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
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>
EID 4966 (Verified) is as follows:Section: 5.1
Original Text:
DK = Tc<0..dkLen-1>
Corrected Text:
DK = T_c<0..dkLen-1>
Notes:
The referenced variable Tc does not exist.
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/
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