[linux-block.git] / crypto / rsa.c

// SPDX-License-Identifier: GPL-2.0-or-later
/* RSA asymmetric public-key algorithm [RFC3447]
 *
 * Copyright (c) 2015, Intel Corporation
 * Authors: Tadeusz Struk <tadeusz.struk@intel.com>
 */

#include <linux/fips.h>
#include <linux/module.h>
#include <linux/mpi.h>
#include <crypto/internal/rsa.h>
#include <crypto/internal/akcipher.h>
#include <crypto/akcipher.h>
#include <crypto/algapi.h>

struct rsa_mpi_key {
	MPI n;
	MPI e;
	MPI d;
	MPI p;
	MPI q;
	MPI dp;
	MPI dq;
	MPI qinv;
};

/*
 * RSAEP function [RFC3447 sec 5.1.1]
 * c = m^e mod n;
 */
static int _rsa_enc(const struct rsa_mpi_key *key, MPI c, MPI m)
{
	/* (1) Validate 0 <= m < n */
	if (mpi_cmp_ui(m, 0) < 0 || mpi_cmp(m, key->n) >= 0)
		return -EINVAL;

	/* (2) c = m^e mod n */
	return mpi_powm(c, m, key->e, key->n);
}

/*
 * RSADP function [RFC3447 sec 5.1.2]
 * m_1 = c^dP mod p;
 * m_2 = c^dQ mod q;
 * h = (m_1 - m_2) * qInv mod p;
 * m = m_2 + q * h;
 */
static int _rsa_dec_crt(const struct rsa_mpi_key *key, MPI m_or_m1_or_h, MPI c)
{
	MPI m2, m12_or_qh;
	int ret = -ENOMEM;

	/* (1) Validate 0 <= c < n */
	if (mpi_cmp_ui(c, 0) < 0 || mpi_cmp(c, key->n) >= 0)
		return -EINVAL;

	m2 = mpi_alloc(0);
	m12_or_qh = mpi_alloc(0);
	if (!m2 || !m12_or_qh)
		goto err_free_mpi;

	/* (2i) m_1 = c^dP mod p */
	ret = mpi_powm(m_or_m1_or_h, c, key->dp, key->p);
	if (ret)
		goto err_free_mpi;

	/* (2i) m_2 = c^dQ mod q */
	ret = mpi_powm(m2, c, key->dq, key->q);
	if (ret)
		goto err_free_mpi;

	/* (2iii) h = (m_1 - m_2) * qInv mod p */
	mpi_sub(m12_or_qh, m_or_m1_or_h, m2);
	mpi_mulm(m_or_m1_or_h, m12_or_qh, key->qinv, key->p);

	/* (2iv) m = m_2 + q * h */
	mpi_mul(m12_or_qh, key->q, m_or_m1_or_h);
	mpi_addm(m_or_m1_or_h, m2, m12_or_qh, key->n);

	ret = 0;

err_free_mpi:
	mpi_free(m12_or_qh);
	mpi_free(m2);
	return ret;
}

static inline struct rsa_mpi_key *rsa_get_key(struct crypto_akcipher *tfm)
{
	return akcipher_tfm_ctx(tfm);
}

static int rsa_enc(struct akcipher_request *req)
{
	struct crypto_akcipher *tfm = crypto_akcipher_reqtfm(req);
	const struct rsa_mpi_key *pkey = rsa_get_key(tfm);
	MPI m, c = mpi_alloc(0);
	int ret = 0;
	int sign;

	if (!c)
		return -ENOMEM;

	if (unlikely(!pkey->n || !pkey->e)) {
		ret = -EINVAL;
		goto err_free_c;
	}

	ret = -ENOMEM;
	m = mpi_read_raw_from_sgl(req->src, req->src_len);
	if (!m)
		goto err_free_c;

	ret = _rsa_enc(pkey, c, m);
	if (ret)
		goto err_free_m;

	ret = mpi_write_to_sgl(c, req->dst, req->dst_len, &sign);
	if (ret)
		goto err_free_m;

	if (sign < 0)
		ret = -EBADMSG;

err_free_m:
	mpi_free(m);
err_free_c:
	mpi_free(c);
	return ret;
}

static int rsa_dec(struct akcipher_request *req)
{
	struct crypto_akcipher *tfm = crypto_akcipher_reqtfm(req);
	const struct rsa_mpi_key *pkey = rsa_get_key(tfm);
	MPI c, m = mpi_alloc(0);
	int ret = 0;
	int sign;

	if (!m)
		return -ENOMEM;

	if (unlikely(!pkey->n || !pkey->d)) {
		ret = -EINVAL;
		goto err_free_m;
	}

	ret = -ENOMEM;
	c = mpi_read_raw_from_sgl(req->src, req->src_len);
	if (!c)
		goto err_free_m;

	ret = _rsa_dec_crt(pkey, m, c);
	if (ret)
		goto err_free_c;

	ret = mpi_write_to_sgl(m, req->dst, req->dst_len, &sign);
	if (ret)
		goto err_free_c;

	if (sign < 0)
		ret = -EBADMSG;
err_free_c:
	mpi_free(c);
err_free_m:
	mpi_free(m);
	return ret;
}

static void rsa_free_mpi_key(struct rsa_mpi_key *key)
{
	mpi_free(key->d);
	mpi_free(key->e);
	mpi_free(key->n);
	mpi_free(key->p);
	mpi_free(key->q);
	mpi_free(key->dp);
	mpi_free(key->dq);
	mpi_free(key->qinv);
	key->d = NULL;
	key->e = NULL;
	key->n = NULL;
	key->p = NULL;
	key->q = NULL;
	key->dp = NULL;
	key->dq = NULL;
	key->qinv = NULL;
}

static int rsa_check_key_length(unsigned int len)
{
	switch (len) {
	case 512:
	case 1024:
	case 1536:
		if (fips_enabled)
			return -EINVAL;
		fallthrough;
	case 2048:
	case 3072:
	case 4096:
		return 0;
	}

	return -EINVAL;
}

static int rsa_set_pub_key(struct crypto_akcipher *tfm, const void *key,
			   unsigned int keylen)
{
	struct rsa_mpi_key *mpi_key = akcipher_tfm_ctx(tfm);
	struct rsa_key raw_key = {0};
	int ret;

	/* Free the old MPI key if any */
	rsa_free_mpi_key(mpi_key);

	ret = rsa_parse_pub_key(&raw_key, key, keylen);
	if (ret)
		return ret;

	mpi_key->e = mpi_read_raw_data(raw_key.e, raw_key.e_sz);
	if (!mpi_key->e)
		goto err;

	mpi_key->n = mpi_read_raw_data(raw_key.n, raw_key.n_sz);
	if (!mpi_key->n)
		goto err;

	if (rsa_check_key_length(mpi_get_size(mpi_key->n) << 3)) {
		rsa_free_mpi_key(mpi_key);
		return -EINVAL;
	}

	return 0;

err:
	rsa_free_mpi_key(mpi_key);
	return -ENOMEM;
}

static int rsa_set_priv_key(struct crypto_akcipher *tfm, const void *key,
			    unsigned int keylen)
{
	struct rsa_mpi_key *mpi_key = akcipher_tfm_ctx(tfm);
	struct rsa_key raw_key = {0};
	int ret;

	/* Free the old MPI key if any */
	rsa_free_mpi_key(mpi_key);

	ret = rsa_parse_priv_key(&raw_key, key, keylen);
	if (ret)
		return ret;

	mpi_key->d = mpi_read_raw_data(raw_key.d, raw_key.d_sz);
	if (!mpi_key->d)
		goto err;

	mpi_key->e = mpi_read_raw_data(raw_key.e, raw_key.e_sz);
	if (!mpi_key->e)
		goto err;

	mpi_key->n = mpi_read_raw_data(raw_key.n, raw_key.n_sz);
	if (!mpi_key->n)
		goto err;

	mpi_key->p = mpi_read_raw_data(raw_key.p, raw_key.p_sz);
	if (!mpi_key->p)
		goto err;

	mpi_key->q = mpi_read_raw_data(raw_key.q, raw_key.q_sz);
	if (!mpi_key->q)
		goto err;

	mpi_key->dp = mpi_read_raw_data(raw_key.dp, raw_key.dp_sz);
	if (!mpi_key->dp)
		goto err;

	mpi_key->dq = mpi_read_raw_data(raw_key.dq, raw_key.dq_sz);
	if (!mpi_key->dq)
		goto err;

	mpi_key->qinv = mpi_read_raw_data(raw_key.qinv, raw_key.qinv_sz);
	if (!mpi_key->qinv)
		goto err;

	if (rsa_check_key_length(mpi_get_size(mpi_key->n) << 3)) {
		rsa_free_mpi_key(mpi_key);
		return -EINVAL;
	}

	return 0;

err:
	rsa_free_mpi_key(mpi_key);
	return -ENOMEM;
}

static unsigned int rsa_max_size(struct crypto_akcipher *tfm)
{
	struct rsa_mpi_key *pkey = akcipher_tfm_ctx(tfm);

	return mpi_get_size(pkey->n);
}

static void rsa_exit_tfm(struct crypto_akcipher *tfm)
{
	struct rsa_mpi_key *pkey = akcipher_tfm_ctx(tfm);

	rsa_free_mpi_key(pkey);
}

static struct akcipher_alg rsa = {
	.encrypt = rsa_enc,
	.decrypt = rsa_dec,
	.set_priv_key = rsa_set_priv_key,
	.set_pub_key = rsa_set_pub_key,
	.max_size = rsa_max_size,
	.exit = rsa_exit_tfm,
	.base = {
		.cra_name = "rsa",
		.cra_driver_name = "rsa-generic",
		.cra_priority = 100,
		.cra_module = THIS_MODULE,
		.cra_ctxsize = sizeof(struct rsa_mpi_key),
	},
};

static int __init rsa_init(void)
{
	int err;

	err = crypto_register_akcipher(&rsa);
	if (err)
		return err;

	err = crypto_register_template(&rsa_pkcs1pad_tmpl);
	if (err) {
		crypto_unregister_akcipher(&rsa);
		return err;
	}

	return 0;
}

static void __exit rsa_exit(void)
{
	crypto_unregister_template(&rsa_pkcs1pad_tmpl);
	crypto_unregister_akcipher(&rsa);
}

subsys_initcall(rsa_init);
module_exit(rsa_exit);
MODULE_ALIAS_CRYPTO("rsa");
MODULE_LICENSE("GPL");
MODULE_DESCRIPTION("RSA generic algorithm");
Commit	Line	Data
b4d0d230	1	// SPDX-License-Identifier: GPL-2.0-or-later
cfc2bb32 TS	2	/* RSA asymmetric public-key algorithm [RFC3447]
	3	*
	4	* Copyright (c) 2015, Intel Corporation
	5	* Authors: Tadeusz Struk <tadeusz.struk@intel.com>
cfc2bb32 TS	6	*/
cfc2bb32 TS	7
1ce1bacc	8	#include <linux/fips.h>
cfc2bb32	9	#include <linux/module.h>
5a7de973	10	#include <linux/mpi.h>
cfc2bb32 TS	11	#include <crypto/internal/rsa.h>
	12	#include <crypto/internal/akcipher.h>
	13	#include <crypto/akcipher.h>
3d5b1ecd	14	#include <crypto/algapi.h>
cfc2bb32	15
5a7de973 TA	16	struct rsa_mpi_key {
	17	MPI n;
	18	MPI e;
	19	MPI d;
f145d411 IK	20	MPI p;
	21	MPI q;
	22	MPI dp;
	23	MPI dq;
	24	MPI qinv;
5a7de973 TA	25	};
5a7de973 TA	26
cfc2bb32 TS	27	/*
	28	* RSAEP function [RFC3447 sec 5.1.1]
	29	* c = m^e mod n;
	30	*/
5a7de973	31	static int _rsa_enc(const struct rsa_mpi_key *key, MPI c, MPI m)
cfc2bb32 TS	32	{
	33	/* (1) Validate 0 <= m < n */
	34	if (mpi_cmp_ui(m, 0) < 0 \|\| mpi_cmp(m, key->n) >= 0)
	35	return -EINVAL;
	36
	37	/* (2) c = m^e mod n */
	38	return mpi_powm(c, m, key->e, key->n);
	39	}
	40
	41	/*
	42	* RSADP function [RFC3447 sec 5.1.2]
f145d411 IK	43	* m_1 = c^dP mod p;
	44	* m_2 = c^dQ mod q;
	45	* h = (m_1 - m_2) * qInv mod p;
	46	* m = m_2 + q * h;
cfc2bb32	47	*/
f145d411	48	static int _rsa_dec_crt(const struct rsa_mpi_key *key, MPI m_or_m1_or_h, MPI c)
cfc2bb32	49	{
f145d411 IK	50	MPI m2, m12_or_qh;
	51	int ret = -ENOMEM;
	52
cfc2bb32 TS	53	/* (1) Validate 0 <= c < n */
	54	if (mpi_cmp_ui(c, 0) < 0 \|\| mpi_cmp(c, key->n) >= 0)
	55	return -EINVAL;
	56
f145d411 IK	57	m2 = mpi_alloc(0);
	58	m12_or_qh = mpi_alloc(0);
	59	if (!m2 \|\| !m12_or_qh)
	60	goto err_free_mpi;
	61
	62	/* (2i) m_1 = c^dP mod p */
	63	ret = mpi_powm(m_or_m1_or_h, c, key->dp, key->p);
	64	if (ret)
	65	goto err_free_mpi;
	66
	67	/* (2i) m_2 = c^dQ mod q */
	68	ret = mpi_powm(m2, c, key->dq, key->q);
	69	if (ret)
	70	goto err_free_mpi;
	71
	72	/* (2iii) h = (m_1 - m_2) * qInv mod p */
	73	mpi_sub(m12_or_qh, m_or_m1_or_h, m2);
	74	mpi_mulm(m_or_m1_or_h, m12_or_qh, key->qinv, key->p);
	75
	76	/* (2iv) m = m_2 + q * h */
	77	mpi_mul(m12_or_qh, key->q, m_or_m1_or_h);
	78	mpi_addm(m_or_m1_or_h, m2, m12_or_qh, key->n);
	79
	80	ret = 0;
	81
	82	err_free_mpi:
	83	mpi_free(m12_or_qh);
	84	mpi_free(m2);
	85	return ret;
cfc2bb32 TS	86	}
cfc2bb32 TS	87
5a7de973	88	static inline struct rsa_mpi_key rsa_get_key(struct crypto_akcipher tfm)
cfc2bb32 TS	89	{
	90	return akcipher_tfm_ctx(tfm);
	91	}
	92
	93	static int rsa_enc(struct akcipher_request *req)
	94	{
	95	struct crypto_akcipher *tfm = crypto_akcipher_reqtfm(req);
5a7de973	96	const struct rsa_mpi_key *pkey = rsa_get_key(tfm);
cfc2bb32 TS	97	MPI m, c = mpi_alloc(0);
	98	int ret = 0;
	99	int sign;
	100
	101	if (!c)
	102	return -ENOMEM;
	103
	104	if (unlikely(!pkey->n \|\| !pkey->e)) {
	105	ret = -EINVAL;
	106	goto err_free_c;
	107	}
	108
22287b0b TS	109	ret = -ENOMEM;
	110	m = mpi_read_raw_from_sgl(req->src, req->src_len);
	111	if (!m)
cfc2bb32	112	goto err_free_c;
cfc2bb32 TS	113
	114	ret = _rsa_enc(pkey, c, m);
	115	if (ret)
	116	goto err_free_m;
	117
9b45b7bb	118	ret = mpi_write_to_sgl(c, req->dst, req->dst_len, &sign);
cfc2bb32 TS	119	if (ret)
	120	goto err_free_m;
	121
22287b0b	122	if (sign < 0)
cfc2bb32	123	ret = -EBADMSG;
cfc2bb32 TS	124
	125	err_free_m:
	126	mpi_free(m);
	127	err_free_c:
	128	mpi_free(c);
	129	return ret;
	130	}
	131
	132	static int rsa_dec(struct akcipher_request *req)
	133	{
	134	struct crypto_akcipher *tfm = crypto_akcipher_reqtfm(req);
5a7de973	135	const struct rsa_mpi_key *pkey = rsa_get_key(tfm);
cfc2bb32 TS	136	MPI c, m = mpi_alloc(0);
	137	int ret = 0;
	138	int sign;
	139
	140	if (!m)
	141	return -ENOMEM;
	142
	143	if (unlikely(!pkey->n \|\| !pkey->d)) {
	144	ret = -EINVAL;
	145	goto err_free_m;
	146	}
	147
22287b0b TS	148	ret = -ENOMEM;
	149	c = mpi_read_raw_from_sgl(req->src, req->src_len);
	150	if (!c)
cfc2bb32	151	goto err_free_m;
cfc2bb32	152
f145d411	153	ret = _rsa_dec_crt(pkey, m, c);
cfc2bb32 TS	154	if (ret)
	155	goto err_free_c;
	156
9b45b7bb	157	ret = mpi_write_to_sgl(m, req->dst, req->dst_len, &sign);
cfc2bb32 TS	158	if (ret)
	159	goto err_free_c;
	160
22287b0b	161	if (sign < 0)
cfc2bb32	162	ret = -EBADMSG;
cfc2bb32 TS	163	err_free_c:
	164	mpi_free(c);
	165	err_free_m:
	166	mpi_free(m);
	167	return ret;
	168	}
	169
5a7de973 TA	170	static void rsa_free_mpi_key(struct rsa_mpi_key *key)
	171	{
	172	mpi_free(key->d);
	173	mpi_free(key->e);
	174	mpi_free(key->n);
f145d411 IK	175	mpi_free(key->p);
	176	mpi_free(key->q);
	177	mpi_free(key->dp);
	178	mpi_free(key->dq);
	179	mpi_free(key->qinv);
5a7de973 TA	180	key->d = NULL;
	181	key->e = NULL;
	182	key->n = NULL;
f145d411 IK	183	key->p = NULL;
	184	key->q = NULL;
	185	key->dp = NULL;
	186	key->dq = NULL;
	187	key->qinv = NULL;
5a7de973 TA	188	}
5a7de973 TA	189
6e8ec66c TS	190	static int rsa_check_key_length(unsigned int len)
	191	{
	192	switch (len) {
	193	case 512:
	194	case 1024:
	195	case 1536:
1ce1bacc SM	196	if (fips_enabled)
	197	return -EINVAL;
	198	fallthrough;
6e8ec66c TS	199	case 2048:
	200	case 3072:
	201	case 4096:
	202	return 0;
	203	}
	204
	205	return -EINVAL;
	206	}
	207
22287b0b TS	208	static int rsa_set_pub_key(struct crypto_akcipher tfm, const void key,
22287b0b TS	209	unsigned int keylen)
cfc2bb32	210	{
5a7de973 TA	211	struct rsa_mpi_key *mpi_key = akcipher_tfm_ctx(tfm);
5a7de973 TA	212	struct rsa_key raw_key = {0};
6e8ec66c	213	int ret;
cfc2bb32	214
5a7de973 TA	215	/* Free the old MPI key if any */
	216	rsa_free_mpi_key(mpi_key);
	217
	218	ret = rsa_parse_pub_key(&raw_key, key, keylen);
6e8ec66c TS	219	if (ret)
	220	return ret;
	221
5a7de973 TA	222	mpi_key->e = mpi_read_raw_data(raw_key.e, raw_key.e_sz);
	223	if (!mpi_key->e)
	224	goto err;
	225
	226	mpi_key->n = mpi_read_raw_data(raw_key.n, raw_key.n_sz);
	227	if (!mpi_key->n)
	228	goto err;
	229
	230	if (rsa_check_key_length(mpi_get_size(mpi_key->n) << 3)) {
	231	rsa_free_mpi_key(mpi_key);
	232	return -EINVAL;
6e8ec66c	233	}
5a7de973 TA	234
	235	return 0;
	236
	237	err:
	238	rsa_free_mpi_key(mpi_key);
	239	return -ENOMEM;
cfc2bb32 TS	240	}
cfc2bb32 TS	241
22287b0b TS	242	static int rsa_set_priv_key(struct crypto_akcipher tfm, const void key,
	243	unsigned int keylen)
	244	{
5a7de973 TA	245	struct rsa_mpi_key *mpi_key = akcipher_tfm_ctx(tfm);
5a7de973 TA	246	struct rsa_key raw_key = {0};
22287b0b TS	247	int ret;
22287b0b TS	248
5a7de973 TA	249	/* Free the old MPI key if any */
	250	rsa_free_mpi_key(mpi_key);
	251
	252	ret = rsa_parse_priv_key(&raw_key, key, keylen);
22287b0b TS	253	if (ret)
	254	return ret;
	255
5a7de973 TA	256	mpi_key->d = mpi_read_raw_data(raw_key.d, raw_key.d_sz);
	257	if (!mpi_key->d)
	258	goto err;
	259
	260	mpi_key->e = mpi_read_raw_data(raw_key.e, raw_key.e_sz);
	261	if (!mpi_key->e)
	262	goto err;
	263
	264	mpi_key->n = mpi_read_raw_data(raw_key.n, raw_key.n_sz);
	265	if (!mpi_key->n)
	266	goto err;
	267
f145d411 IK	268	mpi_key->p = mpi_read_raw_data(raw_key.p, raw_key.p_sz);
	269	if (!mpi_key->p)
	270	goto err;
	271
	272	mpi_key->q = mpi_read_raw_data(raw_key.q, raw_key.q_sz);
	273	if (!mpi_key->q)
	274	goto err;
	275
	276	mpi_key->dp = mpi_read_raw_data(raw_key.dp, raw_key.dp_sz);
	277	if (!mpi_key->dp)
	278	goto err;
	279
	280	mpi_key->dq = mpi_read_raw_data(raw_key.dq, raw_key.dq_sz);
	281	if (!mpi_key->dq)
	282	goto err;
	283
	284	mpi_key->qinv = mpi_read_raw_data(raw_key.qinv, raw_key.qinv_sz);
	285	if (!mpi_key->qinv)
	286	goto err;
	287
5a7de973 TA	288	if (rsa_check_key_length(mpi_get_size(mpi_key->n) << 3)) {
	289	rsa_free_mpi_key(mpi_key);
	290	return -EINVAL;
22287b0b	291	}
5a7de973 TA	292
	293	return 0;
	294
	295	err:
	296	rsa_free_mpi_key(mpi_key);
	297	return -ENOMEM;
22287b0b TS	298	}
22287b0b TS	299
1c23b466	300	static unsigned int rsa_max_size(struct crypto_akcipher *tfm)
22287b0b	301	{
5a7de973	302	struct rsa_mpi_key *pkey = akcipher_tfm_ctx(tfm);
22287b0b	303
1c23b466	304	return mpi_get_size(pkey->n);
22287b0b TS	305	}
22287b0b TS	306
cfc2bb32 TS	307	static void rsa_exit_tfm(struct crypto_akcipher *tfm)
cfc2bb32 TS	308	{
5a7de973	309	struct rsa_mpi_key *pkey = akcipher_tfm_ctx(tfm);
cfc2bb32	310
5a7de973	311	rsa_free_mpi_key(pkey);
cfc2bb32 TS	312	}
	313
	314	static struct akcipher_alg rsa = {
	315	.encrypt = rsa_enc,
	316	.decrypt = rsa_dec,
22287b0b TS	317	.set_priv_key = rsa_set_priv_key,
	318	.set_pub_key = rsa_set_pub_key,
	319	.max_size = rsa_max_size,
cfc2bb32 TS	320	.exit = rsa_exit_tfm,
	321	.base = {
	322	.cra_name = "rsa",
	323	.cra_driver_name = "rsa-generic",
	324	.cra_priority = 100,
	325	.cra_module = THIS_MODULE,
5a7de973	326	.cra_ctxsize = sizeof(struct rsa_mpi_key),
cfc2bb32 TS	327	},
	328	};
	329
33837be3	330	static int __init rsa_init(void)
cfc2bb32	331	{
3d5b1ecd AZ	332	int err;
	333
	334	err = crypto_register_akcipher(&rsa);
	335	if (err)
	336	return err;
	337
	338	err = crypto_register_template(&rsa_pkcs1pad_tmpl);
	339	if (err) {
	340	crypto_unregister_akcipher(&rsa);
	341	return err;
	342	}
	343
	344	return 0;
cfc2bb32 TS	345	}
cfc2bb32 TS	346
33837be3	347	static void __exit rsa_exit(void)
cfc2bb32	348	{
3d5b1ecd	349	crypto_unregister_template(&rsa_pkcs1pad_tmpl);
cfc2bb32 TS	350	crypto_unregister_akcipher(&rsa);
	351	}
	352
c4741b23	353	subsys_initcall(rsa_init);
cfc2bb32 TS	354	module_exit(rsa_exit);
	355	MODULE_ALIAS_CRYPTO("rsa");
	356	MODULE_LICENSE("GPL");
	357	MODULE_DESCRIPTION("RSA generic algorithm");