This is a purely informative rendering of an RFC that includes verified errata. This rendering may not be used as a reference.

The following 'Verified' errata have been incorporated in this document: EID 4966

The following 'Verified' errata have been incorporated in this document: EID 4966

Network Working Group B. Kaliski Request for Comments: 2898 RSA Laboratories Category: Informational September 2000 PKCS #5: Password-Based Cryptography Specification Version 2.0 Status of this Memo This memo provides information for the Internet community. It does not specify an Internet standard of any kind. Distribution of this memo is unlimited. Copyright Notice Copyright (C) The Internet Society (2000). All Rights Reserved. Abstract This memo represents a republication of PKCS #5 v2.0 from RSA Laboratories' Public-Key Cryptography Standards (PKCS) series, and change control is retained within the PKCS process. The body of this document, except for the security considerations section, is taken directly from that specification. This document provides recommendations for the implementation of password-based cryptography, covering key derivation functions, encryption schemes, message-authentication schemes, and ASN.1 syntax identifying the techniques. The recommendations are intended for general application within computer and communications systems, and as such include a fair amount of flexibility. They are particularly intended for the protection of sensitive information such as private keys, as in PKCS #8 [25]. It is expected that application standards and implementation profiles based on these specifications may include additional constraints. Other cryptographic techniques based on passwords, such as password- based key entity authentication and key establishment protocols [4][5][26] are outside the scope of this document. Guidelines for the selection of passwords are also outside the scope. Table of Contents 1. Introduction ............................................... 3 2. Notation ................................................... 3 3. Overview ................................................... 4 4. Salt and iteration count ................................... 6 4.1 Salt ................................................... 6 4.2 Iteration count ........................................ 8 5. Key derivation functions ................................... 8 5.1 PBKDF1 ................................................. 9 5.2 PBKDF2 ................................................. 9 6. Encryption schemes ......................................... 11 6.1 PBES1 .................................................. 12 6.1.1 Encryption operation ............................ 12 6.1.2 Decryption operation ............................ 13 6.2 PBES2 .................................................. 14 6.2.1 Encryption operation ............................ 14 6.2.2 Decryption operation ............................ 15 7. Message authentication schemes ............................. 15 7.1 PBMAC1 ................................................. 16 7.1.1 MAC generation .................................. 16 7.1.2 MAC verification ................................ 16 8. Security Considerations .................................... 17 9. Author's Address............................................ 17 A. ASN.1 syntax ............................................... 18 A.1 PBKDF1 ................................................. 18 A.2 PBKDF2 ................................................. 18 A.3 PBES1 .................................................. 20 A.4 PBES2 .................................................. 20 A.5 PBMAC1 ................................................. 21 B. Supporting techniques ...................................... 22 B.1 Pseudorandom functions ................................. 22 B.2 Encryption schemes ..................................... 23 B.3 Message authentication schemes ......................... 26 C. ASN.1 module ............................................... 26 Intellectual Property Considerations ............................ 30 Revision history ................................................ 30 References ...................................................... 31 Contact Information & About PKCS ................................ 33 Full Copyright Statement ........................................ 34 1. Introduction This document provides recommendations for the implementation of password-based cryptography, covering the following aspects: - key derivation functions - encryption schemes - message-authentication schemes - ASN.1 syntax identifying the techniques The recommendations are intended for general application within computer and communications systems, and as such include a fair amount of flexibility. They are particularly intended for the protection of sensitive information such as private keys, as in PKCS #8 [25]. It is expected that application standards and implementation profiles based on these specifications may include additional constraints. Other cryptographic techniques based on passwords, such as password- based key entity authentication and key establishment protocols [4][5][26] are outside the scope of this document. Guidelines for the selection of passwords are also outside the scope. This document supersedes PKCS #5 version 1.5 [24], but includes compatible techniques. 2. Notation C ciphertext, an octet string c iteration count, a positive integer DK derived key, an octet string dkLen length in octets of derived key, a positive integer EM encoded message, an octet string Hash underlying hash function hLen length in octets of pseudorandom function output, a positive integer l length in blocks of derived key, a positive integer IV initialization vector, an octet string K encryption key, an octet string KDF key derivation function M message, an octet string P password, an octet string PRF underlying pseudorandom function PS padding string, an octet string psLen length in octets of padding string, a positive integer S salt, an octet string T message authentication code, an octet string T_1, ..., T_l, U_1, ..., U_c intermediate values, octet strings 01, 02, ..., 08 octets with value 1, 2, ..., 8 \xor bit-wise exclusive-or of two octet strings || || octet length operator || concatenation operator <i..j> substring extraction operator: extracts octets i through j, 0 <= i <= j 3. Overview In many applications of public-key cryptography, user security is ultimately dependent on one or more secret text values or passwords. Since a password is not directly applicable as a key to any conventional cryptosystem, however, some processing of the password is required to perform cryptographic operations with it. Moreover, as passwords are often chosen from a relatively small space, special care is required in that processing to defend against search attacks. A general approach to password-based cryptography, as described by Morris and Thompson [8] for the protection of password tables, is to combine a password with a salt to produce a key. The salt can be viewed as an index into a large set of keys derived from the password, and need not be kept secret. Although it may be possible for an opponent to construct a table of possible passwords (a so- called "dictionary attack"), constructing a table of possible keys will be difficult, since there will be many possible keys for each password. An opponent will thus be limited to searching through passwords separately for each salt. Another approach to password-based cryptography is to construct key derivation techniques that are relatively expensive, thereby increasing the cost of exhaustive search. One way to do this is to include an iteration count in the key derivation technique, indicating how many times to iterate some underlying function by which keys are derived. A modest number of iterations, say 1000, is not likely to be a burden for legitimate parties when computing a key, but will be a significant burden for opponents. Salt and iteration count formed the basis for password-based encryption in PKCS #5 v1.5, and adopted here as well for the various cryptographic operations. Thus, password-based key derivation as defined here is a function of a password, a salt, and an iteration count, where the latter two quantities need not be kept secret. From a password-based key derivation function, it is straightforward to define password-based encryption and message authentication schemes. As in PKCS #5 v1.5, the password-based encryption schemes here are based on an underlying, conventional encryption scheme, where the key for the conventional scheme is derived from the password. Similarly, the password-based message authentication scheme is based on an underlying conventional scheme. This two-layered approach makes the password-based techniques modular in terms of the underlying techniques they can be based on. It is expected that the password-based key derivation functions may find other applications than just the encryption and message authentication schemes defined here. For instance, one might derive a set of keys with a single application of a key derivation function, rather than derive each key with a separate application of the function. The keys in the set would be obtained as substrings of the output of the key derivation function. This approach might be employed as part of key establishment in a session-oriented protocol. Another application is password checking, where the output of the key derivation function is stored (along with the salt and iteration count) for the purposes of subsequent verification of a password. Throughout this document, a password is considered to be an octet string of arbitrary length whose interpretation as a text string is unspecified. In the interest of interoperability, however, it is recommended that applications follow some common text encoding rules. ASCII and UTF-8 [27] are two possibilities. (ASCII is a subset of UTF-8.) Although the selection of passwords is outside the scope of this document, guidelines have been published [17] that may well be taken into account. 4. Salt and Iteration Count Inasmuch as salt and iteration count are central to the techniques defined in this document, some further discussion is warranted. 4.1 Salt A salt in password-based cryptography has traditionally served the purpose of producing a large set of keys corresponding to a given password, among which one is selected at random according to the salt. An individual key in the set is selected by applying a key derivation function KDF, as DK = KDF (P, S) where DK is the derived key, P is the password, and S is the salt. This has two benefits: 1. It is difficult for an opponent to precompute all the keys corresponding to a dictionary of passwords, or even the most likely keys. If the salt is 64 bits long, for instance, there will be as many as 2^64 keys for each password. An opponent is thus limited to searching for passwords after a password-based operation has been performed and the salt is known. 2. It is unlikely that the same key will be selected twice. Again, if the salt is 64 bits long, the chance of "collision" between keys does not become significant until about 2^32 keys have been produced, according to the Birthday Paradox. This addresses some of the concerns about interactions between multiple uses of the same key, which may apply for some encryption and authentication techniques. In password-based encryption, the party encrypting a message can gain assurance that these benefits are realized simply by selecting a large and sufficiently random salt when deriving an encryption key from a password. A party generating a message authentication code can gain such assurance in a similar fashion. The party decrypting a message or verifying a message authentication code, however, cannot be sure that a salt supplied by another party has actually been generated at random. It is possible, for instance, that the salt may have been copied from another password-based operation, in an attempt to exploit interactions between multiple uses of the same key. For instance, suppose two legitimate parties exchange a encrypted message, where the encryption key is an 80-bit key derived from a shared password with some salt. An opponent could take the salt from that encryption and provide it to one of the parties as though it were for a 40-bit key. If the party reveals the result of decryption with the 40-bit key, the opponent may be able to solve for the 40-bit key. In the case that 40-bit key is the first half of the 80-bit key, the opponent can then readily solve for the remaining 40 bits of the 80-bit key. To defend against such attacks, either the interaction between multiple uses of the same key should be carefully analyzed, or the salt should contain data that explicitly distinguishes between different operations. For instance, the salt might have an additional, non-random octet that specifies whether the derived key is for encryption, for message authentication, or for some other operation. Based on this, the following is recommended for salt selection: 1. If there is no concern about interactions between multiple uses of the same key (or a prefix of that key) with the password- based encryption and authentication techniques supported for a given password, then the salt may be generated at random and need not be checked for a particular format by the party receiving the salt. It should be at least eight octets (64 bits) long. 2. Otherwise, the salt should contain data that explicitly distinguishes between different operations and different key lengths, in addition to a random part that is at least eight octets long, and this data should be checked or regenerated by the party receiving the salt. For instance, the salt could have an additional non-random octet that specifies the purpose of the derived key. Alternatively, it could be the encoding of a structure that specifies detailed information about the derived key, such as the encryption or authentication technique and a sequence number among the different keys derived from the password. The particular format of the additional data is left to the application. Note. If a random number generator or pseudorandom generator is not available, a deterministic alternative for generating the salt (or the random part of it) is to apply a password-based key derivation function to the password and the message M to be processed. For instance, the salt could be computed with a key derivation function as S = KDF (P, M). This approach is not recommended if the message M is known to belong to a small message space (e.g., "Yes" or "No"), however, since then there will only be a small number of possible salts. 4.2 Iteration Count An iteration count has traditionally served the purpose of increasing the cost of producing keys from a password, thereby also increasing the difficulty of attack. For the methods in this document, a minimum of 1000 iterations is recommended. This will increase the cost of exhaustive search for passwords significantly, without a noticeable impact in the cost of deriving individual keys. 5. Key Derivation Functions A key derivation function produces a derived key from a base key and other parameters. In a password-based key derivation function, the base key is a password and the other parameters are a salt value and an iteration count, as outlined in Section 3. The primary application of the password-based key derivation functions defined here is in the encryption schemes in Section 6 and the message authentication scheme in Section 7. Other applications are certainly possible, hence the independent definition of these functions. Two functions are specified in this section: PBKDF1 and PBKDF2. PBKDF2 is recommended for new applications; PBKDF1 is included only for compatibility with existing applications, and is not recommended for new applications. A typical application of the key derivation functions defined here might include the following steps: 1. Select a salt S and an iteration count c, as outlined in Section 4. 2. Select a length in octets for the derived key, dkLen. 3. Apply the key derivation function to the password, the salt, the iteration count and the key length to produce a derived key. 4. Output the derived key. Any number of keys may be derived from a password by varying the salt, as described in Section 3. 5.1 PBKDF1 PBKDF1 applies a hash function, which shall be MD2 [6], MD5 [19] or SHA-1 [18], to derive keys. The length of the derived key is bounded by the length of the hash function output, which is 16 octets for MD2 and MD5 and 20 octets for SHA-1. PBKDF1 is compatible with the key derivation process in PKCS #5 v1.5. PBKDF1 is recommended only for compatibility with existing applications since the keys it produces may not be large enough for some applications. PBKDF1 (P, S, c, dkLen) Options: Hash underlying hash function Input: P password, an octet string S salt, an eight-octet string c iteration count, a positive integer dkLen intended length in octets of derived key, a positive integer, at most 16 for MD2 or MD5 and 20 for SHA-1 Output: DK derived key, a dkLen-octet string Steps: 1. If dkLen > 16 for MD2 and MD5, or dkLen > 20 for SHA-1, output "derived key too long" and stop. 2. Apply the underlying hash function Hash for c iterations to the concatenation of the password P and the salt S, then extract the first dkLen octets to produce a derived key DK: T_1 = Hash (P || S) , T_2 = Hash (T_1) , ... T_c = Hash (T_{c-1}) , DK = T_c<0..dkLen-1>3. Output the derived key DK. 5.2 PBKDF2 PBKDF2 applies a pseudorandom function (see Appendix B.1 for an example) to derive keys. The length of the derived key is essentially unbounded. (However, the maximum effective search space for the derived key may be limited by the structure of the underlying pseudorandom function. See Appendix B.1 for further discussion.) PBKDF2 is recommended for new applications. PBKDF2 (P, S, c, dkLen) Options: PRF underlying pseudorandom function (hLen denotes the length in octets of the pseudorandom function output) Input: P password, an octet string S salt, an octet string c iteration count, a positive integer dkLen intended length in octets of the derived key, a positive integer, at most (2^32 - 1) * hLen Output: DK derived key, a dkLen-octet string Steps: 1. If dkLen > (2^32 - 1) * hLen, output "derived key too long" and stop. 2. Let l be the number of hLen-octet blocks in the derived key, rounding up, and let r be the number of octets in the last block: l = CEIL (dkLen / hLen) , r = dkLen - (l - 1) * hLen . Here, CEIL (x) is the "ceiling" function, i.e. the smallest integer greater than, or equal to, x. 3. For each block of the derived key apply the function F defined below to the password P, the salt S, the iteration count c, and the block index to compute the block: T_1 = F (P, S, c, 1) , T_2 = F (P, S, c, 2) , ... T_l = F (P, S, c, l) , where the function F is defined as the exclusive-or sum of the first c iterates of the underlying pseudorandom function PRF applied to the password P and the concatenation of the salt S and the block index i: F (P, S, c, i) = U_1 \xor U_2 \xor ... \xor U_c where U_1 = PRF (P, S || INT (i)) , U_2 = PRF (P, U_1) , ... U_c = PRF (P, U_{c-1}) . Here, INT (i) is a four-octet encoding of the integer i, most significant octet first. 4. Concatenate the blocks and extract the first dkLen octets to produce a derived key DK: DK = T_1 || T_2 || ... || T_l<0..r-1> 5. Output the derived key DK. Note. The construction of the function F follows a "belt-and- suspenders" approach. The iterates U_i are computed recursively to remove a degree of parallelism from an opponent; they are exclusive- ored together to reduce concerns about the recursion degenerating into a small set of values. 6. Encryption Schemes An encryption scheme, in the symmetric setting, consists of an encryption operation and a decryption operation, where the encryption operation produces a ciphertext from a message under a key, and the decryption operation recovers the message from the ciphertext under the same key. In a password-based encryption scheme, the key is a password. A typical application of a password-based encryption scheme is a private-key protection method, where the message contains private-key information, as in PKCS #8. The encryption schemes defined here would be suitable encryption algorithms in that context. Two schemes are specified in this section: PBES1 and PBES2. PBES2 is recommended for new applications; PBES1 is included only for compatibility with existing applications, and is not recommended for new applications. 6.1 PBES1 PBES1 combines the PBKDF1 function (Section 5.1) with an underlying block cipher, which shall be either DES [15] or RC2(tm) [21] in CBC mode [16]. PBES1 is compatible with the encryption scheme in PKCS #5 v1.5. PBES1 is recommended only for compatibility with existing applications, since it supports only two underlying encryption schemes, each of which has a key size (56 or 64 bits) that may not be large enough for some applications. 6.1.1 Encryption Operation The encryption operation for PBES1 consists of the following steps, which encrypt a message M under a password P to produce a ciphertext C: 1. Select an eight-octet salt S and an iteration count c, as outlined in Section 4. 2. Apply the PBKDF1 key derivation function (Section 5.1) to the password P, the salt S, and the iteration count c to produce at derived key DK of length 16 octets: DK = PBKDF1 (P, S, c, 16) . 3. Separate the derived key DK into an encryption key K consisting of the first eight octets of DK and an initialization vector IV consisting of the next eight octets: K = DK<0..7> , IV = DK<8..15> . 4. Concatenate M and a padding string PS to form an encoded message EM: EM = M || PS , where the padding string PS consists of 8-(||M|| mod 8) octets each with value 8-(||M|| mod 8). The padding string PS will satisfy one of the following statements: PS = 01, if ||M|| mod 8 = 7 ; PS = 02 02, if ||M|| mod 8 = 6 ; ... PS = 08 08 08 08 08 08 08 08, if ||M|| mod 8 = 0. The length in octets of the encoded message will be a multiple of eight and it will be possible to recover the message M unambiguously from the encoded message. (This padding rule is taken from RFC 1423 [3].) 5. Encrypt the encoded message EM with the underlying block cipher (DES or RC2) in cipher block chaining mode under the encryption key K with initialization vector IV to produce the ciphertext C. For DES, the key K shall be considered as a 64-bit encoding of a 56-bit DES key with parity bits ignored (see [9]). For RC2, the "effective key bits" shall be 64 bits. 6. Output the ciphertext C. The salt S and the iteration count c may be conveyed to the party performing decryption in an AlgorithmIdentifier value (see Appendix A.3). 6.1.2 Decryption Operation The decryption operation for PBES1 consists of the following steps, which decrypt a ciphertext C under a password P to recover a message M: 1. Obtain the eight-octet salt S and the iteration count c. 2. Apply the PBKDF1 key derivation function (Section 5.1) to the password P, the salt S, and the iteration count c to produce a derived key DK of length 16 octets: DK = PBKDF1 (P, S, c, 16) 3. Separate the derived key DK into an encryption key K consisting of the first eight octets of DK and an initialization vector IV consisting of the next eight octets: K = DK<0..7> , IV = DK<8..15> . 4. Decrypt the ciphertext C with the underlying block cipher (DES or RC2) in cipher block chaining mode under the encryption key K with initialization vector IV to recover an encoded message EM. If the length in octets of the ciphertext C is not a multiple of eight, output "decryption error" and stop. 5. Separate the encoded message EM into a message M and a padding string PS: EM = M || PS , where the padding string PS consists of some number psLen octets each with value psLen, where psLen is between 1 and 8. If it is not possible to separate the encoded message EM in this manner, output "decryption error" and stop. 6. Output the recovered message M. 6.2 PBES2 PBES2 combines a password-based key derivation function, which shall be PBKDF2 (Section 5.2) for this version of PKCS #5, with an underlying encryption scheme (see Appendix B.2 for examples). The key length and any other parameters for the underlying encryption scheme depend on the scheme. PBES2 is recommended for new applications. 6.2.1 Encryption Operation The encryption operation for PBES2 consists of the following steps, which encrypt a message M under a password P to produce a ciphertext C, applying a selected key derivation function KDF and a selected underlying encryption scheme: 1. Select a salt S and an iteration count c, as outlined in Section 4. 2. Select the length in octets, dkLen, for the derived key for the underlying encryption scheme. 3. Apply the selected key derivation function to the password P, the salt S, and the iteration count c to produce a derived key DK of length dkLen octets: DK = KDF (P, S, c, dkLen) . 4. Encrypt the message M with the underlying encryption scheme under the derived key DK to produce a ciphertext C. (This step may involve selection of parameters such as an initialization vector and padding, depending on the underlying scheme.) 5. Output the ciphertext C. The salt S, the iteration count c, the key length dkLen, and identifiers for the key derivation function and the underlying encryption scheme may be conveyed to the party performing decryption in an AlgorithmIdentifier value (see Appendix A.4). 6.2.2 Decryption Operation The decryption operation for PBES2 consists of the following steps, which decrypt a ciphertext C under a password P to recover a message M: 1. Obtain the salt S for the operation. 2. Obtain the iteration count c for the key derivation function. 3. Obtain the key length in octets, dkLen, for the derived key for the underlying encryption scheme. 4. Apply the selected key derivation function to the password P, the salt S, and the iteration count c to produce a derived key DK of length dkLen octets: DK = KDF (P, S, c, dkLen) . 5. Decrypt the ciphertext C with the underlying encryption scheme under the derived key DK to recover a message M. If the decryption function outputs "decryption error," then output "decryption error" and stop. 6. Output the recovered message M. 7. Message Authentication Schemes A message authentication scheme consists of a MAC (message authentication code) generation operation and a MAC verification operation, where the MAC generation operation produces a message authentication code from a message under a key, and the MAC verification operation verifies the message authentication code under the same key. In a password-based message authentication scheme, the key is a password. One scheme is specified in this section: PBMAC1. 7.1 PBMAC1 PBMAC1 combines a password-based key derivation function, which shall be PBKDF2 (Section 5.2) for this version of PKCS #5, with an underlying message authentication scheme (see Appendix B.3 for an example). The key length and any other parameters for the underlying message authentication scheme depend on the scheme. 7.1.1 MAC Generation The MAC generation operation for PBMAC1 consists of the following steps, which process a message M under a password P to generate a message authentication code T, applying a selected key derivation function KDF and a selected underlying message authentication scheme: 1. Select a salt S and an iteration count c, as outlined in Section 4. 2. Select a key length in octets, dkLen, for the derived key for the underlying message authentication function. 3. Apply the selected key derivation function to the password P, the salt S, and the iteration count c to produce a derived key DK of length dkLen octets: DK = KDF (P, S, c, dkLen) . 4. Process the message M with the underlying message authentication scheme under the derived key DK to generate a message authentication code T. 5. Output the message authentication code T. The salt S, the iteration count c, the key length dkLen, and identifiers for the key derivation function and underlying message authentication scheme may be conveyed to the party performing verification in an AlgorithmIdentifier value (see Appendix A.5). 7.1.2 MAC Verification The MAC verification operation for PBMAC1 consists of the following steps, which process a message M under a password P to verify a message authentication code T: 1. Obtain the salt S and the iteration count c. 2. Obtain the key length in octets, dkLen, for the derived key for the underlying message authentication scheme. 3. Apply the selected key derivation function to the password P, the salt S, and the iteration count c to produce a derived key DK of length dkLen octets: DK = KDF (P, S, c, dkLen) . 4. Process the message M with the underlying message authentication scheme under the derived key DK to verify the message authentication code T. 5. If the message authentication code verifies, output "correct"; else output "incorrect." 8. Security Considerations Password-based cryptography is generally limited in the security that it can provide, particularly for methods such as those defined in this document where off-line password search is possible. While the use of salt and iteration count can increase the complexity of attack (see Section 4 for recommendations), it is essential that passwords are selected well, and relevant guidelines (e.g., [17]) should be taken into account. It is also important that passwords be protected well if stored. In general, different keys should be derived from a password for different uses to minimize the possibility of unintended interactions. For password-based encryption with a single algorithm, a random salt is sufficient to ensure that different keys will be produced. In certain other situations, as outlined in Section 4, a structured salt is necessary. The recommendations in Section 4 should thus be taken into account when selecting the salt value. 9. Author's Address Burt Kaliski RSA Laboratories 20 Crosby Drive Bedford, MA 01730 USA EMail: bkaliski@rsasecurity.com APPENDICES A. ASN.1 Syntax This section defines ASN.1 syntax for the key derivation functions, the encryption schemes, the message authentication scheme, and supporting techniques. The intended application of these definitions includes PKCS #8 and other syntax for key management, encrypted data, and integrity-protected data. (Various aspects of ASN.1 are specified in several ISO/IEC standards [9][10][11][12][13][14].) The object identifier pkcs-5 identifies the arc of the OID tree from which the PKCS #5-specific OIDs in this section are derived: rsadsi OBJECT IDENTIFIER ::= {iso(1) member-body(2) us(840) 113549} pkcs OBJECT IDENTIFIER ::= {rsadsi 1} pkcs-5 OBJECT IDENTIFIER ::= {pkcs 5} A.1 PBKDF1 No object identifier is given for PBKDF1, as the object identifiers for PBES1 are sufficient for existing applications and PBKDF2 is recommended for new applications. A.2 PBKDF2 The object identifier id-PBKDF2 identifies the PBKDF2 key derivation function (Section 5.2). id-PBKDF2 OBJECT IDENTIFIER ::= {pkcs-5 12} The parameters field associated with this OID in an AlgorithmIdentifier shall have type PBKDF2-params: PBKDF2-params ::= SEQUENCE { salt CHOICE { specified OCTET STRING, otherSource AlgorithmIdentifier {{PBKDF2-SaltSources}} }, iterationCount INTEGER (1..MAX), keyLength INTEGER (1..MAX) OPTIONAL, prf AlgorithmIdentifier {{PBKDF2-PRFs}} DEFAULT algid-hmacWithSHA1 } The fields of type PKDF2-params have the following meanings: - salt specifies the salt value, or the source of the salt value. It shall either be an octet string or an algorithm ID with an OID in the set PBKDF2-SaltSources, which is reserved for future versions of PKCS #5. The salt-source approach is intended to indicate how the salt value is to be generated as a function of parameters in the algorithm ID, application data, or both. For instance, it may indicate that the salt value is produced from the encoding of a structure that specifies detailed information about the derived key as suggested in Section 4.1. Some of the information may be carried elsewhere, e.g., in the encryption algorithm ID. However, such facilities are deferred to a future version of PKCS #5. In this version, an application may achieve the benefits mentioned in Section 4.1 by choosing a particular interpretation of the salt value in the specified alternative. PBKDF2-SaltSources ALGORITHM-IDENTIFIER ::= { ... } - iterationCount specifies the iteration count. The maximum iteration count allowed depends on the implementation. It is expected that implementation profiles may further constrain the bounds. - keyLength, an optional field, is the length in octets of the derived key. The maximum key length allowed depends on the implementation; it is expected that implementation profiles may further constrain the bounds. The field is provided for convenience only; the key length is not cryptographically protected. If there is concern about interaction between operations with different key lengths for a given salt (see Section 4.1), the salt should distinguish among the different key lengths. - prf identifies the underlying pseudorandom function. It shall be an algorithm ID with an OID in the set PBKDF2-PRFs, which for this version of PKCS #5 shall consist of id-hmacWithSHA1 (see Appendix B.1.1) and any other OIDs defined by the application. PBKDF2-PRFs ALGORITHM-IDENTIFIER ::= { {NULL IDENTIFIED BY id-hmacWithSHA1}, ... } The default pseudorandom function is HMAC-SHA-1: algid-hmacWithSHA1 AlgorithmIdentifier {{PBKDF2-PRFs}} ::= {algorithm id-hmacWithSHA1, parameters NULL : NULL} A.3 PBES1 Different object identifiers identify the PBES1 encryption scheme (Section 6.1) according to the underlying hash function in the key derivation function and the underlying block cipher, as summarized in the following table: Hash Function Block Cipher OID MD2 DES pkcs-5.1 MD2 RC2 pkcs-5.4 MD5 DES pkcs-5.3 MD5 RC2 pkcs-5.6 SHA-1 DES pkcs-5.10 SHA-1 RC2 pkcs-5.11 pbeWithMD2AndDES-CBC OBJECT IDENTIFIER ::= {pkcs-5 1} pbeWithMD2AndRC2-CBC OBJECT IDENTIFIER ::= {pkcs-5 4} pbeWithMD5AndDES-CBC OBJECT IDENTIFIER ::= {pkcs-5 3} pbeWithMD5AndRC2-CBC OBJECT IDENTIFIER ::= {pkcs-5 6} pbeWithSHA1AndDES-CBC OBJECT IDENTIFIER ::= {pkcs-5 10} pbeWithSHA1AndRC2-CBC OBJECT IDENTIFIER ::= {pkcs-5 11} For each OID, the parameters field associated with the OID in an AlgorithmIdentifier shall have type PBEParameter: PBEParameter ::= SEQUENCE { salt OCTET STRING (SIZE(8)), iterationCount INTEGER } The fields of type PBEParameter have the following meanings: - salt specifies the salt value, an eight-octet string. - iterationCount specifies the iteration count. A.4 PBES2 The object identifier id-PBES2 identifies the PBES2 encryption scheme (Section 6.2). id-PBES2 OBJECT IDENTIFIER ::= {pkcs-5 13} The parameters field associated with this OID in an AlgorithmIdentifier shall have type PBES2-params: PBES2-params ::= SEQUENCE { keyDerivationFunc AlgorithmIdentifier {{PBES2-KDFs}}, encryptionScheme AlgorithmIdentifier {{PBES2-Encs}} } The fields of type PBES2-params have the following meanings: - keyDerivationFunc identifies the underlying key derivation function. It shall be an algorithm ID with an OID in the set PBES2-KDFs, which for this version of PKCS #5 shall consist of id-PBKDF2 (Appendix A.2). PBES2-KDFs ALGORITHM-IDENTIFIER ::= { {PBKDF2-params IDENTIFIED BY id-PBKDF2}, ... } - encryptionScheme identifies the underlying encryption scheme. It shall be an algorithm ID with an OID in the set PBES2-Encs, whose definition is left to the application. Example underlying encryption schemes are given in Appendix B.2. PBES2-Encs ALGORITHM-IDENTIFIER ::= { ... } A.5 PBMAC1 The object identifier id-PBMAC1 identifies the PBMAC1 message authentication scheme (Section 7.1). id-PBMAC1 OBJECT IDENTIFIER ::= {pkcs-5 14} The parameters field associated with this OID in an AlgorithmIdentifier shall have type PBMAC1-params: PBMAC1-params ::= SEQUENCE { keyDerivationFunc AlgorithmIdentifier {{PBMAC1-KDFs}}, messageAuthScheme AlgorithmIdentifier {{PBMAC1-MACs}} } The keyDerivationFunc field has the same meaning as the corresponding field of PBES2-params (Appendix A.4) except that the set of OIDs is PBMAC1-KDFs. PBMAC1-KDFs ALGORITHM-IDENTIFIER ::= { {PBKDF2-params IDENTIFIED BY id-PBKDF2}, ... } The messageAuthScheme field identifies the underlying message authentication scheme. It shall be an algorithm ID with an OID in the set PBMAC1-MACs, whose definition is left to the application. Example underlying encryption schemes are given in Appendix B.3. PBMAC1-MACs ALGORITHM-IDENTIFIER ::= { ... } B. Supporting Techniques This section gives several examples of underlying functions and schemes supporting the password-based schemes in Sections 5, 6 and 7. While these supporting techniques are appropriate for applications to implement, none of them is required to be implemented. It is expected, however, that profiles for PKCS #5 will be developed that specify particular supporting techniques. This section also gives object identifiers for the supporting techniques. The object identifiers digestAlgorithm and encryptionAlgorithm identify the arcs from which certain algorithm OIDs referenced in this section are derived: digestAlgorithm OBJECT IDENTIFIER ::= {rsadsi 2} encryptionAlgorithm OBJECT IDENTIFIER ::= {rsadsi 3} B.1 Pseudorandom functions An example pseudorandom function for PBKDF2 (Section 5.2) is HMAC- SHA-1. B.1.1 HMAC-SHA-1 HMAC-SHA-1 is the pseudorandom function corresponding to the HMAC message authentication code [7] based on the SHA-1 hash function [18]. The pseudorandom function is the same function by which the message authentication code is computed, with a full-length output. (The first argument to the pseudorandom function PRF serves as HMAC's "key," and the second serves as HMAC's "text." In the case of PBKDF2, the "key" is thus the password and the "text" is the salt.) HMAC- SHA-1 has a variable key length and a 20-octet (160-bit) output value. Although the length of the key to HMAC-SHA-1 is essentially unbounded, the effective search space for pseudorandom function outputs may be limited by the structure of the function. In particular, when the key is longer than 512 bits, HMAC-SHA-1 will first hash it to 160 bits. Thus, even if a long derived key consisting of several pseudorandom function outputs is produced from a key, the effective search space for the derived key will be at most 160 bits. Although the specific limitation for other key sizes depends on details of the HMAC construction, one should assume, to be conservative, that the effective search space is limited to 160 bits for other key sizes as well. (The 160-bit limitation should not generally pose a practical limitation in the case of password-based cryptography, since the search space for a password is unlikely to be greater than 160 bits.) The object identifier id-hmacWithSHA1 identifies the HMAC-SHA-1 pseudorandom function: id-hmacWithSHA1 OBJECT IDENTIFIER ::= {digestAlgorithm 7} The parameters field associated with this OID in an AlgorithmIdentifier shall have type NULL. This object identifier is employed in the object set PBKDF2-PRFs (Appendix A.2). Note. Although HMAC-SHA-1 was designed as a message authentication code, its proof of security is readily modified to accommodate requirements for a pseudorandom function, under stronger assumptions. A hash function may also meet the requirements of a pseudorandom function under certain assumptions. For instance, the direct application of a hash function to to the concatenation of the "key" and the "text" may be appropriate, provided that "text" has appropriate structure to prevent certain attacks. HMAC-SHA-1 is preferable, however, because it treats "key" and "text" as separate arguments and does not require "text" to have any structure. B.2 Encryption Schemes Example pseudorandom functions for PBES2 (Section 6.2) are DES-CBC- Pad, DES-EDE2-CBC-Pad, RC2-CBC-Pad, and RC5-CBC-Pad. The object identifiers given in this section are intended to be employed in the object set PBES2-Encs (Appendix A.4). B.2.1 DES-CBC-Pad DES-CBC-Pad is single-key DES [15] in CBC mode [16] with the RFC 1423 padding operation (see Section 6.1.1). DES-CBC-Pad has an eight-octet encryption key and an eight-octet initialization vector. The key is considered as a 64-bit encoding of a 56-bit DES key with parity bits ignored. The object identifier desCBC (defined in the NIST/OSI Implementors' Workshop agreements) identifies the DES-CBC-Pad encryption scheme: desCBC OBJECT IDENTIFIER ::= {iso(1) identified-organization(3) oiw(14) secsig(3) algorithms(2) 7} The parameters field associated with this OID in an AlgorithmIdentifier shall have type OCTET STRING (SIZE(8)), specifying the initialization vector for CBC mode. B.2.2 DES-EDE3-CBC-Pad DES-EDE3-CBC-Pad is three-key triple-DES in CBC mode [1] with the RFC 1423 padding operation. DES-EDE3-CBC-Pad has a 24-octet encryption key and an eight-octet initialization vector. The key is considered as the concatenation of three eight-octet keys, each of which is a 64-bit encoding of a 56-bit DES key with parity bits ignored. The object identifier des-EDE3-CBC identifies the DES-EDE3-CBC-Pad encryption scheme: des-EDE3-CBC OBJECT IDENTIFIER ::= {encryptionAlgorithm 7} The parameters field associated with this OID in an AlgorithmIdentifier shall have type OCTET STRING (SIZE(8)), specifying the initialization vector for CBC mode. Note. An OID for DES-EDE3-CBC without padding is given in ANSI X9.52 [1]; the one given here is preferred since it specifies padding. B.2.3 RC2-CBC-Pad RC2-CBC-Pad is the RC2(tm) encryption algorithm [21] in CBC mode with the RFC 1423 padding operation. RC2-CBC-Pad has a variable key length, from one to 128 octets, a separate "effective key bits" parameter from one to 1024 bits that limits the effective search space independent of the key length, and an eight-octet initialization vector. The object identifier rc2CBC identifies the RC2-CBC-Pad encryption scheme: rc2CBC OBJECT IDENTIFIER ::= {encryptionAlgorithm 2} The parameters field associated with OID in an AlgorithmIdentifier shall have type RC2-CBC-Parameter: RC2-CBC-Parameter ::= SEQUENCE { rc2ParameterVersion INTEGER OPTIONAL, iv OCTET STRING (SIZE(8)) } The fields of type RC2-CBCParameter have the following meanings: - rc2ParameterVersion is a proprietary RSA Security Inc. encoding of the "effective key bits" for RC2. The following encodings are defined: Effective Key Bits Encoding 40 160 64 120 128 58 b >= 256 b If the rc2ParameterVersion field is omitted, the "effective key bits" defaults to 32. (This is for backward compatibility with certain very old implementations.) - iv is the eight-octet initialization vector. B.2.4 RC5-CBC-Pad RC5-CBC-Pad is the RC5(tm) encryption algorithm [20] in CBC mode with a generalization of the RFC 1423 padding operation. This scheme is fully specified in [2]. RC5-CBC-Pad has a variable key length, from 0 to 256 octets, and supports both a 64-bit block size and a 128-bit block size. For the former, it has an eight-octet initialization vector, and for the latter, a 16-octet initialization vector. RC5-CBC-Pad also has a variable number of "rounds" in the encryption operation, from 8 to 127. Note: The generalization of the padding operation is as follows. For RC5 with a 64-bit block size, the padding string is as defined in RFC 1423. For RC5 with a 128-bit block size, the padding string consists of 16-(||M|| mod 16) octets each with value 16-(||M|| mod 16). The object identifier rc5-CBC-PAD [2] identifies RC5-CBC-Pad encryption scheme: rc5-CBC-PAD OBJECT IDENTIFIER ::= {encryptionAlgorithm 9} The parameters field associated with this OID in an AlgorithmIdentifier shall have type RC5-CBC-Parameters: RC5-CBC-Parameters ::= SEQUENCE { version INTEGER {v1-0(16)} (v1-0), rounds INTEGER (8..127), blockSizeInBits INTEGER (64 | 128), iv OCTET STRING OPTIONAL } The fields of type RC5-CBC-Parameters have the following meanings: - version is the version of the algorithm, which shall be v1-0. - rounds is the number of rounds in the encryption operation, which shall be between 8 and 127. - blockSizeInBits is the block size in bits, which shall be 64 or 128. - iv is the initialization vector, an eight-octet string for 64-bit RC5 and a 16-octet string for 128-bit RC5. The default is a string of the appropriate length consisting of zero octets. B.3 Message Authentication Schemes An example message authentication scheme for PBMAC1 (Section 7.1) is HMAC-SHA-1. B.3.1 HMAC-SHA-1 HMAC-SHA-1 is the HMAC message authentication scheme [7] based on the SHA-1 hash function [18]. HMAC-SHA-1 has a variable key length and a 20-octet (160-bit) message authentication code. The object identifier id-hmacWithSHA1 (see Appendix B.1.1) identifies the HMAC-SHA-1 message authentication scheme. (The object identifier is the same for both the pseudorandom function and the message authentication scheme; the distinction is to be understood by context.) This object identifier is intended to be employed in the object set PBMAC1-Macs (Appendix A.5). C. ASN.1 Module For reference purposes, the ASN.1 syntax in the preceding sections is presented as an ASN.1 module here. -- PKCS #5 v2.0 ASN.1 Module -- Revised March 25, 1999 -- This module has been checked for conformance with the -- ASN.1 standard by the OSS ASN.1 Tools PKCS5v2-0 {iso(1) member-body(2) us(840) rsadsi(113549) pkcs(1) pkcs-5(5) modules(16) pkcs5v2-0(1)} DEFINITIONS ::= BEGIN -- Basic object identifiers rsadsi OBJECT IDENTIFIER ::= {iso(1) member-body(2) us(840) 113549} pkcs OBJECT IDENTIFIER ::= {rsadsi 1} pkcs-5 OBJECT IDENTIFIER ::= {pkcs 5} -- Basic types and classes AlgorithmIdentifier { ALGORITHM-IDENTIFIER:InfoObjectSet } ::= SEQUENCE { algorithm ALGORITHM-IDENTIFIER.&id({InfoObjectSet}), parameters ALGORITHM-IDENTIFIER.&Type({InfoObjectSet} {@algorithm}) OPTIONAL } ALGORITHM-IDENTIFIER ::= TYPE-IDENTIFIER -- PBKDF2 PBKDF2Algorithms ALGORITHM-IDENTIFIER ::= { {PBKDF2-params IDENTIFIED BY id-PBKDF2}, ...} id-PBKDF2 OBJECT IDENTIFIER ::= {pkcs-5 12} algid-hmacWithSHA1 AlgorithmIdentifier {{PBKDF2-PRFs}} ::= {algorithm id-hmacWithSHA1, parameters NULL : NULL} PBKDF2-params ::= SEQUENCE { salt CHOICE { specified OCTET STRING, otherSource AlgorithmIdentifier {{PBKDF2-SaltSources}} }, iterationCount INTEGER (1..MAX), keyLength INTEGER (1..MAX) OPTIONAL, prf AlgorithmIdentifier {{PBKDF2-PRFs}} DEFAULT algid-hmacWithSHA1 } PBKDF2-SaltSources ALGORITHM-IDENTIFIER ::= { ... } PBKDF2-PRFs ALGORITHM-IDENTIFIER ::= { {NULL IDENTIFIED BY id-hmacWithSHA1}, ... } -- PBES1 PBES1Algorithms ALGORITHM-IDENTIFIER ::= { {PBEParameter IDENTIFIED BY pbeWithMD2AndDES-CBC} | {PBEParameter IDENTIFIED BY pbeWithMD2AndRC2-CBC} | {PBEParameter IDENTIFIED BY pbeWithMD5AndDES-CBC} | {PBEParameter IDENTIFIED BY pbeWithMD5AndRC2-CBC} | {PBEParameter IDENTIFIED BY pbeWithSHA1AndDES-CBC} | {PBEParameter IDENTIFIED BY pbeWithSHA1AndRC2-CBC}, ... } pbeWithMD2AndDES-CBC OBJECT IDENTIFIER ::= {pkcs-5 1} pbeWithMD2AndRC2-CBC OBJECT IDENTIFIER ::= {pkcs-5 4} pbeWithMD5AndDES-CBC OBJECT IDENTIFIER ::= {pkcs-5 3} pbeWithMD5AndRC2-CBC OBJECT IDENTIFIER ::= {pkcs-5 6} pbeWithSHA1AndDES-CBC OBJECT IDENTIFIER ::= {pkcs-5 10} pbeWithSHA1AndRC2-CBC OBJECT IDENTIFIER ::= {pkcs-5 11} PBEParameter ::= SEQUENCE { salt OCTET STRING (SIZE(8)), iterationCount INTEGER } -- PBES2 PBES2Algorithms ALGORITHM-IDENTIFIER ::= { {PBES2-params IDENTIFIED BY id-PBES2}, ...} id-PBES2 OBJECT IDENTIFIER ::= {pkcs-5 13} PBES2-params ::= SEQUENCE { keyDerivationFunc AlgorithmIdentifier {{PBES2-KDFs}}, encryptionScheme AlgorithmIdentifier {{PBES2-Encs}} } PBES2-KDFs ALGORITHM-IDENTIFIER ::= { {PBKDF2-params IDENTIFIED BY id-PBKDF2}, ... } PBES2-Encs ALGORITHM-IDENTIFIER ::= { ... } -- PBMAC1 PBMAC1Algorithms ALGORITHM-IDENTIFIER ::= { {PBMAC1-params IDENTIFIED BY id-PBMAC1}, ...} id-PBMAC1 OBJECT IDENTIFIER ::= {pkcs-5 14} PBMAC1-params ::= SEQUENCE { keyDerivationFunc AlgorithmIdentifier {{PBMAC1-KDFs}}, messageAuthScheme AlgorithmIdentifier {{PBMAC1-MACs}} } PBMAC1-KDFs ALGORITHM-IDENTIFIER ::= { {PBKDF2-params IDENTIFIED BY id-PBKDF2}, ... } PBMAC1-MACs ALGORITHM-IDENTIFIER ::= { ... } -- Supporting techniques digestAlgorithm OBJECT IDENTIFIER ::= {rsadsi 2} encryptionAlgorithm OBJECT IDENTIFIER ::= {rsadsi 3} SupportingAlgorithms ALGORITHM-IDENTIFIER ::= { {NULL IDENTIFIED BY id-hmacWithSHA1} | {OCTET STRING (SIZE(8)) IDENTIFIED BY desCBC} | {OCTET STRING (SIZE(8)) IDENTIFIED BY des-EDE3-CBC} | {RC2-CBC-Parameter IDENTIFIED BY rc2CBC} | {RC5-CBC-Parameters IDENTIFIED BY rc5-CBC-PAD}, ... } id-hmacWithSHA1 OBJECT IDENTIFIER ::= {digestAlgorithm 7} desCBC OBJECT IDENTIFIER ::= {iso(1) identified-organization(3) oiw(14) secsig(3) algorithms(2) 7} -- from OIW des-EDE3-CBC OBJECT IDENTIFIER ::= {encryptionAlgorithm 7} rc2CBC OBJECT IDENTIFIER ::= {encryptionAlgorithm 2} RC2-CBC-Parameter ::= SEQUENCE { rc2ParameterVersion INTEGER OPTIONAL, iv OCTET STRING (SIZE(8)) } rc5-CBC-PAD OBJECT IDENTIFIER ::= {encryptionAlgorithm 9} RC5-CBC-Parameters ::= SEQUENCE { version INTEGER {v1-0(16)} (v1-0), rounds INTEGER (8..127), blockSizeInBits INTEGER (64 | 128), iv OCTET STRING OPTIONAL } END Intellectual Property Considerations RSA Security makes no patent claims on the general constructions described in this document, although specific underlying techniques may be covered. Among the underlying techniques, the RC5 encryption algorithm (Appendix B.2.4) is protected by U.S. Patents 5,724,428 [22] and 5,835,600 [23]. RC2 and RC5 are trademarks of RSA Security. License to copy this document is granted provided that it is identified as RSA Security Inc. Public-Key Cryptography Standards (PKCS) in all material mentioning or referencing this document. RSA Security makes no representations regarding intellectual property claims by other parties. Such determination is the responsibility of the user. Revision history Versions 1.0-1.3 Versions 1.0-1.3 were distributed to participants in RSA Data Security Inc.'s Public-Key Cryptography Standards meetings in February and March 1991. Version 1.4 Version 1.4 was part of the June 3, 1991 initial public release of PKCS. Version 1.4 was published as NIST/OSI Implementors' Workshop document SEC-SIG-91-20. Version 1.5 Version 1.5 incorporated several editorial changes, including updates to the references and the addition of a revision history. Version 2.0 Version 2.0 incorporates major editorial changes in terms of the document structure, and introduces the PBES2 encryption scheme, the PBMAC1 message authentication scheme, and independent password-based key derivation functions. This version continues to support the encryption process in version 1.5. References [1] American National Standard X9.52 - 1998, Triple Data Encryption Algorithm Modes of Operation. Working draft, Accredited Standards Committee X9, July 27, 1998. [2] Baldwin, R. and R. Rivest, "The RC5, RC5-CBC, RC5-CBC-Pad, and RC5-CTS Algorithms", RFC 2040, October 1996. [3] Balenson, D., "Privacy Enhancement for Internet Electronic Mail: Part III: Algorithms, Modes, and Identifiers", RFC 1423, February 1993. [4] S.M. Bellovin and M. Merritt. Encrypted key exchange: Password-based protocols secure against dictionary attacks. In Proceedings of the 1992 IEEE Computer Society Conference on Research in Security and Privacy, pages 72-84, IEEE Computer Society, 1992. [5] D. Jablon. Strong password-only authenticated key exchange. ACM Computer Communications Review, October 1996. [6] Kaliski, B., "The MD2 Message-Digest Algorithm", RFC 1319, April 1992. [7] Krawczyk, H., Bellare, M. and R. Canetti, "HMAC: Keyed-Hashing for Message Authentication", RFC 2104, February 1997. [8] Robert Morris and Ken Thompson. Password security: A case history. Communications of the ACM, 22(11):594-597, November 1979. [9] ISO/IEC 8824-1:1995: Information technology - Abstract Syntax Notation One (ASN.1) - Specification of basic notation. 1995. [10] ISO/IEC 8824-1:1995/Amd.1:1995 Information technology - Abstract Syntax Notation One (ASN.1) - Specification of basic notation - Amendment 1 - Rules of extensibility. 1995. [11] ISO/IEC 8824-2:1995 Information technology - Abstract Syntax Notation One (ASN.1) - Information object specification. 1995. [12] ISO/IEC 8824-2:1995/Amd.1:1995 Information technology - Abstract Syntax Notation One (ASN.1) - Information object specification - Amendment 1 - Rules of extensibility. 1995. [13] ISO/IEC 8824-3:1995 Information technology - Abstract Syntax Notation One (ASN.1) - Constraint specification. 1995. [14] ISO/IEC 8824-4:1995 Information technology - Abstract Syntax Notation One (ASN.1) - Parameterization of ASN.1 specifications. 1995. [15] National Institute of Standards and Technology (NIST). FIPS PUB 46-2: Data Encryption Standard. December 30, 1993. [16] National Institute of Standards and Technology (NIST). FIPS PUB 81: DES Modes of Operation. December 2, 1980. [17] National Institute of Standards and Technology (NIST). FIPS PUB 112: Password Usage. May 30, 1985. [18] National Institute of Standards and Technology (NIST). FIPS PUB 180-1: Secure Hash Standard. April 1994. [19] Rivest, R., "The MD5 Message-Digest Algorithm", RFC 1321, April 1992. [20] R.L. Rivest. The RC5 encryption algorithm. In Proceedings of the Second International Workshop on Fast Software Encryption, pages 86-96, Springer-Verlag, 1994. [21] Rivest, R., "A Description of the RC2(r) Encryption Algorithm", RFC 2268, March 1998. [22] R.L. Rivest. Block-Encryption Algorithm with Data-Dependent Rotations. U.S. Patent No. 5,724,428, March 3, 1998. [23] R.L. Rivest. Block Encryption Algorithm with Data-Dependent Rotations. U.S. Patent No. 5,835,600, November 10, 1998. [24] RSA Laboratories. PKCS #5: Password-Based Encryption Standard. Version 1.5, November 1993. [25] RSA Laboratories. PKCS #8: Private-Key Information Syntax Standard. Version 1.2, November 1993. [26] T. Wu. The Secure Remote Password protocol. In Proceedings of the 1998 Internet Society Network and Distributed System Security Symposium, pages 97-111, Internet Society, 1998. [27] Yergeau, F., "UTF-8, a transformation format of ISO 10646", RFC 2279, January 1998. Contact Information & About PKCS The Public-Key Cryptography Standards are specifications produced by RSA Laboratories in cooperation with secure systems developers worldwide for the purpose of accelerating the deployment of public- key cryptography. First published in 1991 as a result of meetings with a small group of early adopters of public-key technology, the PKCS documents have become widely referenced and implemented. Contributions from the PKCS series have become part of many formal and de facto standards, including ANSI X9 documents, PKIX, SET, S/MIME, and SSL. Further development of PKCS occurs through mailing list discussions and occasional workshops, and suggestions for improvement are welcome. For more information, contact: PKCS Editor RSA Laboratories 20 Crosby Drive Bedford, MA 01730 USA pkcs-editor@rsasecurity.com http://www.rsalabs.com/pkcs/ Full Copyright Statement Copyright (C) The Internet Society (2000). All Rights Reserved. This document and translations of it may be copied and furnished to others, and derivative works that comment on or otherwise explain it or assist in its implementation may be prepared, copied, published and distributed, in whole or in part, without restriction of any kind, provided that the above copyright notice and this paragraph are included on all such copies and derivative works. However, this document itself may not be modified in any way, such as by removing the copyright notice or references to the Internet Society or other Internet organizations, except as needed for the purpose of developing Internet standards in which case the procedures for copyrights defined in the Internet Standards process must be followed, or as required to translate it into languages other than English. The limited permissions granted above are perpetual and will not be revoked by the Internet Society or its successors or assigns. This document and the information contained herein is provided on an "AS IS" basis and THE INTERNET SOCIETY AND THE INTERNET ENGINEERING TASK FORCE DISCLAIMS ALL WARRANTIES, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO ANY WARRANTY THAT THE USE OF THE INFORMATION HEREIN WILL NOT INFRINGE ANY RIGHTS OR ANY IMPLIED WARRANTIES OF MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE. Acknowledgement Funding for the RFC Editor function is currently provided by the Internet Society.EID 4966 (Verified) is as follows:Section:5.1Original Text:DK = Tc<0..dkLen-1>Corrected Text:DK = T_c<0..dkLen-1>Notes:

The referenced variable Tc does not exist.