// SPDX-License-Identifier: GPL-2.0 /* * Adiantum length-preserving encryption mode * * Copyright 2018 Google LLC */ /* * Adiantum is a tweakable, length-preserving encryption mode designed for fast * and secure disk encryption, especially on CPUs without dedicated crypto * instructions. Adiantum encrypts each sector using the XChaCha12 stream * cipher, two passes of an ε-almost-∆-universal (ε-∆U) hash function based on * NH and Poly1305, and an invocation of the AES-256 block cipher on a single * 16-byte block. See the paper for details: * * Adiantum: length-preserving encryption for entry-level processors * (https://eprint.iacr.org/2018/720.pdf) * * For flexibility, this implementation also allows other ciphers: * * - Stream cipher: XChaCha12 or XChaCha20 * - Block cipher: any with a 128-bit block size and 256-bit key * * This implementation doesn't currently allow other ε-∆U hash functions, i.e. * HPolyC is not supported. This is because Adiantum is ~20% faster than HPolyC * but still provably as secure, and also the ε-∆U hash function of HBSH is * formally defined to take two inputs (tweak, message) which makes it difficult * to wrap with the crypto_shash API. Rather, some details need to be handled * here. Nevertheless, if needed in the future, support for other ε-∆U hash * functions could be added here. */ #include <crypto/b128ops.h> #include <crypto/chacha.h> #include <crypto/internal/hash.h> #include <crypto/internal/skcipher.h> #include <crypto/nhpoly1305.h> #include <crypto/scatterwalk.h> #include <linux/module.h> #include "internal.h" /* * Size of right-hand part of input data, in bytes; also the size of the block * cipher's block size and the hash function's output. */ #define BLOCKCIPHER_BLOCK_SIZE 16 /* Size of the block cipher key (K_E) in bytes */ #define BLOCKCIPHER_KEY_SIZE 32 /* Size of the hash key (K_H) in bytes */ #define HASH_KEY_SIZE (POLY1305_BLOCK_SIZE + NHPOLY1305_KEY_SIZE) /* * The specification allows variable-length tweaks, but Linux's crypto API * currently only allows algorithms to support a single length. The "natural" * tweak length for Adiantum is 16, since that fits into one Poly1305 block for * the best performance. But longer tweaks are useful for fscrypt, to avoid * needing to derive per-file keys. So instead we use two blocks, or 32 bytes. */ #define TWEAK_SIZE 32 struct adiantum_instance_ctx { struct crypto_skcipher_spawn streamcipher_spawn; struct crypto_spawn blockcipher_spawn; struct crypto_shash_spawn hash_spawn; }; struct adiantum_tfm_ctx { struct crypto_skcipher *streamcipher; struct crypto_cipher *blockcipher; struct crypto_shash *hash; struct poly1305_key header_hash_key; }; struct adiantum_request_ctx { /* * Buffer for right-hand part of data, i.e. * * P_L => P_M => C_M => C_R when encrypting, or * C_R => C_M => P_M => P_L when decrypting. * * Also used to build the IV for the stream cipher. */ union { u8 bytes[XCHACHA_IV_SIZE]; __le32 words[XCHACHA_IV_SIZE / sizeof(__le32)]; le128 bignum; /* interpret as element of Z/(2^{128}Z) */ } rbuf; bool enc; /* true if encrypting, false if decrypting */ /* * The result of the Poly1305 ε-∆U hash function applied to * (bulk length, tweak) */ le128 header_hash; /* Sub-requests, must be last */ union { struct shash_desc hash_desc; struct skcipher_request streamcipher_req; } u; }; /* * Given the XChaCha stream key K_S, derive the block cipher key K_E and the * hash key K_H as follows: * * K_E || K_H || ... = XChaCha(key=K_S, nonce=1||0^191) * * Note that this denotes using bits from the XChaCha keystream, which here we * get indirectly by encrypting a buffer containing all 0's. */ static int adiantum_setkey(struct crypto_skcipher *tfm, const u8 *key, unsigned int keylen) { struct adiantum_tfm_ctx *tctx = crypto_skcipher_ctx(tfm); struct { u8 iv[XCHACHA_IV_SIZE]; u8 derived_keys[BLOCKCIPHER_KEY_SIZE + HASH_KEY_SIZE]; struct scatterlist sg; struct crypto_wait wait; struct skcipher_request req; /* must be last */ } *data; u8 *keyp; int err; /* Set the stream cipher key (K_S) */ crypto_skcipher_clear_flags(tctx->streamcipher, CRYPTO_TFM_REQ_MASK); crypto_skcipher_set_flags(tctx->streamcipher, crypto_skcipher_get_flags(tfm) & CRYPTO_TFM_REQ_MASK); err = crypto_skcipher_setkey(tctx->streamcipher, key, keylen); crypto_skcipher_set_flags(tfm, crypto_skcipher_get_flags(tctx->streamcipher) & CRYPTO_TFM_RES_MASK); if (err) return err; /* Derive the subkeys */ data = kzalloc(sizeof(*data) + crypto_skcipher_reqsize(tctx->streamcipher), GFP_KERNEL); if (!data) return -ENOMEM; data->iv[0] = 1; sg_init_one(&data->sg, data->derived_keys, sizeof(data->derived_keys)); crypto_init_wait(&data->wait); skcipher_request_set_tfm(&data->req, tctx->streamcipher); skcipher_request_set_callback(&data->req, CRYPTO_TFM_REQ_MAY_SLEEP | CRYPTO_TFM_REQ_MAY_BACKLOG, crypto_req_done, &data->wait); skcipher_request_set_crypt(&data->req, &data->sg, &data->sg, sizeof(data->derived_keys), data->iv); err = crypto_wait_req(crypto_skcipher_encrypt(&data->req), &data->wait); if (err) goto out; keyp = data->derived_keys; /* Set the block cipher key (K_E) */ crypto_cipher_clear_flags(tctx->blockcipher, CRYPTO_TFM_REQ_MASK); crypto_cipher_set_flags(tctx->blockcipher, crypto_skcipher_get_flags(tfm) & CRYPTO_TFM_REQ_MASK); err = crypto_cipher_setkey(tctx->blockcipher, keyp, BLOCKCIPHER_KEY_SIZE); crypto_skcipher_set_flags(tfm, crypto_cipher_get_flags(tctx->blockcipher) & CRYPTO_TFM_RES_MASK); if (err) goto out; keyp += BLOCKCIPHER_KEY_SIZE; /* Set the hash key (K_H) */ poly1305_core_setkey(&tctx->header_hash_key, keyp); keyp += POLY1305_BLOCK_SIZE; crypto_shash_clear_flags(tctx->hash, CRYPTO_TFM_REQ_MASK); crypto_shash_set_flags(tctx->hash, crypto_skcipher_get_flags(tfm) & CRYPTO_TFM_REQ_MASK); err = crypto_shash_setkey(tctx->hash, keyp, NHPOLY1305_KEY_SIZE); crypto_skcipher_set_flags(tfm, crypto_shash_get_flags(tctx->hash) & CRYPTO_TFM_RES_MASK); keyp += NHPOLY1305_KEY_SIZE; WARN_ON(keyp != &data->derived_keys[ARRAY_SIZE(data->derived_keys)]); out: kzfree(data); return err; } /* Addition in Z/(2^{128}Z) */ static inline void le128_add(le128 *r, const le128 *v1, const le128 *v2) { u64 x = le64_to_cpu(v1->b); u64 y = le64_to_cpu(v2->b); r->b = cpu_to_le64(x + y); r->a = cpu_to_le64(le64_to_cpu(v1->a) + le64_to_cpu(v2->a) + (x + y < x)); } /* Subtraction in Z/(2^{128}Z) */ static inline void le128_sub(le128 *r, const le128 *v1, const le128 *v2) { u64 x = le64_to_cpu(v1->b); u64 y = le64_to_cpu(v2->b); r->b = cpu_to_le64(x - y); r->a = cpu_to_le64(le64_to_cpu(v1->a) - le64_to_cpu(v2->a) - (x - y > x)); } /* * Apply the Poly1305 ε-∆U hash function to (bulk length, tweak) and save the * result to rctx->header_hash. This is the calculation * * H_T ← Poly1305_{K_T}(bin_{128}(|L|) || T) * * from the procedure in section 6.4 of the Adiantum paper. The resulting value * is reused in both the first and second hash steps. Specifically, it's added * to the result of an independently keyed ε-∆U hash function (for equal length * inputs only) taken over the left-hand part (the "bulk") of the message, to * give the overall Adiantum hash of the (tweak, left-hand part) pair. */ static void adiantum_hash_header(struct skcipher_request *req) { struct crypto_skcipher *tfm = crypto_skcipher_reqtfm(req); const struct adiantum_tfm_ctx *tctx = crypto_skcipher_ctx(tfm); struct adiantum_request_ctx *rctx = skcipher_request_ctx(req); const unsigned int bulk_len = req->cryptlen - BLOCKCIPHER_BLOCK_SIZE; struct { __le64 message_bits; __le64 padding; } header = { .message_bits = cpu_to_le64((u64)bulk_len * 8) }; struct poly1305_state state; poly1305_core_init(&state); BUILD_BUG_ON(sizeof(header) % POLY1305_BLOCK_SIZE != 0); poly1305_core_blocks(&state, &tctx->header_hash_key, &header, sizeof(header) / POLY1305_BLOCK_SIZE); BUILD_BUG_ON(TWEAK_SIZE % POLY1305_BLOCK_SIZE != 0); poly1305_core_blocks(&state, &tctx->header_hash_key, req->iv, TWEAK_SIZE / POLY1305_BLOCK_SIZE); poly1305_core_emit(&state, &rctx->header_hash); } /* Hash the left-hand part (the "bulk") of the message using NHPoly1305 */ static int adiantum_hash_message(struct skcipher_request *req, struct scatterlist *sgl, le128 *digest) { struct crypto_skcipher *tfm = crypto_skcipher_reqtfm(req); const struct adiantum_tfm_ctx *tctx = crypto_skcipher_ctx(tfm); struct adiantum_request_ctx *rctx = skcipher_request_ctx(req); const unsigned int bulk_len = req->cryptlen - BLOCKCIPHER_BLOCK_SIZE; struct shash_desc *hash_desc = &rctx->u.hash_desc; struct sg_mapping_iter miter; unsigned int i, n; int err; hash_desc->tfm = tctx->hash; hash_desc->flags = 0; err = crypto_shash_init(hash_desc); if (err) return err; sg_miter_start(&miter, sgl, sg_nents(sgl), SG_MITER_FROM_SG | SG_MITER_ATOMIC); for (i = 0; i < bulk_len; i += n) { sg_miter_next(&miter); n = min_t(unsigned int, miter.length, bulk_len - i); err = crypto_shash_update(hash_desc, miter.addr, n); if (err) break; } sg_miter_stop(&miter); if (err) return err; return crypto_shash_final(hash_desc, (u8 *)digest); } /* Continue Adiantum encryption/decryption after the stream cipher step */ static int adiantum_finish(struct skcipher_request *req) { struct crypto_skcipher *tfm = crypto_skcipher_reqtfm(req); const struct adiantum_tfm_ctx *tctx = crypto_skcipher_ctx(tfm); struct adiantum_request_ctx *rctx = skcipher_request_ctx(req); const unsigned int bulk_len = req->cryptlen - BLOCKCIPHER_BLOCK_SIZE; le128 digest; int err; /* If decrypting, decrypt C_M with the block cipher to get P_M */ if (!rctx->enc) crypto_cipher_decrypt_one(tctx->blockcipher, rctx->rbuf.bytes, rctx->rbuf.bytes); /* * Second hash step * enc: C_R = C_M - H_{K_H}(T, C_L) * dec: P_R = P_M - H_{K_H}(T, P_L) */ err = adiantum_hash_message(req, req->dst, &digest); if (err) return err; le128_add(&digest, &digest, &rctx->header_hash); le128_sub(&rctx->rbuf.bignum, &rctx->rbuf.bignum, &digest); scatterwalk_map_and_copy(&rctx->rbuf.bignum, req->dst, bulk_len, BLOCKCIPHER_BLOCK_SIZE, 1); return 0; } static void adiantum_streamcipher_done(struct crypto_async_request *areq, int err) { struct skcipher_request *req = areq->data; if (!err) err = adiantum_finish(req); skcipher_request_complete(req, err); } static int adiantum_crypt(struct skcipher_request *req, bool enc) { struct crypto_skcipher *tfm = crypto_skcipher_reqtfm(req); const struct adiantum_tfm_ctx *tctx = crypto_skcipher_ctx(tfm); struct adiantum_request_ctx *rctx = skcipher_request_ctx(req); const unsigned int bulk_len = req->cryptlen - BLOCKCIPHER_BLOCK_SIZE; unsigned int stream_len; le128 digest; int err; if (req->cryptlen < BLOCKCIPHER_BLOCK_SIZE) return -EINVAL; rctx->enc = enc; /* * First hash step * enc: P_M = P_R + H_{K_H}(T, P_L) * dec: C_M = C_R + H_{K_H}(T, C_L) */ adiantum_hash_header(req); err = adiantum_hash_message(req, req->src, &digest); if (err) return err; le128_add(&digest, &digest, &rctx->header_hash); scatterwalk_map_and_copy(&rctx->rbuf.bignum, req->src, bulk_len, BLOCKCIPHER_BLOCK_SIZE, 0); le128_add(&rctx->rbuf.bignum, &rctx->rbuf.bignum, &digest); /* If encrypting, encrypt P_M with the block cipher to get C_M */ if (enc) crypto_cipher_encrypt_one(tctx->blockcipher, rctx->rbuf.bytes, rctx->rbuf.bytes); /* Initialize the rest of the XChaCha IV (first part is C_M) */ BUILD_BUG_ON(BLOCKCIPHER_BLOCK_SIZE != 16); BUILD_BUG_ON(XCHACHA_IV_SIZE != 32); /* nonce || stream position */ rctx->rbuf.words[4] = cpu_to_le32(1); rctx->rbuf.words[5] = 0; rctx->rbuf.words[6] = 0; rctx->rbuf.words[7] = 0; /* * XChaCha needs to be done on all the data except the last 16 bytes; * for disk encryption that usually means 4080 or 496 bytes. But ChaCha * implementations tend to be most efficient when passed a whole number * of 64-byte ChaCha blocks, or sometimes even a multiple of 256 bytes. * And here it doesn't matter whether the last 16 bytes are written to, * as the second hash step will overwrite them. Thus, round the XChaCha * length up to the next 64-byte boundary if possible. */ stream_len = bulk_len; if (round_up(stream_len, CHACHA_BLOCK_SIZE) <= req->cryptlen) stream_len = round_up(stream_len, CHACHA_BLOCK_SIZE); skcipher_request_set_tfm(&rctx->u.streamcipher_req, tctx->streamcipher); skcipher_request_set_crypt(&rctx->u.streamcipher_req, req->src, req->dst, stream_len, &rctx->rbuf); skcipher_request_set_callback(&rctx->u.streamcipher_req, req->base.flags, adiantum_streamcipher_done, req); return crypto_skcipher_encrypt(&rctx->u.streamcipher_req) ?: adiantum_finish(req); } static int adiantum_encrypt(struct skcipher_request *req) { return adiantum_crypt(req, true); } static int adiantum_decrypt(struct skcipher_request *req) { return adiantum_crypt(req, false); } static int adiantum_init_tfm(struct crypto_skcipher *tfm) { struct skcipher_instance *inst = skcipher_alg_instance(tfm); struct adiantum_instance_ctx *ictx = skcipher_instance_ctx(inst); struct adiantum_tfm_ctx *tctx = crypto_skcipher_ctx(tfm); struct crypto_skcipher *streamcipher; struct crypto_cipher *blockcipher; struct crypto_shash *hash; unsigned int subreq_size; int err; streamcipher = crypto_spawn_skcipher(&ictx->streamcipher_spawn); if (IS_ERR(streamcipher)) return PTR_ERR(streamcipher); blockcipher = crypto_spawn_cipher(&ictx->blockcipher_spawn); if (IS_ERR(blockcipher)) { err = PTR_ERR(blockcipher); goto err_free_streamcipher; } hash = crypto_spawn_shash(&ictx->hash_spawn); if (IS_ERR(hash)) { err = PTR_ERR(hash); goto err_free_blockcipher; } tctx->streamcipher = streamcipher; tctx->blockcipher = blockcipher; tctx->hash = hash; BUILD_BUG_ON(offsetofend(struct adiantum_request_ctx, u) != sizeof(struct adiantum_request_ctx)); subreq_size = max(FIELD_SIZEOF(struct adiantum_request_ctx, u.hash_desc) + crypto_shash_descsize(hash), FIELD_SIZEOF(struct adiantum_request_ctx, u.streamcipher_req) + crypto_skcipher_reqsize(streamcipher)); crypto_skcipher_set_reqsize(tfm, offsetof(struct adiantum_request_ctx, u) + subreq_size); return 0; err_free_blockcipher: crypto_free_cipher(blockcipher); err_free_streamcipher: crypto_free_skcipher(streamcipher); return err; } static void adiantum_exit_tfm(struct crypto_skcipher *tfm) { struct adiantum_tfm_ctx *tctx = crypto_skcipher_ctx(tfm); crypto_free_skcipher(tctx->streamcipher); crypto_free_cipher(tctx->blockcipher); crypto_free_shash(tctx->hash); } static void adiantum_free_instance(struct skcipher_instance *inst) { struct adiantum_instance_ctx *ictx = skcipher_instance_ctx(inst); crypto_drop_skcipher(&ictx->streamcipher_spawn); crypto_drop_spawn(&ictx->blockcipher_spawn); crypto_drop_shash(&ictx->hash_spawn); kfree(inst); } /* * Check for a supported set of inner algorithms. * See the comment at the beginning of this file. */ static bool adiantum_supported_algorithms(struct skcipher_alg *streamcipher_alg, struct crypto_alg *blockcipher_alg, struct shash_alg *hash_alg) { if (strcmp(streamcipher_alg->base.cra_name, "xchacha12") != 0 && strcmp(streamcipher_alg->base.cra_name, "xchacha20") != 0) return false; if (blockcipher_alg->cra_cipher.cia_min_keysize > BLOCKCIPHER_KEY_SIZE || blockcipher_alg->cra_cipher.cia_max_keysize < BLOCKCIPHER_KEY_SIZE) return false; if (blockcipher_alg->cra_blocksize != BLOCKCIPHER_BLOCK_SIZE) return false; if (strcmp(hash_alg->base.cra_name, "nhpoly1305") != 0) return false; return true; } static int adiantum_create(struct crypto_template *tmpl, struct rtattr **tb) { struct crypto_attr_type *algt; const char *streamcipher_name; const char *blockcipher_name; const char *nhpoly1305_name; struct skcipher_instance *inst; struct adiantum_instance_ctx *ictx; struct skcipher_alg *streamcipher_alg; struct crypto_alg *blockcipher_alg; struct crypto_alg *_hash_alg; struct shash_alg *hash_alg; int err; algt = crypto_get_attr_type(tb); if (IS_ERR(algt)) return PTR_ERR(algt); if ((algt->type ^ CRYPTO_ALG_TYPE_SKCIPHER) & algt->mask) return -EINVAL; streamcipher_name = crypto_attr_alg_name(tb[1]); if (IS_ERR(streamcipher_name)) return PTR_ERR(streamcipher_name); blockcipher_name = crypto_attr_alg_name(tb[2]); if (IS_ERR(blockcipher_name)) return PTR_ERR(blockcipher_name); nhpoly1305_name = crypto_attr_alg_name(tb[3]); if (nhpoly1305_name == ERR_PTR(-ENOENT)) nhpoly1305_name = "nhpoly1305"; if (IS_ERR(nhpoly1305_name)) return PTR_ERR(nhpoly1305_name); inst = kzalloc(sizeof(*inst) + sizeof(*ictx), GFP_KERNEL); if (!inst) return -ENOMEM; ictx = skcipher_instance_ctx(inst); /* Stream cipher, e.g. "xchacha12" */ crypto_set_skcipher_spawn(&ictx->streamcipher_spawn, skcipher_crypto_instance(inst)); err = crypto_grab_skcipher(&ictx->streamcipher_spawn, streamcipher_name, 0, crypto_requires_sync(algt->type, algt->mask)); if (err) goto out_free_inst; streamcipher_alg = crypto_spawn_skcipher_alg(&ictx->streamcipher_spawn); /* Block cipher, e.g. "aes" */ crypto_set_spawn(&ictx->blockcipher_spawn, skcipher_crypto_instance(inst)); err = crypto_grab_spawn(&ictx->blockcipher_spawn, blockcipher_name, CRYPTO_ALG_TYPE_CIPHER, CRYPTO_ALG_TYPE_MASK); if (err) goto out_drop_streamcipher; blockcipher_alg = ictx->blockcipher_spawn.alg; /* NHPoly1305 ε-∆U hash function */ _hash_alg = crypto_alg_mod_lookup(nhpoly1305_name, CRYPTO_ALG_TYPE_SHASH, CRYPTO_ALG_TYPE_MASK); if (IS_ERR(_hash_alg)) { err = PTR_ERR(_hash_alg); goto out_drop_blockcipher; } hash_alg = __crypto_shash_alg(_hash_alg); err = crypto_init_shash_spawn(&ictx->hash_spawn, hash_alg, skcipher_crypto_instance(inst)); if (err) goto out_put_hash; /* Check the set of algorithms */ if (!adiantum_supported_algorithms(streamcipher_alg, blockcipher_alg, hash_alg)) { pr_warn("Unsupported Adiantum instantiation: (%s,%s,%s)\n", streamcipher_alg->base.cra_name, blockcipher_alg->cra_name, hash_alg->base.cra_name); err = -EINVAL; goto out_drop_hash; } /* Instance fields */ err = -ENAMETOOLONG; if (snprintf(inst->alg.base.cra_name, CRYPTO_MAX_ALG_NAME, "adiantum(%s,%s)", streamcipher_alg->base.cra_name, blockcipher_alg->cra_name) >= CRYPTO_MAX_ALG_NAME) goto out_drop_hash; if (snprintf(inst->alg.base.cra_driver_name, CRYPTO_MAX_ALG_NAME, "adiantum(%s,%s,%s)", streamcipher_alg->base.cra_driver_name, blockcipher_alg->cra_driver_name, hash_alg->base.cra_driver_name) >= CRYPTO_MAX_ALG_NAME) goto out_drop_hash; inst->alg.base.cra_flags = streamcipher_alg->base.cra_flags & CRYPTO_ALG_ASYNC; inst->alg.base.cra_blocksize = BLOCKCIPHER_BLOCK_SIZE; inst->alg.base.cra_ctxsize = sizeof(struct adiantum_tfm_ctx); inst->alg.base.cra_alignmask = streamcipher_alg->base.cra_alignmask | hash_alg->base.cra_alignmask; /* * The block cipher is only invoked once per message, so for long * messages (e.g. sectors for disk encryption) its performance doesn't * matter as much as that of the stream cipher and hash function. Thus, * weigh the block cipher's ->cra_priority less. */ inst->alg.base.cra_priority = (4 * streamcipher_alg->base.cra_priority + 2 * hash_alg->base.cra_priority + blockcipher_alg->cra_priority) / 7; inst->alg.setkey = adiantum_setkey; inst->alg.encrypt = adiantum_encrypt; inst->alg.decrypt = adiantum_decrypt; inst->alg.init = adiantum_init_tfm; inst->alg.exit = adiantum_exit_tfm; inst->alg.min_keysize = crypto_skcipher_alg_min_keysize(streamcipher_alg); inst->alg.max_keysize = crypto_skcipher_alg_max_keysize(streamcipher_alg); inst->alg.ivsize = TWEAK_SIZE; inst->free = adiantum_free_instance; err = skcipher_register_instance(tmpl, inst); if (err) goto out_drop_hash; crypto_mod_put(_hash_alg); return 0; out_drop_hash: crypto_drop_shash(&ictx->hash_spawn); out_put_hash: crypto_mod_put(_hash_alg); out_drop_blockcipher: crypto_drop_spawn(&ictx->blockcipher_spawn); out_drop_streamcipher: crypto_drop_skcipher(&ictx->streamcipher_spawn); out_free_inst: kfree(inst); return err; } /* adiantum(streamcipher_name, blockcipher_name [, nhpoly1305_name]) */ static struct crypto_template adiantum_tmpl = { .name = "adiantum", .create = adiantum_create, .module = THIS_MODULE, }; static int __init adiantum_module_init(void) { return crypto_register_template(&adiantum_tmpl); } static void __exit adiantum_module_exit(void) { crypto_unregister_template(&adiantum_tmpl); } module_init(adiantum_module_init); module_exit(adiantum_module_exit); MODULE_DESCRIPTION("Adiantum length-preserving encryption mode"); MODULE_LICENSE("GPL v2"); MODULE_AUTHOR("Eric Biggers <ebiggers@google.com>"); MODULE_ALIAS_CRYPTO("adiantum");