Network Working Group B. Kaliski
Request for Comments: 2313 RSA Laboratories East
Category: Informational March 1998
PKCS #1: RSA Encryption
Version 1.5
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 (1998). All Rights Reserved.
Overview
This document describes a method for encrypting data using the RSA
public-key cryptosystem.
1. Scope
This document describes a method for encrypting data using the RSA
public-key cryptosystem. Its intended use is in the construction of
digital signatures and digital envelopes, as described in PKCS #7:
o For digital signatures, the content to be signed
is first reduced to a message digest with a
message-digest algorithm (such as MD5), and then
an octet string containing the message digest is
encrypted with the RSA private key of the signer
of the content. The content and the encrypted
message digest are represented together according
to the syntax in PKCS #7 to yield a digital
signature. This application is compatible with
Privacy-Enhanced Mail (PEM) methods.
o For digital envelopes, the content to be enveloped
is first encrypted under a content-encryption key
with a content-encryption algorithm (such as DES),
and then the content-encryption key is encrypted
with the RSA public keys of the recipients of the
content. The encrypted content and the encrypted
Kaliski Informational [Page 1]
RFC 2313 PKCS #1: RSA Encryption March 1998
content-encryption key are represented together
according to the syntax in PKCS #7 to yield a
digital envelope. This application is also
compatible with PEM methods.
The document also describes a syntax for RSA public keys and private
keys. The public-key syntax would be used in certificates; the
private-key syntax would be used typically in PKCS #8 private-key
information. The public-key syntax is identical to that in both X.509
and Privacy-Enhanced Mail. Thus X.509/PEM RSA keys can be used in
this document.
The document also defines three signature algorithms for use in
signing X.509/PEM certificates and certificate-revocation lists, PKCS
#6 extended certificates, and other objects employing digital
signatures such as X.401 message tokens.
Details on message-digest and content-encryption algorithms are
outside the scope of this document, as are details on sources of the
pseudorandom bits required by certain methods in this document.
2. References
FIPS PUB 46-1 National Bureau of Standards. FIPS PUB 46-1:
Data Encryption Standard. January 1988.
PKCS #6 RSA Laboratories. PKCS #6: Extended-Certificate
Syntax. Version 1.5, November 1993.
PKCS #7 RSA Laboratories. PKCS #7: Cryptographic Message
Syntax. Version 1.5, November 1993.
PKCS #8 RSA Laboratories. PKCS #8: Private-Key Information
Syntax. Version 1.2, November 1993.
RFC 1319 Kaliski, B., "The MD2 Message-Digest
Algorithm," RFC 1319, April 1992.
RFC 1320 Rivest, R., "The MD4 Message-Digest
Algorithm," RFC 1320, April 1992.
RFC 1321 Rivest, R., "The MD5 Message-Digest
Algorithm," RFC 1321, April 1992.
RFC 1423 Balenson, D., "Privacy Enhancement for
Internet Electronic Mail: Part III: Algorithms,
Modes, and Identifiers," RFC 1423, February 1993.
Kaliski Informational [Page 2]
RFC 2313 PKCS #1: RSA Encryption March 1998
X.208 CCITT. Recommendation X.208: Specification of
Abstract Syntax Notation One (ASN.1). 1988.
X.209 CCITT. Recommendation X.209: Specification of
Basic Encoding Rules for Abstract Syntax Notation
One (ASN.1). 1988.
X.411 CCITT. Recommendation X.411: Message Handling
Systems: Message Transfer System: Abstract Service
Definition and Procedures.1988.
X.509 CCITT. Recommendation X.509: The Directory--
Authentication Framework. 1988.
[dBB92] B. den Boer and A. Bosselaers. An attack on the
last two rounds of MD4. In J. Feigenbaum, editor,
Advances in Cryptology---CRYPTO '91 Proceedings,
volume 576 of Lecture Notes in Computer Science,
pages 194-203. Springer-Verlag, New York, 1992.
[dBB93] B. den Boer and A. Bosselaers. Collisions for the
compression function of MD5. Presented at
EUROCRYPT '93 (Lofthus, Norway, May 24-27, 1993).
[DO86] Y. Desmedt and A.M. Odlyzko. A chosen text attack
on the RSA cryptosystem and some discrete
logarithm schemes. In H.C. Williams, editor,
Advances in Cryptology---CRYPTO '85 Proceedings,
volume 218 of Lecture Notes in Computer Science,
pages 516-521. Springer-Verlag, New York, 1986.
[Has88] Johan Hastad. Solving simultaneous modular
equations. SIAM Journal on Computing,
17(2):336-341, April 1988.
[IM90] Colin I'Anson and Chris Mitchell. Security defects
in CCITT Recommendation X.509--The directory
authentication framework. Computer Communications
Review, :30-34, April 1990.
[Mer90] R.C. Merkle. Note on MD4. Unpublished manuscript,
1990.
[Mil76] G.L. Miller. Riemann's hypothesis and tests for
primality. Journal of Computer and Systems
Sciences, 13(3):300-307, 1976.
Kaliski Informational [Page 3]
RFC 2313 PKCS #1: RSA Encryption March 1998
[QC82] J.-J. Quisquater and C. Couvreur. Fast
decipherment algorithm for RSA public-key
cryptosystem. Electronics Letters, 18(21):905-907,
October 1982.
[RSA78] R.L. Rivest, A. Shamir, and L. Adleman. A method
for obtaining digital signatures and public-key
cryptosystems. Communications of the ACM,
21(2):120-126, February 1978.
3. Definitions
For the purposes of this document, the following definitions apply.
AlgorithmIdentifier: A type that identifies an algorithm (by object
identifier) and associated parameters. This type is defined in X.509.
ASN.1: Abstract Syntax Notation One, as defined in X.208.
BER: Basic Encoding Rules, as defined in X.209.
DES: Data Encryption Standard, as defined in FIPS PUB 46-1.
MD2: RSA Data Security, Inc.'s MD2 message-digest algorithm, as
defined in RFC 1319.
MD4: RSA Data Security, Inc.'s MD4 message-digest algorithm, as
defined in RFC 1320.
MD5: RSA Data Security, Inc.'s MD5 message-digest algorithm, as
defined in RFC 1321.
modulus: Integer constructed as the product of two primes.
PEM: Internet Privacy-Enhanced Mail, as defined in RFC 1423 and
related documents.
RSA: The RSA public-key cryptosystem, as defined in [RSA78].
private key: Modulus and private exponent.
public key: Modulus and public exponent.
4. Symbols and abbreviations
Upper-case symbols (e.g., BT) denote octet strings and bit strings
(in the case of the signature S); lower-case symbols (e.g., c) denote
integers.
Kaliski Informational [Page 4]
RFC 2313 PKCS #1: RSA Encryption March 1998
ab hexadecimal octet value c exponent
BT block type d private exponent
D data e public exponent
EB encryption block k length of modulus in
octets
ED encrypted data n modulus
M message p, q prime factors of modulus
MD message digest x integer encryption block
MD' comparative message y integer encrypted data
digest
PS padding string mod n modulo n
S signature X || Y concatenation of X, Y
||X|| length in octets of X
5. General overview
The next six sections specify key generation, key syntax, the
encryption process, the decryption process, signature algorithms, and
object identifiers.
Each entity shall generate a pair of keys: a public key and a private
key. The encryption process shall be performed with one of the keys
and the decryption process shall be performed with the other key.
Thus the encryption process can be either a public-key operation or a
private-key operation, and so can the decryption process. Both
processes transform an octet string to another octet string. The
processes are inverses of each other if one process uses an entity's
public key and the other process uses the same entity's private key.
The encryption and decryption processes can implement either the
classic RSA transformations, or variations with padding.
6. Key generation
This section describes RSA key generation.
Each entity shall select a positive integer e as its public exponent.
Each entity shall privately and randomly select two distinct odd
primes p and q such that (p-1) and e have no common divisors, and
(q-1) and e have no common divisors.
The public modulus n shall be the product of the private prime
factors p and q:
n = pq .
The private exponent shall be a positive integer d such that de-1 is
divisible by both p-1 and q-1.
Kaliski Informational [Page 5]
RFC 2313 PKCS #1: RSA Encryption March 1998
The length of the modulus n in octets is the integer k satisfying
2^(8(k-1)) <= n < 2^(8k) .
The length k of the modulus must be at least 12 octets to accommodate
the block formats in this document (see Section 8).
Notes.
1. The public exponent may be standardized in
specific applications. The values 3 and F4 (65537) may have
some practical advantages, as noted in X.509 Annex C.
2. Some additional conditions on the choice of primes
may well be taken into account in order to deter
factorization of the modulus. These security conditions
fall outside the scope of this document. The lower bound on
the length k is to accommodate the block formats, not for
security.
7. Key syntax
This section gives the syntax for RSA public and private keys.
7.1 Public-key syntax
An RSA public key shall have ASN.1 type RSAPublicKey:
RSAPublicKey ::= SEQUENCE {
modulus INTEGER, -- n
publicExponent INTEGER -- e }
(This type is specified in X.509 and is retained here for
compatibility.)
The fields of type RSAPublicKey have the following meanings:
o modulus is the modulus n.
o publicExponent is the public exponent e.
Kaliski Informational [Page 6]
RFC 2313 PKCS #1: RSA Encryption March 1998
7.2 Private-key syntax
An RSA private key shall have ASN.1 type RSAPrivateKey:
RSAPrivateKey ::= SEQUENCE {
version Version,
modulus INTEGER, -- n
publicExponent INTEGER, -- e
privateExponent INTEGER, -- d
prime1 INTEGER, -- p
prime2 INTEGER, -- q
exponent1 INTEGER, -- d mod (p-1)
exponent2 INTEGER, -- d mod (q-1)
coefficient INTEGER -- (inverse of q) mod p }
Version ::= INTEGER
The fields of type RSAPrivateKey have the following meanings:
o version is the version number, for compatibility
with future revisions of this document. It shall
be 0 for this version of the document.
o modulus is the modulus n.
o publicExponent is the public exponent e.
o privateExponent is the private exponent d.
o prime1 is the prime factor p of n.
o prime2 is the prime factor q of n.
o exponent1 is d mod (p-1).
o exponent2 is d mod (q-1).
o coefficient is the Chinese Remainder Theorem
coefficient q-1 mod p.
Notes.
1. An RSA private key logically consists of only the
modulus n and the private exponent d. The presence of the
values p, q, d mod (p-1), d mod (p-1), and q-1 mod p is
intended for efficiency, as Quisquater and Couvreur have
shown [QC82]. A private-key syntax that does not include
Kaliski Informational [Page 7]
RFC 2313 PKCS #1: RSA Encryption March 1998
all the extra values can be converted readily to the syntax
defined here, provided the public key is known, according
to a result by Miller [Mil76].
2. The presence of the public exponent e is intended
to make it straightforward to derive a public key from the
private key.
8. Encryption process
This section describes the RSA encryption process.
The encryption process consists of four steps: encryption- block
formatting, octet-string-to-integer conversion, RSA computation, and
integer-to-octet-string conversion. The input to the encryption
process shall be an octet string D, the data; an integer n, the
modulus; and an integer c, the exponent. For a public-key operation,
the integer c shall be an entity's public exponent e; for a private-
key operation, it shall be an entity's private exponent d. The output
from the encryption process shall be an octet string ED, the
encrypted data.
The length of the data D shall not be more than k-11 octets, which is
positive since the length k of the modulus is at least 12 octets.
This limitation guarantees that the length of the padding string PS
is at least eight octets, which is a security condition.
Notes.
1. In typical applications of this document to
encrypt content-encryption keys and message digests, one
would have ||D|| <= 30. Thus the length of the RSA modulus
will need to be at least 328 bits (41 octets), which is
reasonable and consistent with security recommendations.
2. The encryption process does not provide an
explicit integrity check to facilitate error detection
should the encrypted data be corrupted in transmission.
However, the structure of the encryption block guarantees
that the probability that corruption is undetected is less
than 2-16, which is an upper bound on the probability that
a random encryption block looks like block type 02.
3. Application of private-key operations as defined
here to data other than an octet string containing a
message digest is not recommended and is subject to further
study.
Kaliski Informational [Page 8]
RFC 2313 PKCS #1: RSA Encryption March 1998
4. This document may be extended to handle data of
length more than k-11 octets.
8.1 Encryption-block formatting
A block type BT, a padding string PS, and the data D shall be
formatted into an octet string EB, the encryption block.
EB = 00 || BT || PS || 00 || D . (1)
The block type BT shall be a single octet indicating the structure of
the encryption block. For this version of the document it shall have
value 00, 01, or 02. For a private- key operation, the block type
shall be 00 or 01. For a public-key operation, it shall be 02.
The padding string PS shall consist of k-3-||D|| octets. For block
type 00, the octets shall have value 00; for block type 01, they
shall have value FF; and for block type 02, they shall be
pseudorandomly generated and nonzero. This makes the length of the
encryption block EB equal to k.
Notes.
1. The leading 00 octet ensures that the encryption
block, converted to an integer, is less than the modulus.
2. For block type 00, the data D must begin with a
nonzero octet or have known length so that the encryption
block can be parsed unambiguously. For block types 01 and
02, the encryption block can be parsed unambiguously since
the padding string PS contains no octets with value 00 and
the padding string is separated from the data D by an octet
with value 00.
3. Block type 01 is recommended for private-key
operations. Block type 01 has the property that the
encryption block, converted to an integer, is guaranteed to
be large, which prevents certain attacks of the kind
proposed by Desmedt and Odlyzko [DO86].
4. Block types 01 and 02 are compatible with PEM RSA
encryption of content-encryption keys and message digests
as described in RFC 1423.
Kaliski Informational [Page 9]
RFC 2313 PKCS #1: RSA Encryption March 1998
5. For block type 02, it is recommended that the
pseudorandom octets be generated independently for each
encryption process, especially if the same data is input to
more than one encryption process. Hastad's results [Has88]
motivate this recommendation.
6. For block type 02, the padding string is at least
eight octets long, which is a security condition for
public-key operations that prevents an attacker from
recoving data by trying all possible encryption blocks. For
simplicity, the minimum length is the same for block type
01.
7. This document may be extended in the future to
include other block types.
8.2 Octet-string-to-integer conversion
The encryption block EB shall be converted to an integer x, the
integer encryption block. Let EB1, ..., EBk be the octets of EB from
first to last. Then the integer x shall satisfy
k
x = SUM 2^(8(k-i)) EBi . (2)
i = 1
In other words, the first octet of EB has the most significance in
the integer and the last octet of EB has the least significance.
Note. The integer encryption block x satisfies 0 <= x < n since EB1
= 00 and 2^(8(k-1)) <= n.
8.3 RSA computation
The integer encryption block x shall be raised to the power c modulo
n to give an integer y, the integer encrypted data.
y = x^c mod n, 0 <= y < n .
This is the classic RSA computation.
8.4 Integer-to-octet-string conversion
The integer encrypted data y shall be converted to an octet string ED
of length k, the encrypted data. The encrypted data ED shall satisfy
Kaliski Informational [Page 10]
RFC 2313 PKCS #1: RSA Encryption March 1998
k
y = SUM 2^(8(k-i)) EDi . (3)
i = 1
where ED1, ..., EDk are the octets of ED from first to last.
In other words, the first octet of ED has the most significance in
the integer and the last octet of ED has the least significance.
9. Decryption process
This section describes the RSA decryption process.
The decryption process consists of four steps: octet-string-to-
integer conversion, RSA computation, integer-to-octet-string
conversion, and encryption-block parsing. The input to the decryption
process shall be an octet string ED, the encrypted data; an integer
n, the modulus; and an integer c, the exponent. For a public-key
operation, the integer c shall be an entity's public exponent e; for
a private-key operation, it shall be an entity's private exponent d.
The output from the decryption process shall be an octet string D,
the data.
It is an error if the length of the encrypted data ED is not k.
For brevity, the decryption process is described in terms of the
encryption process.
9.1 Octet-string-to-integer conversion
The encrypted data ED shall be converted to an integer y, the integer
encrypted data, according to Equation (3).
It is an error if the integer encrypted data y does not satisfy 0 <=
y < n.
9.2 RSA computation
The integer encrypted data y shall be raised to the power c modulo n
to give an integer x, the integer encryption block.
x = y^c mod n, 0 <= x < n .
This is the classic RSA computation.
Kaliski Informational [Page 11]
RFC 2313 PKCS #1: RSA Encryption March 1998
9.3 Integer-to-octet-string conversion
The integer encryption block x shall be converted to an octet string
EB of length k, the encryption block, according to Equation (2).
9.4 Encryption-block parsing
The encryption block EB shall be parsed into a block type BT, a
padding string PS, and the data D according to Equation (1).
It is an error if any of the following conditions occurs:
o The encryption block EB cannot be parsed
unambiguously (see notes to Section 8.1).
o The padding string PS consists of fewer than eight
octets, or is inconsistent with the block type BT.
o The decryption process is a public-key operation
and the block type BT is not 00 or 01, or the decryption
process is a private-key operation and the block type is
not 02.
10. Signature algorithms
This section defines three signature algorithms based on the RSA
encryption process described in Sections 8 and 9. The intended use of
the signature algorithms is in signing X.509/PEM certificates and
certificate-revocation lists, PKCS #6 extended certificates, and
other objects employing digital signatures such as X.401 message
tokens. The algorithms are not intended for use in constructing
digital signatures in PKCS #7. The first signature algorithm
(informally, "MD2 with RSA") combines the MD2 message-digest
algorithm with RSA, the second (informally, "MD4 with RSA") combines
the MD4 message-digest algorithm with RSA, and the third (informally,
"MD5 with RSA") combines the MD5 message-digest algorithm with RSA.
This section describes the signature process and the verification
process for the two algorithms. The "selected" message-digest
algorithm shall be either MD2 or MD5, depending on the signature
algorithm. The signature process shall be performed with an entity's
private key and the verification process shall be performed with an
entity's public key. The signature process transforms an octet string
(the message) to a bit string (the signature); the verification
process determines whether a bit string (the signature) is the
signature of an octet string (the message).
Kaliski Informational [Page 12]
RFC 2313 PKCS #1: RSA Encryption March 1998
Note. The only difference between the signature algorithms defined
here and one of the the methods by which signatures (encrypted
message digests) are constructed in PKCS #7 is that signatures here
are represented here as bit strings, for consistency with the X.509
SIGNED macro. In PKCS #7 encrypted message digests are octet strings.
10.1 Signature process
The signature process consists of four steps: message digesting, data
encoding, RSA encryption, and octet-string-to-bit-string conversion.
The input to the signature process shall be an octet string M, the
message; and a signer's private key. The output from the signature
process shall be a bit string S, the signature.
10.1.1 Message digesting
The message M shall be digested with the selected message- digest
algorithm to give an octet string MD, the message digest.
10.1.2 Data encoding
The message digest MD and a message-digest algorithm identifier shall
be combined into an ASN.1 value of type DigestInfo, described below,
which shall be BER-encoded to give an octet string D, the data.
DigestInfo ::= SEQUENCE {
digestAlgorithm DigestAlgorithmIdentifier,
digest Digest }
DigestAlgorithmIdentifier ::= AlgorithmIdentifier
Digest ::= OCTET STRING
The fields of type DigestInfo have the following meanings:
o digestAlgorithm identifies the message-digest
algorithm (and any associated parameters). For
this application, it should identify the selected
message-digest algorithm, MD2, MD4 or MD5. For
reference, the relevant object identifiers are the
following:
Kaliski Informational [Page 13]
RFC 2313 PKCS #1: RSA Encryption March 1998
md2 OBJECT IDENTIFIER ::=
{ iso(1) member-body(2) US(840) rsadsi(113549)
digestAlgorithm(2) 2 } md4 OBJECT IDENTIFIER ::=
{ iso(1) member-body(2) US(840) rsadsi(113549)
digestAlgorithm(2) 4 } md5 OBJECT IDENTIFIER ::=
{ iso(1) member-body(2) US(840) rsadsi(113549)
digestAlgorithm(2) 5 }
For these object identifiers, the parameters field of the
digestAlgorithm value should be NULL.
o digest is the result of the message-digesting
process, i.e., the message digest MD.
Notes.
1. A message-digest algorithm identifier is included
in the DigestInfo value to limit the damage resulting from
the compromise of one message-digest algorithm. For
instance, suppose an adversary were able to find messages
with a given MD2 message digest. That adversary might try
to forge a signature on a message by finding an innocuous-
looking message with the same MD2 message digest, and
coercing a signer to sign the innocuous-looking message.
This attack would succeed only if the signer used MD2. If
the DigestInfo value contained only the message digest,
however, an adversary could attack signers that use any
message digest.
2. Although it may be claimed that the use of a
SEQUENCE type violates the literal statement in the X.509
SIGNED and SIGNATURE macros that a signature is an
ENCRYPTED OCTET STRING (as opposed to ENCRYPTED SEQUENCE),
such a literal interpretation need not be required, as
I'Anson and Mitchell point out [IM90].
3. No reason is known that MD4 would not be
for very high security digital signature schemes, but
because MD4 was designed to be exceptionally fast, it is
"at the edge" in terms of risking successful cryptanalytic
attack. A message-digest algorithm can be considered
"broken" if someone can find a collision: two messages with
the same digest. While collisions have been found in
variants of MD4 with only two digesting "rounds"
Kaliski Informational [Page 14]
RFC 2313 PKCS #1: RSA Encryption March 1998
[Mer90][dBB92], none have been found in MD4 itself, which
has three rounds. After further critical review, it may be
appropriate to consider MD4 for very high security
applications.
MD5, which has four rounds and is proportionally slower
than MD4, is recommended until the completion of MD4's
review. The reported "pseudocollisions" in MD5's internal
compression function [dBB93] do not appear to have any
practical impact on MD5's security.
MD2, the slowest of the three, has the most conservative
design. No attacks on MD2 have been published.
10.1.3 RSA encryption
The data D shall be encrypted with the signer's RSA private key as
described in Section 7 to give an octet string ED, the encrypted
data. The block type shall be 01. (See Section 8.1.)
10.1.4 Octet-string-to-bit-string conversion
The encrypted data ED shall be converted into a bit string S, the
signature. Specifically, the most significant bit of the first octet
of the encrypted data shall become the first bit of the signature,
and so on through the least significant bit of the last octet of the
encrypted data, which shall become the last bit of the signature.
Note. The length in bits of the signature S is a multiple of eight.
10.2 Verification process
The verification process for both signature algorithms consists of
four steps: bit-string-to-octet-string conversion, RSA decryption,
data decoding, and message digesting and comparison. The input to the
verification process shall be an octet string M, the message; a
signer's public key; and a bit string S, the signature. The output
from the verification process shall be an indication of success or
failure.
10.2.1 Bit-string-to-octet-string conversion
The signature S shall be converted into an octet string ED, the
encrypted data. Specifically, assuming that the length in bits of the
signature S is a multiple of eight, the first bit of the signature
shall become the most significant bit of the first octet of the
Kaliski Informational [Page 15]
RFC 2313 PKCS #1: RSA Encryption March 1998
encrypted data, and so on through the last bit of the signature,
which shall become the least significant bit of the last octet of the
encrypted data.
It is an error if the length in bits of the signature S is not a
multiple of eight.
10.2.2 RSA decryption
The encrypted data ED shall be decrypted with the signer's RSA public
key as described in Section 8 to give an octet string D, the data.
It is an error if the block type recovered in the decryption process
is not 01. (See Section 9.4.)
10.2.3 Data decoding
The data D shall be BER-decoded to give an ASN.1 value of type
DigestInfo, which shall be separated into a message digest MD and a
message-digest algorithm identifier. The message-digest algorithm
identifier shall determine the "selected" message-digest algorithm
for the next step.
It is an error if the message-digest algorithm identifier does not
identify the MD2, MD4 or MD5 message-digest algorithm.
10.2.4 Message digesting and comparison
The message M shall be digested with the selected message-digest
algorithm to give an octet string MD', the comparative message
digest. The verification process shall succeed if the comparative
message digest MD' is the same as the message digest MD, and the
verification process shall fail otherwise.
11. Object identifiers
This document defines five object identifiers: pkcs-1, rsaEncryption,
md2WithRSAEncryption, md4WithRSAEncryption, and md5WithRSAEncryption.
The object identifier pkcs-1 identifies this document.
pkcs-1 OBJECT IDENTIFIER ::=
{ iso(1) member-body(2) US(840) rsadsi(113549)
pkcs(1) 1 }
Kaliski Informational [Page 16]
RFC 2313 PKCS #1: RSA Encryption March 1998
The object identifier rsaEncryption identifies RSA public and private
keys as defined in Section 7 and the RSA encryption and decryption
processes defined in Sections 8 and 9.
rsaEncryption OBJECT IDENTIFIER ::= { pkcs-1 1 }
The rsaEncryption object identifier is intended to be used in the
algorithm field of a value of type AlgorithmIdentifier. The
parameters field of that type, which has the algorithm-specific
syntax ANY DEFINED BY algorithm, would have ASN.1 type NULL for this
algorithm.
The object identifiers md2WithRSAEncryption, md4WithRSAEncryption,
md5WithRSAEncryption, identify, respectively, the "MD2 with RSA,"
"MD4 with RSA," and "MD5 with RSA" signature and verification
processes defined in Section 10.
md2WithRSAEncryption OBJECT IDENTIFIER ::= { pkcs-1 2 }
md4WithRSAEncryption OBJECT IDENTIFIER ::= { pkcs-1 3 }
md5WithRSAEncryption OBJECT IDENTIFIER ::= { pkcs-1 4 }
These object identifiers are intended to be used in the algorithm
field of a value of type AlgorithmIdentifier. The parameters field of
that type, which has the algorithm-specific syntax ANY DEFINED BY
algorithm, would have ASN.1 type NULL for these algorithms.
Note. X.509's object identifier rsa also identifies RSA public keys
as defined in Section 7, but does not identify private keys, and
identifies different encryption and decryption processes. It is
expected that some applications will identify public keys by rsa.
Such public keys are compatible with this document; an rsaEncryption
process under an rsa public key is the same as the rsaEncryption
process under an rsaEncryption public key.
Security Considerations
Security issues are discussed throughout this memo.
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.
Kaliski Informational [Page 17]
RFC 2313 PKCS #1: RSA Encryption March 1998
Version 1.4
Version 1.4 is part of the June 3, 1991 initial public release of
PKCS. Version 1.4 was published as NIST/OSI Implementors' Workshop
document SEC-SIG-91-18.
Version 1.5
Version 1.5 incorporates several editorial changes, including updates
to the references and the addition of a revision history. The
following substantive changes were made:
o Section 10: "MD4 with RSA" signature and
verification processes are added.
o Section 11: md4WithRSAEncryption object identifier
is added.
Supersedes June 3, 1991 version, which was also published as NIST/OSI
Implementors' Workshop document SEC-SIG-91-18.
Acknowledgements
This document is based on a contribution of RSA Laboratories, a
division of RSA Data Security, Inc. Any substantial use of the text
from this document must acknowledge RSA Data Security, Inc. RSA Data
Security, Inc. requests that all material mentioning or referencing
this document identify this as "RSA Data Security, Inc. PKCS #1".
Author's Address
Burt Kaliski
RSA Laboratories East
20 Crosby Drive
Bedford, MA 01730
Phone: (617) 687-7000
EMail:
[email protected]
Kaliski Informational [Page 18]
RFC 2313 PKCS #1: RSA Encryption March 1998
Full Copyright Statement
Copyright (C) The Internet Society (1998). 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.
Kaliski Informational [Page 19]
