rfc2313.txt

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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





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             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.




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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.





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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.



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   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.



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   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.











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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 }