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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






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                                     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.







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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).





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   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:










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   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"






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             [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





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   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 }






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   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.






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   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: burt@rsa.com













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Full Copyright Statement

   Copyright (C) The Internet Society (1998).  All Rights Reserved.

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