include <openssl/rand.h> |
| #include <openssl/sha.h> |
| #include <openssl/thread.h> |
| |
| #include "internal.h" |
| |
| #define OPENSSL_DSA_MAX_MODULUS_BITS 10000 |
| |
| /* Primality test according to FIPS PUB 186[-1], Appendix 2.1: 50 rounds of |
| * Rabin-Miller */ |
| #define DSS_prime_checks 50 |
| |
| static int sign_setup(const DSA *dsa, BN_CTX *ctx_in, BIGNUM **kinvp, |
| BIGNUM **rp, const uint8_t *digest, size_t digest_len) { |
| BN_CTX *ctx; |
| BIGNUM k, kq, *K, *kinv = NULL, *r = NULL; |
| int ret = 0; |
| |
| if (!dsa->p || !dsa->q || !dsa->g) { |
| OPENSSL_PUT_ERROR(DSA, DSA_R_MISSING_PARAMETERS); |
| return 0; |
| } |
| |
| BN_init(&k); |
| BN_init(&kq); |
| |
| ctx = ctx_in; |
| if (ctx == NULL) { |
| ctx = BN_CTX_new(); |
| if (ctx == NULL) { |
| goto err; |
| } |
| } |
| |
| r = BN_new(); |
| if (r == NULL) { |
| goto err; |
| } |
| |
| /* Get random k */ |
| do { |
| /* If possible, we'll include the private key and message digest in the k |
| * generation. The |digest| argument is only empty if |DSA_sign_setup| is |
| * being used. */ |
| int ok; |
| |
| if (digest_len > 0) { |
| ok = BN_generate_dsa_nonce(&k, dsa->q, dsa->priv_key, digest, digest_len, |
| ctx); |
| } else { |
| ok = BN_rand_range(&k, dsa->q); |
| } |
| if (!ok) { |
| goto err; |
| } |
| } while (BN_is_zero(&k)); |
| |
| BN_set_flags(&k, BN_FLG_CONSTTIME); |
| |
| if (BN_MONT_CTX_set_locked((BN_MONT_CTX **)&dsa->method_mont_p, |
| (CRYPTO_MUTEX *)&dsa->method_mont_p_lock, dsa->p, |
| ctx) == NULL) { |
| goto err; |
| } |
| |
| /* Compute r = (g^k mod p) mod q */ |
| if (!BN_copy(&kq, &k)) { |
| goto err; |
| } |
| |
| /* We do not want timing information to leak the length of k, |
| * so we compute g^k using an equivalent exponent of fixed length. |
| * |
| * (This is a kludge that we need because the BN_mod_exp_mont() |
| * does not let us specify the desired timing behaviour.) */ |
| |
| if (!BN_add(&kq, &kq, dsa->q)) { |
| goto err; |
| } |
| if (BN_num_bits(&kq) <= BN_num_bits(dsa->q) && !BN_add(&kq, &kq, dsa->q)) { |
| goto err; |
| } |
| |
| K = &kq; |
| |
| if (!BN_mod_exp_mont(r, dsa->g, K, dsa->p, ctx, dsa->method_mont_p)) { |
| goto err; |
| } |
| if (!BN_mod(r, r, dsa->q, ctx)) { |
| goto err; |
| } |
| |
| /* Compute part of 's = inv(k) (m + xr) mod q' */ |
| kinv = BN_mod_inverse(NULL, &k, dsa->q, ctx); |
| if (kinv == NULL) { |
| goto err; |
| } |
| |
| BN_clear_free(*kinvp); |
| *kinvp = kinv; |
| kinv = NULL; |
| BN_clear_free(*rp); |
| *rp = r; |
| ret = 1; |
| |
| err: |
| if (!ret) { |
| OPENSSL_PUT_ERROR(DSA, ERR_R_BN_LIB); |
| if (r != NULL) { |
| BN_clear_free(r); |
| } |
| } |
| |
| if (ctx_in == NULL) { |
| BN_CTX_free(ctx); |
| } |
| BN_clear_free(&k); |
| BN_clear_free(&kq); |
| return ret; |
| } |
| |
| static DSA_SIG *sign(const uint8_t *digest, size_t digest_len, DSA *dsa) { |
| BIGNUM *kinv = NULL, *r = NULL, *s = NULL; |
| BIGNUM m; |
| BIGNUM xr; |
| BN_CTX *ctx = NULL; |
| int reason = ERR_R_BN_LIB; |
| DSA_SIG *ret = NULL; |
| int noredo = 0; |
| |
| BN_init(&m); |
| BN_init(&xr); |
| |
| if (!dsa->p || !dsa->q || !dsa->g) { |
| reason = DSA_R_MISSING_PARAMETERS; |
| goto err; |
| } |
| |
| s = BN_new(); |
| if (s == NULL) { |
| goto err; |
| } |
| ctx = BN_CTX_new(); |
| if (ctx == NULL) { |
| goto err; |
| } |
| |
| redo: |
| if (dsa->kinv == NULL || dsa->r == NULL) { |
| if (!DSA_sign_setup(dsa, ctx, &kinv, &r)) { |
| goto err; |
| } |
| } else { |
| kinv = dsa->kinv; |
| dsa->kinv = NULL; |
| r = dsa->r; |
| dsa->r = NULL; |
| noredo = 1; |
| } |
| |
| if (digest_len > BN_num_bytes(dsa->q)) { |
| /* if the digest length is greater than the size of q use the |
| * BN_num_bits(dsa->q) leftmost bits of the digest, see |
| * fips 186-3, 4.2 */ |
| digest_len = BN_num_bytes(dsa->q); |
| } |
| |
| if (BN_bin2bn(digest, digest_len, &m) == NULL) { |
| goto err; |
| } |
| |
| /* Compute s = inv(k) (m + xr) mod q */ |
| if (!BN_mod_mul(&xr, dsa->priv_key, r, dsa->q, ctx)) { |
| goto err; /* s = xr */ |
| } |
| if (!BN_add(s, &xr, &m)) { |
| goto err; /* s = m + xr */ |
| } |
| if (BN_cmp(s, dsa->q) > 0) { |
| if (!BN_sub(s, s, dsa->q)) { |
| goto err; |
| } |
| } |
| if (!BN_mod_mul(s, s, kinv, dsa->q, ctx)) { |
| goto err; |
| } |
| |
| ret = DSA_SIG_new(); |
| if (ret == NULL) { |
| goto err; |
| } |
| /* Redo if r or s is zero as required by FIPS 186-3: this is |
| * very unlikely. */ |
| if (BN_is_zero(r) || BN_is_zero(s)) { |
| if (noredo) { |
| reason = DSA_R_NEED_NEW_SETUP_VALUES; |
| goto err; |
| } |
| goto redo; |
| } |
| ret->r = r; |
| ret->s = s; |
| |
| err: |
| if (!ret) { |
| OPENSSL_PUT_ERROR(DSA, reason); |
| BN_free(r); |
| BN_free(s); |
| } |
| BN_CTX_free(ctx); |
| BN_clear_free(&m); |
| BN_clear_free(&xr); |
| BN_clear_free(kinv); |
| |
| return ret; |
| } |
| |
| static int verify(int *out_valid, const uint8_t *dgst, size_t digest_len, |
| DSA_SIG *sig, const DSA *dsa) { |
| BN_CTX *ctx; |
| BIGNUM u1, u2, t1; |
| BN_MONT_CTX *mont = NULL; |
| int ret = 0; |
| unsigned i; |
| |
| *out_valid = 0; |
| |
| if (!dsa->p || !dsa->q || !dsa->g) { |
| OPENSSL_PUT_ERROR(DSA, DSA_R_MISSING_PARAMETERS); |
| return 0; |
| } |
| |
| i = BN_num_bits(dsa->q); |
| /* fips 186-3 allows only different sizes for q */ |
| if (i != 160 && i != 224 && i != 256) { |
| OPENSSL_PUT_ERROR(DSA, DSA_R_BAD_Q_VALUE); |
| return 0; |
| } |
| |
| if (BN_num_bits(dsa->p) > OPENSSL_DSA_MAX_MODULUS_BITS) { |
| OPENSSL_PUT_ERROR(DSA, DSA_R_MODULUS_TOO_LARGE); |
| return 0; |
| } |
| |
| BN_init(&u1); |
| BN_init(&u2); |
| BN_init(&t1); |
| |
| ctx = BN_CTX_new(); |
| if (ctx == NULL) { |
| goto err; |
| } |
| |
| if (BN_is_zero(sig->r) || BN_is_negative(sig->r) || |
| BN_ucmp(sig->r, dsa->q) >= 0) { |
| ret = 1; |
| goto err; |
| } |
| if (BN_is_zero(sig->s) || BN_is_negative(sig->s) || |
| BN_ucmp(sig->s, dsa->q) >= 0) { |
| ret = 1; |
| goto err; |
| } |
| |
| /* Calculate W = inv(S) mod Q |
| * save W in u2 */ |
| if (BN_mod_inverse(&u2, sig->s, dsa->q, ctx) == NULL) { |
| goto err; |
| } |
| |
| /* save M in u1 */ |
| if (digest_len > (i >> 3)) { |
| /* if the digest length is greater than the size of q use the |
| * BN_num_bits(dsa->q) leftmost bits of the digest, see |
| * fips 186-3, 4.2 */ |
| digest_len = (i >> 3); |
| } |
| |
| if (BN_bin2bn(dgst, digest_len, &u1) == NULL) { |
| goto err; |
| } |
| |
| /* u1 = M * w mod q */ |
| if (!BN_mod_mul(&u1, &u1, &u2, dsa->q, ctx)) { |
| goto err; |
| } |
| |
| /* u2 = r * w mod q */ |
| if (!BN_mod_mul(&u2, sig->r, &u2, dsa->q, ctx)) { |
| goto err; |
| } |
| |
| mont = BN_MONT_CTX_set_locked((BN_MONT_CTX **)&dsa->method_mont_p, |
| (CRYPTO_MUTEX *)&dsa->method_mont_p_lock, |
| dsa->p, ctx); |
| if (!mont) { |
| goto err; |
| } |
| |
| if (!BN_mod_exp2_mont(&t1, dsa->g, &u1, dsa->pub_key, &u2, dsa->p, ctx, |
| mont)) { |
| goto err; |
| } |
| |
| /* BN_copy(&u1,&t1); */ |
| /* let u1 = u1 mod q */ |
| if (!BN_mod(&u1, &t1, dsa->q, ctx)) { |
| goto err; |
| } |
| |
| /* V is now in u1. If the signature is correct, it will be |
| * equal to R. */ |
| *out_valid = BN_ucmp(&u1, sig->r) == 0; |
| ret = 1; |
| |
| err: |
| if (ret != 1) { |
| OPENSSL_PUT_ERROR(DSA, ERR_R_BN_LIB); |
| } |
| BN_CTX_free(ctx); |
| BN_free(&u1); |
| BN_free(&u2); |
| BN_free(&t1); |
| |
| return ret; |
| } |
| |
| static int keygen(DSA *dsa) { |
| int ok = 0; |
| BN_CTX *ctx = NULL; |
| BIGNUM *pub_key = NULL, *priv_key = NULL; |
| BIGNUM prk; |
| |
| ctx = BN_CTX_new(); |
| if (ctx == NULL) { |
| goto err; |
| } |
| |
| priv_key = dsa->priv_key; |
| if (priv_key == NULL) { |
| priv_key = BN_new(); |
| if (priv_key == NULL) { |
| goto err; |
| } |
| } |
| |
| do { |
| if (!BN_rand_range(priv_key, dsa->q)) { |
| goto err; |
| } |
| } while (BN_is_zero(priv_key)); |
| |
| pub_key = dsa->pub_key; |
| if (pub_key == NULL) { |
| pub_key = BN_new(); |
| if (pub_key == NULL) { |
| goto err; |
| } |
| } |
| |
| BN_init(&prk); |
| BN_with_flags(&prk, priv_key, BN_FLG_CONSTTIME); |
| |
| if (!BN_mod_exp(pub_key, dsa->g, &prk, dsa->p, ctx)) { |
| goto err; |
| } |
| |
| dsa->priv_key = priv_key; |
| dsa->pub_key = pub_key; |
| ok = 1; |
| |
| err: |
| if (dsa->pub_key == NULL) { |
| BN_free(pub_key); |
| } |
| if (dsa->priv_key == NULL) { |
| BN_free(priv_key); |
| } |
| BN_CTX_free(ctx); |
| |
| return ok; |
| } |
| |
| static int paramgen(DSA *ret, unsigned bits, const uint8_t *seed_in, |
| size_t seed_len, int *counter_ret, unsigned long *h_ret, |
| BN_GENCB *cb) { |
| int ok = 0; |
| unsigned char seed[SHA256_DIGEST_LENGTH]; |
| unsigned char md[SHA256_DIGEST_LENGTH]; |
| unsigned char buf[SHA256_DIGEST_LENGTH], buf2[SHA256_DIGEST_LENGTH]; |
| BIGNUM *r0, *W, *X, *c, *test; |
| BIGNUM *g = NULL, *q = NULL, *p = NULL; |
| BN_MONT_CTX *mont = NULL; |
| int k, n = 0, m = 0; |
| unsigned i; |
| int counter = 0; |
| int r = 0; |
| BN_CTX *ctx = NULL; |
| unsigned int h = 2; |
| unsigned qbits, qsize; |
| const EVP_MD *evpmd; |
| |
| if (bits >= 2048) { |
| qbits = 256; |
| evpmd = EVP_sha256(); |
| } else { |
| qbits = 160; |
| evpmd = EVP_sha1(); |
| } |
| qsize = qbits / 8; |
| |
| if (qsize != SHA_DIGEST_LENGTH && qsize != SHA224_DIGEST_LENGTH && |
| qsize != SHA256_DIGEST_LENGTH) { |
| /* invalid q size */ |
| return 0; |
| } |
| |
| if (bits < 512) { |
| bits = 512; |
| } |
| |
| bits = (bits + 63) / 64 * 64; |
| |
| /* NB: seed_len == 0 is special case: copy generated seed to |
| * seed_in if it is not NULL. */ |
| if (seed_len && (seed_len < (size_t)qsize)) { |
| seed_in = NULL; /* seed buffer too small -- ignore */ |
| } |
| if (seed_len > (size_t)qsize) { |
| seed_len = qsize; /* App. 2.2 of FIPS PUB 186 allows larger SEED, |
| * but our internal buffers are restricted to 160 bits*/ |
| } |
| if (seed_in != NULL) { |
| memcpy(seed, seed_in, seed_len); |
| } |
| |
| ctx = BN_CTX_new(); |
| if (ctx == NULL) { |
| goto err; |
| } |
| BN_CTX_start(ctx); |
| |
| mont = BN_MONT_CTX_new(); |
| if (mont == NULL) { |
| goto err; |
| } |
| |
| r0 = BN_CTX_get(ctx); |
| g = BN_CTX_get(ctx); |
| W = BN_CTX_get(ctx); |
| q = BN_CTX_get(ctx); |
| X = BN_CTX_get(ctx); |
| c = BN_CTX_get(ctx); |
| p = BN_CTX_get(ctx); |
| test = BN_CTX_get(ctx); |
| |
| if (test == NULL || !BN_lshift(test, BN_value_one(), bits - 1)) { |
| goto err; |
| } |
| |
| for (;;) { |
| /* Find q. */ |
| for (;;) { |
| int seed_is_random; |
| |
| /* step 1 */ |
| if (!BN_GENCB_call(cb, 0, m++)) { |
| goto err; |
| } |
| |
| if (!seed_len) { |
| if (!RAND_bytes(seed, qsize)) { |
| goto err; |
| } |
| seed_is_random = 1; |
| } else { |
| seed_is_random = 0; |
| seed_len = 0; /* use random seed if 'seed_in' turns out to be bad*/ |
| } |
| memcpy(buf, seed, qsize); |
| memcpy(buf2, seed, qsize); |
| /* precompute "SEED + 1" for step 7: */ |
| for (i = qsize - 1; i < qsize; i--) { |
| buf[i]++; |
| if (buf[i] != 0) { |
| break; |
| } |
| } |
| |
| /* step 2 */ |
| if (!EVP_Digest(seed, qsize, md, NULL, evpmd, NULL) || |
| !EVP_Digest(buf, qsize, buf2, NULL, evpmd, NULL)) { |
| goto err; |
| } |
| for (i = 0; i < qsize; i++) { |
| md[i] ^= buf2[i]; |
| } |
| |
| /* step 3 */ |
| md[0] |= 0x80; |
| md[qsize - 1] |= 0x01; |
| if (!BN_bin2bn(md, qsize, q)) { |
| goto err; |
| } |
| |
| /* step 4 */ |
| r = BN_is_prime_fasttest_ex(q, DSS_prime_checks, ctx, seed_is_random, cb); |
| if (r > 0) { |
| break; |
| } |
| if (r != 0) { |
| goto err; |
| } |
| |
| /* do a callback call */ |
| /* step 5 */ |
| } |
| |
| if (!BN_GENCB_call(cb, 2, 0) || !BN_GENCB_call(cb, 3, 0)) { |
| goto err; |
| } |
| |
| /* step 6 */ |
| counter = 0; |
| /* "offset = 2" */ |
| |
| n = (bits - 1) / 160; |
| |
| for (;;) { |
| if ((counter != 0) && !BN_GENCB_call(cb, 0, counter)) { |
| goto err; |
| } |
| |
| /* step 7 */ |
| BN_zero(W); |
| /* now 'buf' contains "SEED + offset - 1" */ |
| for (k = 0; k <= n; k++) { |
| /* obtain "SEED + offset + k" by incrementing: */ |
| for (i = qsize - 1; i < qsize; i--) { |
| buf[i]++; |
| if (buf[i] != 0) { |
| break; |
| } |
| } |
| |
| if (!EVP_Digest(buf, qsize, md, NULL, evpmd, NULL)) { |
| goto err; |
| } |
| |
| /* step 8 */ |
| if (!BN_bin2bn(md, qsize, r0) || |
| !BN_lshift(r0, r0, (qsize << 3) * k) || |
| !BN_add(W, W, r0)) { |
| goto err; |
| } |
| } |
| |
| /* more of step 8 */ |
| if (!BN_mask_bits(W, bits - 1) || |
| !BN_copy(X, W) || |
| !BN_add(X, X, test)) { |
| goto err; |
| } |
| |
| /* step 9 */ |
| if (!BN_lshift1(r0, q) || |
| !BN_mod(c, X, r0, ctx) || |
| !BN_sub(r0, c, BN_value_one()) || |
| !BN_sub(p, X, r0)) { |
| goto err; |
| } |
| |
| /* step 10 */ |
| if (BN_cmp(p, test) >= 0) { |
| /* step 11 */ |
| r = BN_is_prime_fasttest_ex(p, DSS_prime_checks, ctx, 1, cb); |
| if (r > 0) { |
| goto end; /* found it */ |
| } |
| if (r != 0) { |
| goto err; |
| } |
| } |
| |
| /* step 13 */ |
| counter++; |
| /* "offset = offset + n + 1" */ |
| |
| /* step 14 */ |
| if (counter >= 4096) { |
| break; |
| } |
| } |
| } |
| end: |
| if (!BN_GENCB_call(cb, 2, 1)) { |
| goto err; |
| } |
| |
| /* We now need to generate g */ |
| /* Set r0=(p-1)/q */ |
| if (!BN_sub(test, p, BN_value_one()) || |
| !BN_div(r0, NULL, test, q, ctx)) { |
| goto err; |
| } |
| |
| if (!BN_set_word(test, h) || |
| !BN_MONT_CTX_set(mont, p, ctx)) { |
| goto err; |
| } |
| |
| for (;;) { |
| /* g=test^r0%p */ |
| if (!BN_mod_exp_mont(g, test, r0, p, ctx, mont)) { |
| goto err; |
| } |
| if (!BN_is_one(g)) { |
| break; |
| } |
| if (!BN_add(test, test, BN_value_one())) { |
| goto err; |
| } |
| h++; |
| } |
| |
| if (!BN_GENCB_call(cb, 3, 1)) { |
| goto err; |
| } |
| |
| ok = 1; |
| |
| err: |
| if (ok) { |
| BN_free(ret->p); |
| BN_free(ret->q); |
| BN_free(ret->g); |
| ret->p = BN_dup(p); |
| ret->q = BN_dup(q); |
| ret->g = BN_dup(g); |
| if (ret->p == NULL || ret->q == NULL || ret->g == NULL) { |
| ok = 0; |
| goto err; |
| } |
| if (counter_ret != NULL) { |
| *counter_ret = counter; |
| } |
| if (h_ret != NULL) { |
| *h_ret = h; |
| } |
| } |
| |
| if (ctx) { |
| BN_CTX_end(ctx); |
| BN_CTX_free(ctx); |
| } |
| |
| BN_MONT_CTX_free(mont); |
| |
| return ok; |
| } |
| |
| static int finish(DSA *dsa) { |
| BN_MONT_CTX_free(dsa->method_mont_p); |
| dsa->method_mont_p = NULL; |
| return 1; |
| } |
| |
| const struct dsa_method DSA_default_method = { |
| { |
| 0 /* references */, |
| 1 /* is_static */, |
| }, |
| NULL /* app_data */, |
| |
| NULL /* init */, |
| finish /* finish */, |
| |
| sign, |
| sign_setup, |
| verify, |
| |
| paramgen, |
| keygen, |
| }; |