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Obsoleted by:2437 INFORMATIONAL
Network Working Group                                      B. KaliskiRequest for Comments: 2313                      RSA Laboratories EastCategory: Informational                                    March 1998PKCS #1: RSA EncryptionVersion 1.5Status 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 encryptedKaliski                      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 inRFC 1319.   MD4: RSA Data Security, Inc.'s MD4 message-digest algorithm, as   defined inRFC 1320.   MD5: RSA Data Security, Inc.'s MD5 message-digest algorithm, as   defined inRFC 1321.   modulus: Integer constructed as the product of two primes.   PEM: Internet Privacy-Enhanced Mail, as defined inRFC 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 X5. 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 (seeSection 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 19987.2 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 includeKaliski                      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 inRFC 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 satisfyKaliski                      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 19989.3 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 toSection 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 Sections8 and9. 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 inSection 7 to give an octet string ED, the encrypted   data. The block type shall be 01. (SeeSection 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 theKaliski                      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 inSection 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. (SeeSection 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 inSection 7 and the RSA encryption and decryption   processes defined in Sections8 and9.   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 inSection 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 inSection 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:        oSection 10: "MD4 with RSA" signature and             verification processes are added.        oSection 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.comKaliski                      Informational                     [Page 18]

RFC 2313                PKCS #1: RSA Encryption               March 1998Full 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]

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