OpenCloudOS-Kernel/crypto/essiv.c

// SPDX-License-Identifier: GPL-2.0
/*
 * ESSIV skcipher and aead template for block encryption
 *
 * This template encapsulates the ESSIV IV generation algorithm used by
 * dm-crypt and fscrypt, which converts the initial vector for the skcipher
 * used for block encryption, by encrypting it using the hash of the
 * skcipher key as encryption key. Usually, the input IV is a 64-bit sector
 * number in LE representation zero-padded to the size of the IV, but this
 * is not assumed by this driver.
 *
 * The typical use of this template is to instantiate the skcipher
 * 'essiv(cbc(aes),sha256)', which is the only instantiation used by
 * fscrypt, and the most relevant one for dm-crypt. However, dm-crypt
 * also permits ESSIV to be used in combination with the authenc template,
 * e.g., 'essiv(authenc(hmac(sha256),cbc(aes)),sha256)', in which case
 * we need to instantiate an aead that accepts the same special key format
 * as the authenc template, and deals with the way the encrypted IV is
 * embedded into the AAD area of the aead request. This means the AEAD
 * flavor produced by this template is tightly coupled to the way dm-crypt
 * happens to use it.
 *
 * Copyright (c) 2019 Linaro, Ltd. <ard.biesheuvel@linaro.org>
 *
 * Heavily based on:
 * adiantum length-preserving encryption mode
 *
 * Copyright 2018 Google LLC
 */

#include <crypto/authenc.h>
#include <crypto/internal/aead.h>
#include <crypto/internal/hash.h>
#include <crypto/internal/skcipher.h>
#include <crypto/scatterwalk.h>
#include <linux/module.h>

#include "internal.h"

struct essiv_instance_ctx {
	union {
		struct crypto_skcipher_spawn	skcipher_spawn;
		struct crypto_aead_spawn	aead_spawn;
	} u;
	char	essiv_cipher_name[CRYPTO_MAX_ALG_NAME];
	char	shash_driver_name[CRYPTO_MAX_ALG_NAME];
};

struct essiv_tfm_ctx {
	union {
		struct crypto_skcipher	*skcipher;
		struct crypto_aead	*aead;
	} u;
	struct crypto_cipher		*essiv_cipher;
	struct crypto_shash		*hash;
	int				ivoffset;
};

struct essiv_aead_request_ctx {
	struct scatterlist		sg[4];
	u8				*assoc;
	struct aead_request		aead_req;
};

static int essiv_skcipher_setkey(struct crypto_skcipher *tfm,
				 const u8 *key, unsigned int keylen)
{
	struct essiv_tfm_ctx *tctx = crypto_skcipher_ctx(tfm);
	SHASH_DESC_ON_STACK(desc, tctx->hash);
	u8 salt[HASH_MAX_DIGESTSIZE];
	int err;

	crypto_skcipher_clear_flags(tctx->u.skcipher, CRYPTO_TFM_REQ_MASK);
	crypto_skcipher_set_flags(tctx->u.skcipher,
				  crypto_skcipher_get_flags(tfm) &
				  CRYPTO_TFM_REQ_MASK);
	err = crypto_skcipher_setkey(tctx->u.skcipher, key, keylen);
	crypto_skcipher_set_flags(tfm,
				  crypto_skcipher_get_flags(tctx->u.skcipher) &
				  CRYPTO_TFM_RES_MASK);
	if (err)
		return err;

	desc->tfm = tctx->hash;
	err = crypto_shash_digest(desc, key, keylen, salt);
	if (err)
		return err;

	crypto_cipher_clear_flags(tctx->essiv_cipher, CRYPTO_TFM_REQ_MASK);
	crypto_cipher_set_flags(tctx->essiv_cipher,
				crypto_skcipher_get_flags(tfm) &
				CRYPTO_TFM_REQ_MASK);
	err = crypto_cipher_setkey(tctx->essiv_cipher, salt,
				   crypto_shash_digestsize(tctx->hash));
	crypto_skcipher_set_flags(tfm,
				  crypto_cipher_get_flags(tctx->essiv_cipher) &
				  CRYPTO_TFM_RES_MASK);

	return err;
}

static int essiv_aead_setkey(struct crypto_aead *tfm, const u8 *key,
			     unsigned int keylen)
{
	struct essiv_tfm_ctx *tctx = crypto_aead_ctx(tfm);
	SHASH_DESC_ON_STACK(desc, tctx->hash);
	struct crypto_authenc_keys keys;
	u8 salt[HASH_MAX_DIGESTSIZE];
	int err;

	crypto_aead_clear_flags(tctx->u.aead, CRYPTO_TFM_REQ_MASK);
	crypto_aead_set_flags(tctx->u.aead, crypto_aead_get_flags(tfm) &
					    CRYPTO_TFM_REQ_MASK);
	err = crypto_aead_setkey(tctx->u.aead, key, keylen);
	crypto_aead_set_flags(tfm, crypto_aead_get_flags(tctx->u.aead) &
				   CRYPTO_TFM_RES_MASK);
	if (err)
		return err;

	if (crypto_authenc_extractkeys(&keys, key, keylen) != 0) {
		crypto_aead_set_flags(tfm, CRYPTO_TFM_RES_BAD_KEY_LEN);
		return -EINVAL;
	}

	desc->tfm = tctx->hash;
	err = crypto_shash_init(desc) ?:
	      crypto_shash_update(desc, keys.enckey, keys.enckeylen) ?:
	      crypto_shash_finup(desc, keys.authkey, keys.authkeylen, salt);
	if (err)
		return err;

	crypto_cipher_clear_flags(tctx->essiv_cipher, CRYPTO_TFM_REQ_MASK);
	crypto_cipher_set_flags(tctx->essiv_cipher, crypto_aead_get_flags(tfm) &
						    CRYPTO_TFM_REQ_MASK);
	err = crypto_cipher_setkey(tctx->essiv_cipher, salt,
				   crypto_shash_digestsize(tctx->hash));
	crypto_aead_set_flags(tfm, crypto_cipher_get_flags(tctx->essiv_cipher) &
				   CRYPTO_TFM_RES_MASK);

	return err;
}

static int essiv_aead_setauthsize(struct crypto_aead *tfm,
				  unsigned int authsize)
{
	struct essiv_tfm_ctx *tctx = crypto_aead_ctx(tfm);

	return crypto_aead_setauthsize(tctx->u.aead, authsize);
}

static void essiv_skcipher_done(struct crypto_async_request *areq, int err)
{
	struct skcipher_request *req = areq->data;

	skcipher_request_complete(req, err);
}

static int essiv_skcipher_crypt(struct skcipher_request *req, bool enc)
{
	struct crypto_skcipher *tfm = crypto_skcipher_reqtfm(req);
	const struct essiv_tfm_ctx *tctx = crypto_skcipher_ctx(tfm);
	struct skcipher_request *subreq = skcipher_request_ctx(req);

	crypto_cipher_encrypt_one(tctx->essiv_cipher, req->iv, req->iv);

	skcipher_request_set_tfm(subreq, tctx->u.skcipher);
	skcipher_request_set_crypt(subreq, req->src, req->dst, req->cryptlen,
				   req->iv);
	skcipher_request_set_callback(subreq, skcipher_request_flags(req),
				      essiv_skcipher_done, req);

	return enc ? crypto_skcipher_encrypt(subreq) :
		     crypto_skcipher_decrypt(subreq);
}

static int essiv_skcipher_encrypt(struct skcipher_request *req)
{
	return essiv_skcipher_crypt(req, true);
}

static int essiv_skcipher_decrypt(struct skcipher_request *req)
{
	return essiv_skcipher_crypt(req, false);
}

static void essiv_aead_done(struct crypto_async_request *areq, int err)
{
	struct aead_request *req = areq->data;
	struct essiv_aead_request_ctx *rctx = aead_request_ctx(req);

	if (err == -EINPROGRESS)
		goto out;

	kfree(rctx->assoc);

out:
	aead_request_complete(req, err);
}

static int essiv_aead_crypt(struct aead_request *req, bool enc)
{
	struct crypto_aead *tfm = crypto_aead_reqtfm(req);
	const struct essiv_tfm_ctx *tctx = crypto_aead_ctx(tfm);
	struct essiv_aead_request_ctx *rctx = aead_request_ctx(req);
	struct aead_request *subreq = &rctx->aead_req;
	struct scatterlist *src = req->src;
	int err;

	crypto_cipher_encrypt_one(tctx->essiv_cipher, req->iv, req->iv);

	/*
	 * dm-crypt embeds the sector number and the IV in the AAD region, so
	 * we have to copy the converted IV into the right scatterlist before
	 * we pass it on.
	 */
	rctx->assoc = NULL;
	if (req->src == req->dst || !enc) {
		scatterwalk_map_and_copy(req->iv, req->dst,
					 req->assoclen - crypto_aead_ivsize(tfm),
					 crypto_aead_ivsize(tfm), 1);
	} else {
		u8 *iv = (u8 *)aead_request_ctx(req) + tctx->ivoffset;
		int ivsize = crypto_aead_ivsize(tfm);
		int ssize = req->assoclen - ivsize;
		struct scatterlist *sg;
		int nents;

		if (ssize < 0)
			return -EINVAL;

		nents = sg_nents_for_len(req->src, ssize);
		if (nents < 0)
			return -EINVAL;

		memcpy(iv, req->iv, ivsize);
		sg_init_table(rctx->sg, 4);

		if (unlikely(nents > 1)) {
			/*
			 * This is a case that rarely occurs in practice, but
			 * for correctness, we have to deal with it nonetheless.
			 */
			rctx->assoc = kmalloc(ssize, GFP_ATOMIC);
			if (!rctx->assoc)
				return -ENOMEM;

			scatterwalk_map_and_copy(rctx->assoc, req->src, 0,
						 ssize, 0);
			sg_set_buf(rctx->sg, rctx->assoc, ssize);
		} else {
			sg_set_page(rctx->sg, sg_page(req->src), ssize,
				    req->src->offset);
		}

		sg_set_buf(rctx->sg + 1, iv, ivsize);
		sg = scatterwalk_ffwd(rctx->sg + 2, req->src, req->assoclen);
		if (sg != rctx->sg + 2)
			sg_chain(rctx->sg, 3, sg);

		src = rctx->sg;
	}

	aead_request_set_tfm(subreq, tctx->u.aead);
	aead_request_set_ad(subreq, req->assoclen);
	aead_request_set_callback(subreq, aead_request_flags(req),
				  essiv_aead_done, req);
	aead_request_set_crypt(subreq, src, req->dst, req->cryptlen, req->iv);

	err = enc ? crypto_aead_encrypt(subreq) :
		    crypto_aead_decrypt(subreq);

	if (rctx->assoc && err != -EINPROGRESS && err != -EBUSY)
		kfree(rctx->assoc);
	return err;
}

static int essiv_aead_encrypt(struct aead_request *req)
{
	return essiv_aead_crypt(req, true);
}

static int essiv_aead_decrypt(struct aead_request *req)
{
	return essiv_aead_crypt(req, false);
}

static int essiv_init_tfm(struct essiv_instance_ctx *ictx,
			  struct essiv_tfm_ctx *tctx)
{
	struct crypto_cipher *essiv_cipher;
	struct crypto_shash *hash;
	int err;

	essiv_cipher = crypto_alloc_cipher(ictx->essiv_cipher_name, 0, 0);
	if (IS_ERR(essiv_cipher))
		return PTR_ERR(essiv_cipher);

	hash = crypto_alloc_shash(ictx->shash_driver_name, 0, 0);
	if (IS_ERR(hash)) {
		err = PTR_ERR(hash);
		goto err_free_essiv_cipher;
	}

	tctx->essiv_cipher = essiv_cipher;
	tctx->hash = hash;

	return 0;

err_free_essiv_cipher:
	crypto_free_cipher(essiv_cipher);
	return err;
}

static int essiv_skcipher_init_tfm(struct crypto_skcipher *tfm)
{
	struct skcipher_instance *inst = skcipher_alg_instance(tfm);
	struct essiv_instance_ctx *ictx = skcipher_instance_ctx(inst);
	struct essiv_tfm_ctx *tctx = crypto_skcipher_ctx(tfm);
	struct crypto_skcipher *skcipher;
	int err;

	skcipher = crypto_spawn_skcipher(&ictx->u.skcipher_spawn);
	if (IS_ERR(skcipher))
		return PTR_ERR(skcipher);

	crypto_skcipher_set_reqsize(tfm, sizeof(struct skcipher_request) +
				         crypto_skcipher_reqsize(skcipher));

	err = essiv_init_tfm(ictx, tctx);
	if (err) {
		crypto_free_skcipher(skcipher);
		return err;
	}

	tctx->u.skcipher = skcipher;
	return 0;
}

static int essiv_aead_init_tfm(struct crypto_aead *tfm)
{
	struct aead_instance *inst = aead_alg_instance(tfm);
	struct essiv_instance_ctx *ictx = aead_instance_ctx(inst);
	struct essiv_tfm_ctx *tctx = crypto_aead_ctx(tfm);
	struct crypto_aead *aead;
	unsigned int subreq_size;
	int err;

	BUILD_BUG_ON(offsetofend(struct essiv_aead_request_ctx, aead_req) !=
		     sizeof(struct essiv_aead_request_ctx));

	aead = crypto_spawn_aead(&ictx->u.aead_spawn);
	if (IS_ERR(aead))
		return PTR_ERR(aead);

	subreq_size = FIELD_SIZEOF(struct essiv_aead_request_ctx, aead_req) +
		      crypto_aead_reqsize(aead);

	tctx->ivoffset = offsetof(struct essiv_aead_request_ctx, aead_req) +
			 subreq_size;
	crypto_aead_set_reqsize(tfm, tctx->ivoffset + crypto_aead_ivsize(aead));

	err = essiv_init_tfm(ictx, tctx);
	if (err) {
		crypto_free_aead(aead);
		return err;
	}

	tctx->u.aead = aead;
	return 0;
}

static void essiv_skcipher_exit_tfm(struct crypto_skcipher *tfm)
{
	struct essiv_tfm_ctx *tctx = crypto_skcipher_ctx(tfm);

	crypto_free_skcipher(tctx->u.skcipher);
	crypto_free_cipher(tctx->essiv_cipher);
	crypto_free_shash(tctx->hash);
}

static void essiv_aead_exit_tfm(struct crypto_aead *tfm)
{
	struct essiv_tfm_ctx *tctx = crypto_aead_ctx(tfm);

	crypto_free_aead(tctx->u.aead);
	crypto_free_cipher(tctx->essiv_cipher);
	crypto_free_shash(tctx->hash);
}

static void essiv_skcipher_free_instance(struct skcipher_instance *inst)
{
	struct essiv_instance_ctx *ictx = skcipher_instance_ctx(inst);

	crypto_drop_skcipher(&ictx->u.skcipher_spawn);
	kfree(inst);
}

static void essiv_aead_free_instance(struct aead_instance *inst)
{
	struct essiv_instance_ctx *ictx = aead_instance_ctx(inst);

	crypto_drop_aead(&ictx->u.aead_spawn);
	kfree(inst);
}

static bool parse_cipher_name(char *essiv_cipher_name, const char *cra_name)
{
	const char *p, *q;
	int len;

	/* find the last opening parens */
	p = strrchr(cra_name, '(');
	if (!p++)
		return false;

	/* find the first closing parens in the tail of the string */
	q = strchr(p, ')');
	if (!q)
		return false;

	len = q - p;
	if (len >= CRYPTO_MAX_ALG_NAME)
		return false;

	memcpy(essiv_cipher_name, p, len);
	essiv_cipher_name[len] = '\0';
	return true;
}

static bool essiv_supported_algorithms(const char *essiv_cipher_name,
				       struct shash_alg *hash_alg,
				       int ivsize)
{
	struct crypto_alg *alg;
	bool ret = false;

	alg = crypto_alg_mod_lookup(essiv_cipher_name,
				    CRYPTO_ALG_TYPE_CIPHER,
				    CRYPTO_ALG_TYPE_MASK);
	if (IS_ERR(alg))
		return false;

	if (hash_alg->digestsize < alg->cra_cipher.cia_min_keysize ||
	    hash_alg->digestsize > alg->cra_cipher.cia_max_keysize)
		goto out;

	if (ivsize != alg->cra_blocksize)
		goto out;

	if (crypto_shash_alg_has_setkey(hash_alg))
		goto out;

	ret = true;

out:
	crypto_mod_put(alg);
	return ret;
}

static int essiv_create(struct crypto_template *tmpl, struct rtattr **tb)
{
	struct crypto_attr_type *algt;
	const char *inner_cipher_name;
	const char *shash_name;
	struct skcipher_instance *skcipher_inst = NULL;
	struct aead_instance *aead_inst = NULL;
	struct crypto_instance *inst;
	struct crypto_alg *base, *block_base;
	struct essiv_instance_ctx *ictx;
	struct skcipher_alg *skcipher_alg = NULL;
	struct aead_alg *aead_alg = NULL;
	struct crypto_alg *_hash_alg;
	struct shash_alg *hash_alg;
	int ivsize;
	u32 type;
	int err;

	algt = crypto_get_attr_type(tb);
	if (IS_ERR(algt))
		return PTR_ERR(algt);

	inner_cipher_name = crypto_attr_alg_name(tb[1]);
	if (IS_ERR(inner_cipher_name))
		return PTR_ERR(inner_cipher_name);

	shash_name = crypto_attr_alg_name(tb[2]);
	if (IS_ERR(shash_name))
		return PTR_ERR(shash_name);

	type = algt->type & algt->mask;

	switch (type) {
	case CRYPTO_ALG_TYPE_BLKCIPHER:
		skcipher_inst = kzalloc(sizeof(*skcipher_inst) +
					sizeof(*ictx), GFP_KERNEL);
		if (!skcipher_inst)
			return -ENOMEM;
		inst = skcipher_crypto_instance(skcipher_inst);
		base = &skcipher_inst->alg.base;
		ictx = crypto_instance_ctx(inst);

		/* Symmetric cipher, e.g., "cbc(aes)" */
		crypto_set_skcipher_spawn(&ictx->u.skcipher_spawn, inst);
		err = crypto_grab_skcipher(&ictx->u.skcipher_spawn,
					   inner_cipher_name, 0,
					   crypto_requires_sync(algt->type,
								algt->mask));
		if (err)
			goto out_free_inst;
		skcipher_alg = crypto_spawn_skcipher_alg(&ictx->u.skcipher_spawn);
		block_base = &skcipher_alg->base;
		ivsize = crypto_skcipher_alg_ivsize(skcipher_alg);
		break;

	case CRYPTO_ALG_TYPE_AEAD:
		aead_inst = kzalloc(sizeof(*aead_inst) +
				    sizeof(*ictx), GFP_KERNEL);
		if (!aead_inst)
			return -ENOMEM;
		inst = aead_crypto_instance(aead_inst);
		base = &aead_inst->alg.base;
		ictx = crypto_instance_ctx(inst);

		/* AEAD cipher, e.g., "authenc(hmac(sha256),cbc(aes))" */
		crypto_set_aead_spawn(&ictx->u.aead_spawn, inst);
		err = crypto_grab_aead(&ictx->u.aead_spawn,
				       inner_cipher_name, 0,
				       crypto_requires_sync(algt->type,
							    algt->mask));
		if (err)
			goto out_free_inst;
		aead_alg = crypto_spawn_aead_alg(&ictx->u.aead_spawn);
		block_base = &aead_alg->base;
		if (!strstarts(block_base->cra_name, "authenc(")) {
			pr_warn("Only authenc() type AEADs are supported by ESSIV\n");
			err = -EINVAL;
			goto out_drop_skcipher;
		}
		ivsize = aead_alg->ivsize;
		break;

	default:
		return -EINVAL;
	}

	if (!parse_cipher_name(ictx->essiv_cipher_name, block_base->cra_name)) {
		pr_warn("Failed to parse ESSIV cipher name from skcipher cra_name\n");
		err = -EINVAL;
		goto out_drop_skcipher;
	}

	/* Synchronous hash, e.g., "sha256" */
	_hash_alg = crypto_alg_mod_lookup(shash_name,
					  CRYPTO_ALG_TYPE_SHASH,
					  CRYPTO_ALG_TYPE_MASK);
	if (IS_ERR(_hash_alg)) {
		err = PTR_ERR(_hash_alg);
		goto out_drop_skcipher;
	}
	hash_alg = __crypto_shash_alg(_hash_alg);

	/* Check the set of algorithms */
	if (!essiv_supported_algorithms(ictx->essiv_cipher_name, hash_alg,
					ivsize)) {
		pr_warn("Unsupported essiv instantiation: essiv(%s,%s)\n",
			block_base->cra_name, hash_alg->base.cra_name);
		err = -EINVAL;
		goto out_free_hash;
	}

	/* record the driver name so we can instantiate this exact algo later */
	strlcpy(ictx->shash_driver_name, hash_alg->base.cra_driver_name,
		CRYPTO_MAX_ALG_NAME);

	/* Instance fields */

	err = -ENAMETOOLONG;
	if (snprintf(base->cra_name, CRYPTO_MAX_ALG_NAME,
		     "essiv(%s,%s)", block_base->cra_name,
		     hash_alg->base.cra_name) >= CRYPTO_MAX_ALG_NAME)
		goto out_free_hash;
	if (snprintf(base->cra_driver_name, CRYPTO_MAX_ALG_NAME,
		     "essiv(%s,%s)", block_base->cra_driver_name,
		     hash_alg->base.cra_driver_name) >= CRYPTO_MAX_ALG_NAME)
		goto out_free_hash;

	base->cra_flags		= block_base->cra_flags & CRYPTO_ALG_ASYNC;
	base->cra_blocksize	= block_base->cra_blocksize;
	base->cra_ctxsize	= sizeof(struct essiv_tfm_ctx);
	base->cra_alignmask	= block_base->cra_alignmask;
	base->cra_priority	= block_base->cra_priority;

	if (type == CRYPTO_ALG_TYPE_BLKCIPHER) {
		skcipher_inst->alg.setkey	= essiv_skcipher_setkey;
		skcipher_inst->alg.encrypt	= essiv_skcipher_encrypt;
		skcipher_inst->alg.decrypt	= essiv_skcipher_decrypt;
		skcipher_inst->alg.init		= essiv_skcipher_init_tfm;
		skcipher_inst->alg.exit		= essiv_skcipher_exit_tfm;

		skcipher_inst->alg.min_keysize	= crypto_skcipher_alg_min_keysize(skcipher_alg);
		skcipher_inst->alg.max_keysize	= crypto_skcipher_alg_max_keysize(skcipher_alg);
		skcipher_inst->alg.ivsize	= ivsize;
		skcipher_inst->alg.chunksize	= crypto_skcipher_alg_chunksize(skcipher_alg);
		skcipher_inst->alg.walksize	= crypto_skcipher_alg_walksize(skcipher_alg);

		skcipher_inst->free		= essiv_skcipher_free_instance;

		err = skcipher_register_instance(tmpl, skcipher_inst);
	} else {
		aead_inst->alg.setkey		= essiv_aead_setkey;
		aead_inst->alg.setauthsize	= essiv_aead_setauthsize;
		aead_inst->alg.encrypt		= essiv_aead_encrypt;
		aead_inst->alg.decrypt		= essiv_aead_decrypt;
		aead_inst->alg.init		= essiv_aead_init_tfm;
		aead_inst->alg.exit		= essiv_aead_exit_tfm;

		aead_inst->alg.ivsize		= ivsize;
		aead_inst->alg.maxauthsize	= crypto_aead_alg_maxauthsize(aead_alg);
		aead_inst->alg.chunksize	= crypto_aead_alg_chunksize(aead_alg);

		aead_inst->free			= essiv_aead_free_instance;

		err = aead_register_instance(tmpl, aead_inst);
	}

	if (err)
		goto out_free_hash;

	crypto_mod_put(_hash_alg);
	return 0;

out_free_hash:
	crypto_mod_put(_hash_alg);
out_drop_skcipher:
	if (type == CRYPTO_ALG_TYPE_BLKCIPHER)
		crypto_drop_skcipher(&ictx->u.skcipher_spawn);
	else
		crypto_drop_aead(&ictx->u.aead_spawn);
out_free_inst:
	kfree(skcipher_inst);
	kfree(aead_inst);
	return err;
}

/* essiv(cipher_name, shash_name) */
static struct crypto_template essiv_tmpl = {
	.name	= "essiv",
	.create	= essiv_create,
	.module	= THIS_MODULE,
};

static int __init essiv_module_init(void)
{
	return crypto_register_template(&essiv_tmpl);
}

static void __exit essiv_module_exit(void)
{
	crypto_unregister_template(&essiv_tmpl);
}

subsys_initcall(essiv_module_init);
module_exit(essiv_module_exit);

MODULE_DESCRIPTION("ESSIV skcipher/aead wrapper for block encryption");
MODULE_LICENSE("GPL v2");
MODULE_ALIAS_CRYPTO("essiv");