Support for the Ruby 2.4 series has ended. See here for reference.
Object
Provides symmetric algorithms for encryption and decryption. The algorithms that are available depend on the particular version of OpenSSL
that is installed.
A list of supported algorithms can be obtained by
puts OpenSSL::Cipher.ciphers
Cipher
¶ ↑There are several ways to create a Cipher
instance. Generally, a Cipher
algorithm is categorized by its name, the key length in bits and the cipher mode to be used. The most generic way to create a Cipher
is the following
cipher = OpenSSL::Cipher.new('<name>-<key length>-<mode>')
That is, a string consisting of the hyphenated concatenation of the individual components name, key length and mode. Either all uppercase or all lowercase strings may be used, for example:
cipher = OpenSSL::Cipher.new('AES-128-CBC')
For each algorithm supported, there is a class defined under the Cipher
class that goes by the name of the cipher, e.g. to obtain an instance of AES, you could also use
# these are equivalent cipher = OpenSSL::Cipher::AES.new(128, :CBC) cipher = OpenSSL::Cipher::AES.new(128, 'CBC') cipher = OpenSSL::Cipher::AES.new('128-CBC')
Finally, due to its wide-spread use, there are also extra classes defined for the different key sizes of AES
cipher = OpenSSL::Cipher::AES128.new(:CBC) cipher = OpenSSL::Cipher::AES192.new(:CBC) cipher = OpenSSL::Cipher::AES256.new(:CBC)
Encryption and decryption are often very similar operations for symmetric algorithms, this is reflected by not having to choose different classes for either operation, both can be done using the same class. Still, after obtaining a Cipher
instance, we need to tell the instance what it is that we intend to do with it, so we need to call either
cipher.encrypt
or
cipher.decrypt
on the Cipher
instance. This should be the first call after creating the instance, otherwise configuration that has already been set could get lost in the process.
Symmetric encryption requires a key that is the same for the encrypting and for the decrypting party and after initial key establishment should be kept as private information. There are a lot of ways to create insecure keys, the most notable is to simply take a password as the key without processing the password further. A simple and secure way to create a key for a particular Cipher
is
cipher = OpenSSL::AES256.new(:CFB) cipher.encrypt key = cipher.random_key # also sets the generated key on the Cipher
If you absolutely need to use passwords as encryption keys, you should use Password-Based Key Derivation Function 2 (PBKDF2) by generating the key with the help of the functionality provided by OpenSSL::PKCS5.pbkdf2_hmac_sha1
or OpenSSL::PKCS5.pbkdf2_hmac
.
Although there is Cipher#pkcs5_keyivgen
, its use is deprecated and it should only be used in legacy applications because it does not use the newer PKCS#5 v2 algorithms.
The cipher modes CBC, CFB, OFB and CTR all need an “initialization vector”, or short, IV. ECB mode is the only mode that does not require an IV, but there is almost no legitimate use case for this mode because of the fact that it does not sufficiently hide plaintext patterns. Therefore
You should never use ECB mode unless you are absolutely sure that you absolutely need it
Because of this, you will end up with a mode that explicitly requires an IV in any case. Although the IV can be seen as public information, i.e. it may be transmitted in public once generated, it should still stay unpredictable to prevent certain kinds of attacks. Therefore, ideally
Always create a secure random IV for every encryption of your Cipher
A new, random IV should be created for every encryption of data. Think of the IV as a nonce (number used once) - it's public but random and unpredictable. A secure random IV can be created as follows
cipher = ... cipher.encrypt key = cipher.random_key iv = cipher.random_iv # also sets the generated IV on the Cipher
Although the key is generally a random value, too, it is a bad choice as an IV. There are elaborate ways how an attacker can take advantage of such an IV. As a general rule of thumb, exposing the key directly or indirectly should be avoided at all cost and exceptions only be made with good reason.
Cipher#final
¶ ↑ECB (which should not be used) and CBC are both block-based modes. This means that unlike for the other streaming-based modes, they operate on fixed-size blocks of data, and therefore they require a “finalization” step to produce or correctly decrypt the last block of data by appropriately handling some form of padding. Therefore it is essential to add the output of OpenSSL::Cipher#final
to your encryption/decryption buffer or you will end up with decryption errors or truncated data.
Although this is not really necessary for streaming-mode ciphers, it is still recommended to apply the same pattern of adding the output of Cipher#final
there as well - it also enables you to switch between modes more easily in the future.
data = "Very, very confidential data" cipher = OpenSSL::Cipher::AES.new(128, :CBC) cipher.encrypt key = cipher.random_key iv = cipher.random_iv encrypted = cipher.update(data) + cipher.final ... decipher = OpenSSL::Cipher::AES.new(128, :CBC) decipher.decrypt decipher.key = key decipher.iv = iv plain = decipher.update(encrypted) + decipher.final puts data == plain #=> true
If the OpenSSL
version used supports it, an Authenticated Encryption mode (such as GCM or CCM) should always be preferred over any unauthenticated mode. Currently, OpenSSL
supports AE only in combination with Associated Data (AEAD) where additional associated data is included in the encryption process to compute a tag at the end of the encryption. This tag will also be used in the decryption process and by verifying its validity, the authenticity of a given ciphertext is established.
This is superior to unauthenticated modes in that it allows to detect if somebody effectively changed the ciphertext after it had been encrypted. This prevents malicious modifications of the ciphertext that could otherwise be exploited to modify ciphertexts in ways beneficial to potential attackers.
An associated data is used where there is additional information, such as headers or some metadata, that must be also authenticated but not necessarily need to be encrypted. If no associated data is needed for encryption and later decryption, the OpenSSL
library still requires a value to be set - “” may be used in case none is available.
An example using the GCM (Galois/Counter Mode). You have 16 bytes key
, 12 bytes (96 bits) nonce
and the associated data auth_data
. Be sure not to reuse the key
and nonce
pair. Reusing an nonce ruins the security gurantees of GCM mode.
cipher = OpenSSL::Cipher::AES.new(128, :GCM).encrypt cipher.key = key cipher.iv = nonce cipher.auth_data = auth_data encrypted = cipher.update(data) + cipher.final tag = cipher.auth_tag # produces 16 bytes tag by default
Now you are the receiver. You know the key
and have received nonce
, auth_data
, encrypted
and tag
through an untrusted network. Note that GCM accepts an arbitrary length tag between 1 and 16 bytes. You may additionally need to check that the received tag has the correct length, or you allow attackers to forge a valid single byte tag for the tampered ciphertext with a probability of 1/256.
raise "tag is truncated!" unless tag.bytesize == 16 decipher = OpenSSL::Cipher::AES.new(128, :GCM).decrypt decipher.key = key decipher.iv = nonce decipher.auth_tag = tag decipher.auth_data = auth_data decrypted = decipher.update(encrypted) + decipher.final puts data == decrypted #=> true
Returns the names of all available ciphers in an array.
static VALUE ossl_s_ciphers(VALUE self) { VALUE ary; ary = rb_ary_new(); OBJ_NAME_do_all_sorted(OBJ_NAME_TYPE_CIPHER_METH, (void(*)(const OBJ_NAME*,void*))add_cipher_name_to_ary, (void*)ary); return ary; }
The string must contain a valid cipher name like “AES-128-CBC” or “3DES”.
A list of cipher names is available by calling OpenSSL::Cipher.ciphers
.
static VALUE ossl_cipher_initialize(VALUE self, VALUE str) { EVP_CIPHER_CTX *ctx; const EVP_CIPHER *cipher; char *name; name = StringValueCStr(str); GetCipherInit(self, ctx); if (ctx) { ossl_raise(rb_eRuntimeError, "Cipher already inititalized!"); } AllocCipher(self, ctx); if (!(cipher = EVP_get_cipherbyname(name))) { ossl_raise(rb_eRuntimeError, "unsupported cipher algorithm (%"PRIsVALUE")", str); } if (EVP_CipherInit_ex(ctx, cipher, NULL, NULL, NULL, -1) != 1) ossl_raise(eCipherError, NULL); return self; }
Sets the cipher's additional authenticated data. This field must be set when using AEAD cipher modes such as GCM or CCM. If no associated data shall be used, this method must still be called with a value of “”. The contents of this field should be non-sensitive data which will be added to the ciphertext to generate the authentication tag which validates the contents of the ciphertext.
The AAD must be set prior to encryption or decryption. In encryption mode, it must be set after calling Cipher#encrypt
and setting Cipher#key=
and Cipher#iv=
. When decrypting, the authenticated data must be set after key, iv and especially after the authentication tag has been set. I.e. set it only after calling Cipher#decrypt
, Cipher#key=
, Cipher#iv=
and Cipher#auth_tag=
first.
static VALUE ossl_cipher_set_auth_data(VALUE self, VALUE data) { EVP_CIPHER_CTX *ctx; unsigned char *in; long in_len, out_len; StringValue(data); in = (unsigned char *) RSTRING_PTR(data); in_len = RSTRING_LEN(data); GetCipher(self, ctx); if (!ossl_cipher_update_long(ctx, NULL, &out_len, in, in_len)) ossl_raise(eCipherError, "couldn't set additional authenticated data"); return data; }
Gets the authentication tag generated by Authenticated Encryption Cipher
modes (GCM for example). This tag may be stored along with the ciphertext, then set on the decryption cipher to authenticate the contents of the ciphertext against changes. If the optional integer parameter tag_len
is given, the returned tag will be tag_len
bytes long. If the parameter is omitted, the default length of 16 bytes or the length previously set by auth_tag_len=
will be used. For maximum security, the longest possible should be chosen.
The tag may only be retrieved after calling Cipher#final
.
static VALUE ossl_cipher_get_auth_tag(int argc, VALUE *argv, VALUE self) { VALUE vtag_len, ret; EVP_CIPHER_CTX *ctx; int tag_len = 16; rb_scan_args(argc, argv, "01", &vtag_len); if (NIL_P(vtag_len)) vtag_len = rb_attr_get(self, id_auth_tag_len); if (!NIL_P(vtag_len)) tag_len = NUM2INT(vtag_len); GetCipher(self, ctx); if (!(EVP_CIPHER_CTX_flags(ctx) & EVP_CIPH_FLAG_AEAD_CIPHER)) ossl_raise(eCipherError, "authentication tag not supported by this cipher"); ret = rb_str_new(NULL, tag_len); if (!EVP_CIPHER_CTX_ctrl(ctx, EVP_CTRL_AEAD_GET_TAG, tag_len, RSTRING_PTR(ret))) ossl_raise(eCipherError, "retrieving the authentication tag failed"); return ret; }
Sets the authentication tag to verify the contents of the ciphertext. The tag must be set after calling Cipher#decrypt
, Cipher#key=
and Cipher#iv=
, but before assigning the associated authenticated data using Cipher#auth_data=
and of course, before decrypting any of the ciphertext. After all decryption is performed, the tag is verified automatically in the call to Cipher#final
.
For OCB mode, the tag length must be supplied with auth_tag_len=
beforehand.
static VALUE ossl_cipher_set_auth_tag(VALUE self, VALUE vtag) { EVP_CIPHER_CTX *ctx; unsigned char *tag; int tag_len; StringValue(vtag); tag = (unsigned char *) RSTRING_PTR(vtag); tag_len = RSTRING_LENINT(vtag); GetCipher(self, ctx); if (!(EVP_CIPHER_CTX_flags(ctx) & EVP_CIPH_FLAG_AEAD_CIPHER)) ossl_raise(eCipherError, "authentication tag not supported by this cipher"); if (!EVP_CIPHER_CTX_ctrl(ctx, EVP_CTRL_AEAD_SET_TAG, tag_len, tag)) ossl_raise(eCipherError, "unable to set AEAD tag"); return vtag; }
Sets the length of the authentication tag to be generated or to be given for AEAD ciphers that requires it as in input parameter. Note that not all AEAD ciphers support this method.
In OCB mode, the length must be supplied both when encrypting and when decrypting, and must be before specifying an IV.
static VALUE ossl_cipher_set_auth_tag_len(VALUE self, VALUE vlen) { int tag_len = NUM2INT(vlen); EVP_CIPHER_CTX *ctx; GetCipher(self, ctx); if (!(EVP_CIPHER_CTX_flags(ctx) & EVP_CIPH_FLAG_AEAD_CIPHER)) ossl_raise(eCipherError, "AEAD not supported by this cipher"); if (!EVP_CIPHER_CTX_ctrl(ctx, EVP_CTRL_AEAD_SET_TAG, tag_len, NULL)) ossl_raise(eCipherError, "unable to set authentication tag length"); /* for #auth_tag */ rb_ivar_set(self, id_auth_tag_len, INT2NUM(tag_len)); return vlen; }
Indicated whether this Cipher
instance uses an Authenticated Encryption mode.
static VALUE ossl_cipher_is_authenticated(VALUE self) { EVP_CIPHER_CTX *ctx; GetCipher(self, ctx); #if defined(HAVE_AUTHENTICATED_ENCRYPTION) return (EVP_CIPHER_CTX_flags(ctx) & EVP_CIPH_FLAG_AEAD_CIPHER) ? Qtrue : Qfalse; #else return Qfalse; #endif }
Returns the size in bytes of the blocks on which this Cipher
operates on.
static VALUE ossl_cipher_block_size(VALUE self) { EVP_CIPHER_CTX *ctx; GetCipher(self, ctx); return INT2NUM(EVP_CIPHER_CTX_block_size(ctx)); }
Initializes the Cipher
for decryption.
Make sure to call Cipher#encrypt
or Cipher#decrypt
before using any of the following methods:
Internally calls EVP_CipherInit_ex(ctx, NULL, NULL, NULL, NULL, 0).
static VALUE ossl_cipher_decrypt(int argc, VALUE *argv, VALUE self) { return ossl_cipher_init(argc, argv, self, 0); }
Initializes the Cipher
for encryption.
Make sure to call Cipher#encrypt
or Cipher#decrypt
before using any of the following methods:
Internally calls EVP_CipherInit_ex(ctx, NULL, NULL, NULL, NULL, 1).
static VALUE ossl_cipher_encrypt(int argc, VALUE *argv, VALUE self) { return ossl_cipher_init(argc, argv, self, 1); }
Returns the remaining data held in the cipher object. Further calls to Cipher#update
or Cipher#final
will return garbage. This call should always be made as the last call of an encryption or decryption operation, after after having fed the entire plaintext or ciphertext to the Cipher
instance.
If an authenticated cipher was used, a CipherError
is raised if the tag could not be authenticated successfully. Only call this method after setting the authentication tag and passing the entire contents of the ciphertext into the cipher.
static VALUE ossl_cipher_final(VALUE self) { EVP_CIPHER_CTX *ctx; int out_len; VALUE str; GetCipher(self, ctx); str = rb_str_new(0, EVP_CIPHER_CTX_block_size(ctx)); if (!EVP_CipherFinal_ex(ctx, (unsigned char *)RSTRING_PTR(str), &out_len)) ossl_raise(eCipherError, NULL); assert(out_len <= RSTRING_LEN(str)); rb_str_set_len(str, out_len); return str; }
Sets the cipher IV. Please note that since you should never be using ECB mode, an IV is always explicitly required and should be set prior to encryption. The IV itself can be safely transmitted in public, but it should be unpredictable to prevent certain kinds of attacks. You may use Cipher#random_iv
to create a secure random IV.
Only call this method after calling Cipher#encrypt
or Cipher#decrypt
.
static VALUE ossl_cipher_set_iv(VALUE self, VALUE iv) { EVP_CIPHER_CTX *ctx; int iv_len = 0; StringValue(iv); GetCipher(self, ctx); #if defined(HAVE_AUTHENTICATED_ENCRYPTION) if (EVP_CIPHER_CTX_flags(ctx) & EVP_CIPH_FLAG_AEAD_CIPHER) iv_len = (int)(VALUE)EVP_CIPHER_CTX_get_app_data(ctx); #endif if (!iv_len) iv_len = EVP_CIPHER_CTX_iv_length(ctx); if (RSTRING_LEN(iv) != iv_len) ossl_raise(rb_eArgError, "iv must be %d bytes", iv_len); if (EVP_CipherInit_ex(ctx, NULL, NULL, NULL, (unsigned char *)RSTRING_PTR(iv), -1) != 1) ossl_raise(eCipherError, NULL); return iv; }
Returns the expected length in bytes for an IV for this Cipher
.
static VALUE ossl_cipher_iv_length(VALUE self) { EVP_CIPHER_CTX *ctx; int len = 0; GetCipher(self, ctx); #if defined(HAVE_AUTHENTICATED_ENCRYPTION) if (EVP_CIPHER_CTX_flags(ctx) & EVP_CIPH_FLAG_AEAD_CIPHER) len = (int)(VALUE)EVP_CIPHER_CTX_get_app_data(ctx); #endif if (!len) len = EVP_CIPHER_CTX_iv_length(ctx); return INT2NUM(len); }
Sets the IV/nonce length of the Cipher
. Normally block ciphers don't allow changing the IV length, but some make use of IV for 'nonce'. You may need this for interoperability with other applications.
static VALUE ossl_cipher_set_iv_length(VALUE self, VALUE iv_length) { int len = NUM2INT(iv_length); EVP_CIPHER_CTX *ctx; GetCipher(self, ctx); if (!(EVP_CIPHER_CTX_flags(ctx) & EVP_CIPH_FLAG_AEAD_CIPHER)) ossl_raise(eCipherError, "cipher does not support AEAD"); if (!EVP_CIPHER_CTX_ctrl(ctx, EVP_CTRL_AEAD_SET_IVLEN, len, NULL)) ossl_raise(eCipherError, "unable to set IV length"); /* * EVP_CIPHER_CTX_iv_length() returns the default length. So we need to save * the length somewhere. Luckily currently we aren't using app_data. */ EVP_CIPHER_CTX_set_app_data(ctx, (void *)(VALUE)len); return iv_length; }
Sets the cipher key. To generate a key, you should either use a secure random byte string or, if the key is to be derived from a password, you should rely on PBKDF2 functionality provided by OpenSSL::PKCS5
. To generate a secure random-based key, Cipher#random_key
may be used.
Only call this method after calling Cipher#encrypt
or Cipher#decrypt
.
static VALUE ossl_cipher_set_key(VALUE self, VALUE key) { EVP_CIPHER_CTX *ctx; int key_len; StringValue(key); GetCipher(self, ctx); key_len = EVP_CIPHER_CTX_key_length(ctx); if (RSTRING_LEN(key) != key_len) ossl_raise(rb_eArgError, "key must be %d bytes", key_len); if (EVP_CipherInit_ex(ctx, NULL, NULL, (unsigned char *)RSTRING_PTR(key), NULL, -1) != 1) ossl_raise(eCipherError, NULL); rb_ivar_set(self, id_key_set, Qtrue); return key; }
Returns the key length in bytes of the Cipher
.
static VALUE ossl_cipher_key_length(VALUE self) { EVP_CIPHER_CTX *ctx; GetCipher(self, ctx); return INT2NUM(EVP_CIPHER_CTX_key_length(ctx)); }
Sets the key length of the cipher. If the cipher is a fixed length cipher then attempting to set the key length to any value other than the fixed value is an error.
Under normal circumstances you do not need to call this method (and probably shouldn't).
See EVP_CIPHER_CTX_set_key_length for further information.
static VALUE ossl_cipher_set_key_length(VALUE self, VALUE key_length) { int len = NUM2INT(key_length); EVP_CIPHER_CTX *ctx; GetCipher(self, ctx); if (EVP_CIPHER_CTX_set_key_length(ctx, len) != 1) ossl_raise(eCipherError, NULL); return key_length; }
Returns the name of the cipher which may differ slightly from the original name provided.
static VALUE ossl_cipher_name(VALUE self) { EVP_CIPHER_CTX *ctx; GetCipher(self, ctx); return rb_str_new2(EVP_CIPHER_name(EVP_CIPHER_CTX_cipher(ctx))); }
Enables or disables padding. By default encryption operations are padded using standard block padding and the padding is checked and removed when decrypting. If the pad parameter is zero then no padding is performed, the total amount of data encrypted or decrypted must then be a multiple of the block size or an error will occur.
See EVP_CIPHER_CTX_set_padding for further information.
static VALUE ossl_cipher_set_padding(VALUE self, VALUE padding) { EVP_CIPHER_CTX *ctx; int pad = NUM2INT(padding); GetCipher(self, ctx); if (EVP_CIPHER_CTX_set_padding(ctx, pad) != 1) ossl_raise(eCipherError, NULL); return padding; }
Generates and sets the key/IV based on a password.
WARNING: This method is only PKCS5
v1.5 compliant when using RC2, RC4-40, or DES with MD5 or SHA1. Using anything else (like AES) will generate the key/iv using an OpenSSL
specific method. This method is deprecated and should no longer be used. Use a PKCS5
v2 key generation method from OpenSSL::PKCS5
instead.
salt
must be an 8 byte string if provided.
iterations
is an integer with a default of 2048.
digest
is a Digest
object that defaults to 'MD5'
A minimum of 1000 iterations is recommended.
static VALUE ossl_cipher_pkcs5_keyivgen(int argc, VALUE *argv, VALUE self) { EVP_CIPHER_CTX *ctx; const EVP_MD *digest; VALUE vpass, vsalt, viter, vdigest; unsigned char key[EVP_MAX_KEY_LENGTH], iv[EVP_MAX_IV_LENGTH], *salt = NULL; int iter; rb_scan_args(argc, argv, "13", &vpass, &vsalt, &viter, &vdigest); StringValue(vpass); if(!NIL_P(vsalt)){ StringValue(vsalt); if(RSTRING_LEN(vsalt) != PKCS5_SALT_LEN) ossl_raise(eCipherError, "salt must be an 8-octet string"); salt = (unsigned char *)RSTRING_PTR(vsalt); } iter = NIL_P(viter) ? 2048 : NUM2INT(viter); digest = NIL_P(vdigest) ? EVP_md5() : GetDigestPtr(vdigest); GetCipher(self, ctx); EVP_BytesToKey(EVP_CIPHER_CTX_cipher(ctx), digest, salt, (unsigned char *)RSTRING_PTR(vpass), RSTRING_LENINT(vpass), iter, key, iv); if (EVP_CipherInit_ex(ctx, NULL, NULL, key, iv, -1) != 1) ossl_raise(eCipherError, NULL); OPENSSL_cleanse(key, sizeof key); OPENSSL_cleanse(iv, sizeof iv); rb_ivar_set(self, id_key_set, Qtrue); return Qnil; }
Generate a random IV with OpenSSL::Random.random_bytes
and sets it to the cipher, and returns it.
You must call encrypt
or decrypt
before calling this method.
# File openssl/lib/openssl/cipher.rb, line 55 def random_iv str = OpenSSL::Random.random_bytes(self.iv_len) self.iv = str end
Generate a random key with OpenSSL::Random.random_bytes
and sets it to the cipher, and returns it.
You must call encrypt
or decrypt
before calling this method.
# File openssl/lib/openssl/cipher.rb, line 43 def random_key str = OpenSSL::Random.random_bytes(self.key_len) self.key = str end
Fully resets the internal state of the Cipher
. By using this, the same Cipher
instance may be used several times for encryption or decryption tasks.
Internally calls EVP_CipherInit_ex(ctx, NULL, NULL, NULL, NULL, -1).
static VALUE ossl_cipher_reset(VALUE self) { EVP_CIPHER_CTX *ctx; GetCipher(self, ctx); if (EVP_CipherInit_ex(ctx, NULL, NULL, NULL, NULL, -1) != 1) ossl_raise(eCipherError, NULL); return self; }
Encrypts data in a streaming fashion. Hand consecutive blocks of data to the update
method in order to encrypt it. Returns the encrypted data chunk. When done, the output of Cipher#final
should be additionally added to the result.
If buffer
is given, the encryption/decryption result will be written to it. buffer
will be resized automatically.
static VALUE ossl_cipher_update(int argc, VALUE *argv, VALUE self) { EVP_CIPHER_CTX *ctx; unsigned char *in; long in_len, out_len; VALUE data, str; rb_scan_args(argc, argv, "11", &data, &str); if (!RTEST(rb_attr_get(self, id_key_set))) ossl_raise(eCipherError, "key not set"); StringValue(data); in = (unsigned char *)RSTRING_PTR(data); if ((in_len = RSTRING_LEN(data)) == 0) ossl_raise(rb_eArgError, "data must not be empty"); GetCipher(self, ctx); out_len = in_len+EVP_CIPHER_CTX_block_size(ctx); if (out_len <= 0) { ossl_raise(rb_eRangeError, "data too big to make output buffer: %ld bytes", in_len); } if (NIL_P(str)) { str = rb_str_new(0, out_len); } else { StringValue(str); rb_str_resize(str, out_len); } if (!ossl_cipher_update_long(ctx, (unsigned char *)RSTRING_PTR(str), &out_len, in, in_len)) ossl_raise(eCipherError, NULL); assert(out_len < RSTRING_LEN(str)); rb_str_set_len(str, out_len); return str; }