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Use of the RSA-KEM Key Transport Algorithm in the Cryptographic Message Syntax (CMS)
draft-ietf-smime-cms-rsa-kem-13

The information below is for an old version of the document that is already published as an RFC.
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This is an older version of an Internet-Draft that was ultimately published as RFC 5990.
Authors John Brainard , Burt Kaliski , Sean Turner , James Randall
Last updated 2015-10-14 (Latest revision 2010-06-01)
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draft-ietf-smime-cms-rsa-kem-13
S/MIME WG                             James Randall, Randall Consulting 
Internet Draft                                        Burt Kaliski, EMC 
Intended Status: Standards Track                     John Brainard, RSA 
                                                      Sean Turner, IECA 
Expires: November 29, 2010                                 May 29, 2010 
 
 
                                      
             Use of the RSA-KEM Key Transport Algorithm in CMS 
                   <draft-ietf-smime-cms-rsa-kem-13.txt> 

Abstract 

   The RSA-KEM Key Transport Algorithm is a one-pass (store-and-forward) 
   mechanism for transporting keying data to a recipient using the 
   recipient's RSA public key. This document specifies the conventions 
   for using the RSA-KEM Key Transport Algorithm with the Cryptographic 
   Message Syntax (CMS). The ASN.1 syntax is aligned with an expected 
   forthcoming change to ANS X9.44. 

Status of this Memo 

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   provisions of BCP 78 and BCP 79. This document may contain material 
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   The list of Internet-Draft Shadow Directories can be accessed at 
   http://www.ietf.org/shadow.html 

   This Internet-Draft will expire on November 29, 2010. 

Copyright Notice 

   Copyright (c) 2010 IETF Trust and the persons identified as the 
   document authors.  All rights reserved. 

   This document is subject to BCP 78 and the IETF Trust's Legal 
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   (http://trustee.ietf.org/license-info) in effect on the date of 
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   include Simplified BSD License text as described in Section 4.e of 
   the Trust Legal Provisions and are provided without warranty as 
   described in the Simplified BSD License. 

Conventions Used in This Document 

   The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT", 
   "SHOULD", "SHOULD NOT", "RECOMMENDED",  "MAY", and "OPTIONAL" in this 
   document are to be interpreted as described in RFC 2119 [STDWORDS]. 

Table of Contents 

   1. Introduction...................................................3 
   2. Use in CMS.....................................................4 
      2.1. Underlying Components.....................................4 
      2.2. RecipientInfo Conventions.................................5 
      2.3. Certificate Conventions...................................5 
      2.4. SMIMECapabilities Attribute Conventions...................6 
   3. Security Considerations........................................7 
   4. IANA Considerations............................................9 
   5. Acknowledgements...............................................9 
   6. References....................................................10 
      6.1. Normative References.....................................10 
      6.2. Informative References...................................11 
   Appendix A. RSA-KEM Key Transport Algorithm......................11 
      A.1. Underlying Components....................................12 
      A.2. Sender's Operations......................................12 
      A.3. Recipient's Operations...................................13 
   Appendix B. ASN.1 Syntax.........................................15 
      B.1. RSA-KEM Key Transport Algorithm..........................15 
      B.2. Selected Underlying Components...........................17 
 
 
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         B.2.1. Key Derivation Functions............................17 
         B.2.2. Symmetric Key-Wrapping Schemes......................19 
      B.3. ASN.1 module.............................................20 
      B.4. Examples.................................................26 
   Authors' Addresses...............................................28 
 

1. Introduction 

   The RSA-KEM Key Transport Algorithm is a one-pass (store-and-forward) 
   mechanism for transporting keying data to a recipient using the 
   recipient's RSA public key. 

   Most previous key transport algorithms based on the RSA public-key 
   cryptosystem (e.g., the popular PKCS #1 v1.5 algorithm [PKCS1]) have 
   the following general form: 

    1. Format or "pad" the keying data to obtain an integer m. 

    2. Encrypt the integer m with the recipient's RSA public key: 

          c = m^e mod n 

    3. Output c as the encrypted keying data. 

   The RSA-KEM Key Transport Algorithm takes a different approach that 
   provides higher security assurance, by encrypting a _random_ integer 
   with the recipient's public key, and using a symmetric key-wrapping 
   scheme to encrypt the keying data. It has the following form: 

    1. Generate a random integer z between 0 and n-1. 

    2. Encrypt the integer z with the recipient's RSA public key: 

         c = z^e mod n 

    3. Derive a key-encrypting key KEK from the integer z. 

    4. Wrap the keying data using KEK to obtain wrapped keying data WK. 

    5. Output c and WK as the encrypted keying data. 

   This different approach provides higher security assurance because 
   (a) the input to the underlying RSA operation is effectively a random 
   integer between 0 and n-1, where n is the RSA modulus, so it does not 
   have any structure that could be exploited by an adversary, and (b) 
   the input is independent of the keying data so the result of the RSA 
 
 
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   decryption operation is not directly available to an adversary.  As a 
   result, the algorithm enjoys a "tight" security proof in the random 
   oracle model. (In other padding schemes, such as PKCS #1 v1.5, the 
   input has structure and/or depends on the keying data, and the 
   provable security assurances are not as strong.) The approach is also 
   architecturally convenient because the public-key operations are 
   separate from the symmetric operations on the keying data. Another 
   benefit is that the length of the keying data is bounded only by the 
   symmetric key-wrapping scheme, not the size of the RSA modulus. 

   The RSA-KEM Key Transport Algorithm in various forms is being adopted 
   in several draft standards as well as in ANS-X9.44 [ANS-9.44]. It has 
   also been recommended by the NESSIE project [NESSIE].  Originally, 
   [ANS-9.44] specified the of different object identifier to identify 
   the RSA-KEM Key Transport Algorithm. [ANS-9.44] used id-ac-generic-
   hybrid while this document uses id-rsa-kem.  These OIDs are used in 
   the KeyTransportInfo field to indicate the key encryption algorithm, 
   in certificates to allow recipients to restrict their public keys for 
   use with RSA-KEM only, and in SMIME Capability attributes to allow 
   recipients to advertise their support for RSA-KEM.  Legacy 
   implementations that wish to interoperate with [ANS-X9.44] should 
   consult that specification for more information on id-ac-generic-
   hybrid. 

   For completeness, a specification of the algorithm is given in 
   Appendix A of this document; ASN.1 syntax is given in Appendix B. 

   NOTE: The term KEM stands for "key encapsulation mechanism" and 
   refers to the first three steps of the process above. The 
   formalization of key transport algorithms (or more generally, 
   asymmetric encryption schemes) in terms of key encapsulation 
   mechanisms is described further in research by Victor Shoup leading 
   to the development of the ISO/IEC 18033-2 standard [SHOUP]. 

2. Use in CMS 

   The RSA-KEM Key Transport Algorithm MAY be employed for one or more 
   recipients in the CMS enveloped-data content type (Section 6 of 
   [CMS]), where the keying data processed by the algorithm is the CMS 
   content-encryption key. 

2.1. Underlying Components 

   A CMS implementation that supports the RSA-KEM Key Transport 
   Algorithm MUST support at least the following underlying components: 

 
 
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     o For the key derivation function, KDF3 (see [ANS-9.44]) based on 
       SHA-256 (see [FIPS-180-3]). KDF3 is an instantiation of the 
       Concatenation Key Derivation Function defined in [NIST-SP800-
       56A]. 

     o For the key-wrapping scheme, AES-Wrap-128, i.e., the AES Key 
       Wrap with a 128-bit key encrypting key (see [AES-WRAP]).  

   An implementation SHOULD also support KDF2 (see [ANS-X9.44]) based on 
   SHA-1 (this function is also specified as the key derivation function 
   in [ANS-X9.63]). The Camellia key wrap algorithm (see [CAMELLIA]) 
   SHOULD be supported if Camellia is supported as a content-encryption 
   cipher.  The Triple-DES Key Wrap (see [3DES-WRAP]) SHOULD also be 
   supported if Triple-DES is supported as a content-encryption cipher. 

   It MAY support other underlying components. When AES or Camellia are 
   used, the data block size is 128 bits and the key size can be 128, 
   192, or 256 bits, while Triple DES requires a data block size of 64 
   bits and a key size of 112 or 168 bits. 

2.2. RecipientInfo Conventions 

   When the RSA-KEM Key Transport Algorithm is employed for a recipient, 
   the RecipientInfo alternative for that recipient MUST be 
   KeyTransRecipientInfo. The algorithm-specific fields of the 
   KeyTransRecipientInfo value MUST have the following values: 

     o keyEncryptionAlgorithm.algorithm MUST be id-rsa-kem (see 
       Appendix B); 

     o keyEncryptionAlgorithm.parameters MUST be a value of type 
       GenericHybridParameters, identifying the RSA-KEM key 
       encapsulation mechanism (see Appendix B);  

     o encryptedKey MUST be the encrypted keying data output by the 
       algorithm, where the keying data is the content-encryption key 
       (see Appendix A).  

2.3. Certificate Conventions 

   The conventions specified in this section augment RFC 5280 [PROFILE]. 

   A recipient who employs the RSA-KEM Key Transport Algorithm MAY 
   identify the public key in a certificate by the same 
   AlgorithmIdentifier as for the PKCS #1 v1.5 algorithm, i.e., using 
   the rsaEncryption object identifier [PKCS1]. The fact that the user 
   will accept RSA-KEM with this public key is not indicated by the use 
 
 
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   of this identifier.  This MAY be signaled by the use of the 
   appropriate SMIME Capabilities either in a message or in the 
   certificate. 

   If the recipient wishes only to employ the RSA-KEM Key Transport 
   Algorithm with a given public key, the recipient MUST identify the 
   public key in the certificate using the id-rsa-kem object identifier 
   (see Appendix B). When the id-rsa-kem algorithm identifier appears in 
   the SubjectPublicKeyInfo algorithm field, the encoding SHALL omit the 
   parameters field from AlgorithmIdentifier. That is, the 
   AlgorithmIdentifier SHALL be a SEQUENCE of one component, the object 
   identifier id-rsa-kem. 

   Regardless of the AlgorithmIdentifier used, the RSA public key is 
   encoded in the same manner in the subject public key information. The 
   RSA public key MUST be encoded using the type RSAPublicKey type: 

      RSAPublicKey ::= SEQUENCE { 
         modulus            INTEGER, -- n 
         publicExponent     INTEGER  -- e 
      } 

   Here, the modulus is the modulus n, and publicExponent is the public 
   exponent e. The DER encoded RSAPublicKey is carried in the 
   subjectPublicKey BIT STRING within the subject public key 
   information. 

   The intended application for the key MAY be indicated in the key 
   usage certificate extension (see [PROFILE], Section 4.2.1.3). If the 
   keyUsage extension is present in a certificate that conveys an RSA 
   public key with the id-rsa-kem object identifier as discussed above, 
   then the key usage extension MUST contain the following value: 

       keyEncipherment. 

   dataEncipherment SHOULD NOT be present. That is, a key intended to be 
   employed only with the RSA-KEM Key Transport Algorithm SHOULD NOT 
   also be employed for data encryption or for authentication such as in 
   signatures. Good cryptographic practice employs a given RSA key pair 
   in only one scheme.  This practice avoids the risk that vulnerability 
   in one scheme may compromise the security of the other, and may be 
   essential to maintain provable security. 

2.4. SMIMECapabilities Attribute Conventions 

   RFC 3851 [MSG], Section 2.5.2 defines the SMIMECapabilities signed 
   attribute (defined as a SEQUENCE of SMIMECapability SEQUENCEs) to be 
 
 
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   used to specify a partial list of algorithms that the software 
   announcing the SMIMECapabilities can support. When constructing a 
   signedData object, compliant software MAY include the 
   SMIMECapabilities signed attribute announcing that it supports the 
   RSA-KEM Key Transport algorithm.  

   The SMIMECapability SEQUENCE representing the RSA-KEM Key Transport 
   Algorithm MUST include the id-rsa-kem object identifier (see Appendix 
   B) in the capabilityID field and MUST include a 
   GenericHybridParameters value in the parameters field identifying the 
   components with which the algorithm is to be employed. 

   The DER encoding of a SMIMECapability SEQUENCE is the same as the DER 
   encoding of an AlgorithmIdentifier. Example DER encodings for typical 
   sets of components are given in Appendix B.4. 

3. Security Considerations 

   The RSA-KEM Key Transport Algorithm should be considered for new CMS-
   based applications as a replacement for the widely implemented RSA 
   encryption algorithm specified originally in PKCS #1 v1.5 (see 
   [PKCS1] and Section 4.2.1 of [CMSALGS]), which is vulnerable to 
   chosen-ciphertext attacks.  The RSAES-OAEP Key Transport Algorithm 
   has also been proposed as a replacement (see [PKCS1] and [CMS-OAEP]). 
   RSA-KEM has the advantage over RSAES-OAEP of a tighter security 
   proof, but the disadvantage of slightly longer encrypted keying data. 

   The security of the RSA-KEM Key Transport Algorithm described in this 
   document can be shown to be tightly related to the difficulty of 
   either solving the RSA problem or breaking the underlying symmetric 
   key-wrapping scheme, if the underlying key derivation function is 
   modeled as a random oracle, and assuming that the symmetric key-
   wrapping scheme satisfies the properties of a data encapsulation 
   mechanism [SHOUP]. While in practice a random-oracle result does not 
   provide an actual security proof for any particular key derivation 
   function, the result does provide assurance that the general 
   construction is reasonable; a key derivation function would need to 
   be particularly weak to lead to an attack that is not possible in the 
   random oracle model. 

   The RSA key size and the underlying components should be selected 
   consistent with the desired symmetric security level for an 
   application. Several security levels have been identified in NIST 
   FIPS PUB 800-57 [NIST-GUIDELINE]. For brevity, the first three levels 
   are mentioned here: 

 
 
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     o 80-bit security. The RSA key size SHOULD be at least 1024 bits, 
       the hash function underlying the KDF SHOULD be SHA-1 or above, 
       and the symmetric key-wrapping scheme SHOULD be AES Key Wrap, 
       Triple-DES Key Wrap, or Camellia Key Wrap.  

     o 112-bit security. The RSA key size SHOULD be at least 2048 bits, 
       the hash function underlying the KDF SHOULD be SHA-224 or above, 
       and the symmetric key-wrapping scheme SHOULD be AES Key Wrap, 
       Triple-DES Key Wrap, or Camellia Key Wrap.  

     o 128-bit security. The RSA key size SHOULD be at least 3072 bits, 
       the hash function underlying the KDF SHOULD be SHA-256 or above, 
       and the symmetric key-wrapping scheme SHOULD be AES Key Wrap or 
       Camellia Key Wrap.  

   Note that the AES Key Wrap or Camellia Key Wrap MAY be used at all 
   three of these levels; the use of AES or Camellia does not require a 
   128-bit security level for other components. 

   Implementations MUST protect the RSA private key and the content-
   encryption key. Compromise of the RSA private key may result in the 
   disclosure of all messages protected with that key. Compromise of the 
   content-encryption key may result in disclosure of the associated 
   encrypted content. 

   Additional considerations related to key management may be found in 
   [NIST-GUIDELINE]. 

   The security of the algorithm also depends on the strength of the 
   random number generator, which SHOULD have a comparable security 
   level. For further discussion on random number generation, please see 
   [RANDOM]. 

   Implementations SHOULD NOT reveal information about intermediate 
   values or calculations, whether by timing or other "side channels", 
   or otherwise an opponent may be able to determine information about 
   the keying data and/or the recipient's private key. Although not all 
   intermediate information may be useful to an opponent, it is 
   preferable to conceal as much information as is practical, unless 
   analysis specifically indicates that the information would not be 
   useful. 

   Generally, good cryptographic practice employs a given RSA key pair 
   in only one scheme.  This practice avoids the risk that vulnerability 
   in one scheme may compromise the security of the other, and may be 
   essential to maintain provable security.  While RSA public keys have 
   often been employed for multiple purposes such as key transport and 
 
 
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   digital signature without any known bad interactions, for increased 
   security assurance, such combined use of an RSA key pair is NOT 
   RECOMMENDED in the future (unless the different schemes are 
   specifically designed to be used together). 

   Accordingly, an RSA key pair used for the RSA-KEM Key Transport 
   Algorithm SHOULD NOT also be used for digital signatures. (Indeed, 
   ASC X9 requires such a separation between key establishment key pairs 
   and digital signature key pairs.) Continuing this principle of key 
   separation, a key pair used for the RSA-KEM Key Transport Algorithm 
   SHOULD NOT be used with other key establishment schemes, or for data 
   encryption, or with more than one set of underlying algorithm 
   components. 

   Parties MAY formalize the assurance that one another's 
   implementations are correct through implementation validation, e.g. 
   NIST's Cryptographic Module Validation Program (CMVP). 

4. IANA Considerations 

   Within the CMS, algorithms are identified by object identifiers 
   (OIDs). With one exception, all of the OIDs used in this document 
   were assigned in other IETF documents, in ISO/IEC standards 
   documents, by the National Institute of Standards and Technology 
   (NIST), and in Public-Key Cryptography Standards (PKCS) documents. 
   The one exception is that the ASN.1 module's identifier (see Appendix 
   B.3) is assigned in this document. No further action by the IANA is 
   necessary for this document or any anticipated updates.  

5. Acknowledgements 

   This document is one part of a strategy to align algorithm standards 
   produced by ASC X9, ISO/IEC JTC1 SC27, NIST, and the IETF. We would 
   like to thank the members of the ASC X9F1 working group for their 
   contributions to drafts of ANS X9.44 which led to this specification. 

   Our thanks to Russ Housley as well for his guidance and 
   encouragement. We also appreciate the helpful direction we've 
   received from Blake Ramsdell and Jim Schaad in bringing this document 
   to fruition. A special thanks to Magnus Nystrom for his assistance on 
   Appendix B. Thanks also to Bob Griffin and John Linn for both 
   editorial direction and procedural guidance. 

 
 
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6. References 

6.1. Normative References 

   [3DES-WRAP]       Housley, R. Triple-DES and RC2 Key Wrapping. RFC 
                     3217. December 2001. 

   [AES-WRAP]        Schaad, J. and R. Housley. Advanced Encryption 
                     Standard (AES) Key Wrap Algorithm. RFC 3394. 
                     September 2002. 

   [ANS-X9.44]       ASC X9F1 Working Group. American National Standard 
                     X9.44: Public Key Cryptography for the Financial 
                     Services Industry -- Key Establishment Using 
                     Integer Factorization Cryptography. 2007. 

   [ANS-X9.63]       American National Standard X9.63-2002: Public Key 
                     Cryptography for the Financial Services Industry: 
                     Key Agreement and Key Transport Using Elliptic 
                     Curve Cryptography. 

   [CAMELLIA]        Kato, A., Moriai, S., and Kanda, M.: Use of the 
                     Camellia Encryption Algorithm in Cryptographic 
                     Message Syntax. RFC 3657. December 2005. 

   [CMS]             Housley, R. Cryptographic Message Syntax. RFC 
                     5652. September 20009. 

   [CMSALGS]         Housley, R. Cryptographic Message Syntax (CMS) 
                     Algorithms. RFC 3370. August 2002. 

   [FIPS-180-3]      National Institute of Standards and Technology 
                     (NIST). FIPS 180-3: Secure Hash Standard. October 
                     2008. 

   [MSG]             Ramsdell, B., and S. Turner. S/MIME Version 3.2 
                     Message Specification. RFC 5751. January 2010. 

   [PROFILE]         Cooper, D., Santesson, S., Farrell, S., Boeyen, 
                     S., Housley, R., and W. Polk. Internet X.509 
                     Public Key Infrastructure Certificate and 
                     Certificate Revocation List (CRL) Profile. RFC 
                     5280. May 2008. 

   [STDWORDS]        Bradner, S. Key Words for Use in RFCs to Indicate 
                     Requirement Levels. RFC 2119. March 1997. 

 
 
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6.2. Informative References 

   [AES-WRAP-PAD]    Housley, R., and M. Dworkin. Advanced Encryption 
                     Standard (AES) Key Wrap with Padding Algorithm. 
                     RFC 5649. August 2009. 

   [CMS-OAEP]        Housley, R. Use of the RSAES-OAEP Key Transport 
                     Algorithm in the Cryptographic Message Syntax 
                     (CMS). RFC 3560. July 2003. 

   [NESSIE]          NESSIE Consortium. Portfolio of Recommended 
                     Cryptographic Primitives. February 27, 2003. 
                     Available via http://www.cryptonessie.org/. 

   [NIST-GUIDELINE]  National Institute of Standards and Technology. 
                     Special Publication 800-57: Recommendation for 
                     Pairwise Key Establishment Schemes Using Discrete 
                     Logarithm Cryptography. March 2007. Available via:  
                     http://csrc.nist.gov/publications/index.html.  

   [NIST-SP800-56A]  National Institute of Standards and Technology.  
                     Special Publication 800-56A: Recommendation for 
                     Key Management. Part 1: General Guideline. August 
                     2005. Available via: 
                     http://csrc.nist.gov/publications/index.html.  

   [PKCS1]           Jonsson, J. and B. Kaliski. PKCS #1: RSA 
                     Cryptography Specifications Version 2.1. RFC 3447. 
                     February 2003. 

   [RANDOM]          Eastlake, D., S. Crocker, and J. Schiller. 
                     Randomness Recommendations for Security. RFC 4086. 
                     June 2005. 

   [SHOUP]           Shoup, V. A Proposal for an ISO Standard for 
                     Public Key Encryption. Version 2.1, December 20, 
                     2001. Available via http://www.shoup.net/papers/. 

Appendix A. RSA-KEM Key Transport Algorithm 

   The RSA-KEM Key Transport Algorithm is a one-pass (store-and-forward) 
   mechanism for transporting keying data to a recipient using the 
   recipient's RSA public key. 

   With this type of algorithm, a sender encrypts the keying data using 
   the recipient's public key to obtain encrypted keying data. The 

 
 
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   recipient decrypts the encrypted keying data using the recipient's 
   private key to recover the keying data. 

A.1. Underlying Components 

   The algorithm has the following underlying components: 

     o KDF, a key derivation function, which derives keying data of a 
       specified length from a shared secret value;  

     o Wrap, a symmetric key-wrapping scheme, which encrypts keying 
       Data using a key-encrypting key.  

   In the following, kekLen denotes the length in bytes of the key-
   encrypting key for the underlying symmetric key-wrapping scheme. 

   In this scheme, the length of the keying data to be transported MUST 
   be among the lengths supported by the underlying symmetric key-
   wrapping scheme. (Both the AES and Camellia Key Wraps, for instance, 
   require the length of the keying data to be a multiple of 8 bytes, 
   and at least 16 bytes.) Usage and formatting of the keying data 
   (e.g., parity adjustment for Triple-DES keys) is outside the scope of 
   this algorithm. With some key derivation functions, it is possible to 
   include other information besides the shared secret value in the 
   input to the function. Also, with some symmetric key-wrapping 
   schemes, it is possible to associate a label with the keying data. 
   Such uses are outside the scope of this document, as they are not 
   directly supported by CMS. 

A.2. Sender's Operations 

   Let (n,e) be the recipient's RSA public key (see [PKCS1] for details) 
   and let K be the keying data to be transported. 

   Let nLen denote the length in bytes of the modulus n, i.e., the least 
   integer such that 2^{8*nLen} > n. 

   The sender performs the following operations: 

   1. Generate a random integer z between 0 and n-1 (see Note), and 
   convert z to a byte string Z of length nLen, most significant byte 
   first: 

         z = RandomInteger (0, n-1) 

         Z = IntegerToString (z, nLen) 

 
 
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   2. Encrypt the random integer z using the recipient's public key 
   (n,e) and convert the resulting integer c to a ciphertext C, a byte 
   string of length nLen: 

        c = z^e mod n 

        C = IntegerToString (c, nLen) 

   3. Derive a key-encrypting key KEK of length kekLen bytes from the 
   byte string Z using the underlying key derivation function: 

        KEK = KDF (Z, kekLen) 

   4. Wrap the keying data K with the key-encrypting key KEK using the 
   underlying key-wrapping scheme to obtain wrapped keying data WK: 

        WK = Wrap (KEK, K) 

   5. Concatenate the ciphertext C and the wrapped keying data WK to 
   obtain the encrypted keying data EK: 

        EK = C || WK 

   6. Output the encrypted keying data EK. 

   NOTE: The random integer z MUST be generated independently at random 
   for different encryption operations, whether for the same or 
   different recipients. 

A.3. Recipient's Operations 

   Let (n,d) be the recipient's RSA private key (see [PKCS1]; other 
   private key formats are allowed) and let EK be the encrypted keying 
   data. 

   Let nLen denote the length in bytes of the modulus n. 

   The recipient performs the following operations: 

   1. Separate the encrypted keying data EK into a ciphertext C of 
     length nLen bytes and wrapped keying data WK: 

        C || WK = EK  

     If the length of the encrypted keying data is less than nLen 
     bytes, output "decryption error" and stop.  

 
 
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   2. Convert the ciphertext C to an integer c, most significant byte 
     first. Decrypt the integer c using the recipient's private key 
     (n,d) to recover an integer z (see Note): 

         c = StringToInteger (C)  

         z = c^d mod n  

      If the integer c is not between 0 and n-1, output "decryption 
      error" and stop. 

   3. Convert the integer z to a byte string Z of length nLen, most 
   significant byte first (see Note): 

        Z = IntegerToString (z, nLen) 

   4. Derive a key-encrypting key KEK of length kekLen bytes from the 
   byte string Z using the underlying key derivation function (see 
   Note): 

        KEK = KDF (Z, kekLen) 

   5. Unwrap the wrapped keying data WK with the key-encrypting key KEK 
      using the underlying key-wrapping scheme to recover the keying 
      data K: 

        K = Unwrap (KEK, WK) 

      If the unwrapping operation outputs an error, output "decryption 
      error" and stop.  

   6. Output the keying data K. 

   NOTE: Implementations SHOULD NOT reveal information about the integer 
   z and the string Z, nor about the calculation of the exponentiation 
   in Step 2, the conversion in Step 3, or the key derivation in Step 4, 
   whether by timing or other "side channels". The observable behavior 
   of the implementation SHOULD be the same at these steps for all 
   ciphertexts C that are in range. (For example, IntegerToString 
   conversion should take the same amount of time regardless of the 
   actual value of the integer z.) The integer z, the string Z and other 
   intermediate results MUST be securely deleted when they are no longer 
   needed. 

 
 
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Appendix B. ASN.1 Syntax 

   The ASN.1 syntax for identifying the RSA-KEM Key Transport Algorithm 
   is an extension of the syntax for the "generic hybrid cipher" in ANS 
   X9.44 [ANS-X9.44]. The syntax for the scheme is given in Section B.1. 
   The syntax for selected underlying components including those 
   mentioned above is given in B.2. 

   The following object identifier prefixes are used in the definitions 
   below: 

     is18033-2 OID ::= { iso(1) standard(0) is18033(18033) part2(2) } 

     nistAlgorithm OID ::= { 
        joint-iso-itu-t(2) country(16) us(840) organization(1) 
        gov(101) csor(3) nistAlgorithm(4) 
     } 

     pkcs-1 OID ::= { 
        iso(1) member-body(2) us(840) rsadsi(113549) pkcs(1) pkcs-1(1) 
     } 

     x9-44 OID ::= { iso(1) identified-organization(3) tc68(133) 
       country(16) x9(840) x9Standards(9) x9-44(44) } 

     x9-44-components OID ::= { x9-44 components(1) } 

   NullParms is a more descriptive synonym for NULL when an algorithm 
   identifier has null parameters: 

     NullParms ::= NULL 

   The material in this Appendix is based on ANS X9.44. 

B.1. RSA-KEM Key Transport Algorithm 

   The object identifier for the RSA-KEM Key Transport Algorithm is id-
   rsa-kem, which is defined in the draft as: 

     id-rsa-kem OID ::= { 
        iso(1) member-body(2) us(840) rsadsi(113549) pkcs(1) 
        pkcs-9(9) smime(16) alg(3) 14 
     } 

   When id-rsa-kem is used in an AlgorithmIdentifier, the parameters 
   MUST employ the GenericHybridParameters syntax. The parameters MUST 

 
 
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   be absent when used in the subjectPublicKeyInfo field. The syntax for 
   GenericHybridParameters is as follows: 

     GenericHybridParameters ::= { 
        kem  KeyEncapsulationMechanism, 
        dem  DataEncapsulationMechanism 
     } 

   The fields of type GenericHybridParameters have the following 
   meanings: 

     o kem identifies the underlying key encapsulation mechanism, which 
       in this case is also denoted as RSA-KEM.  

      The object identifier for RSA-KEM (as a key encapsulation 
      mechanism) is id-kem-rsa as: 

         id-kem-rsa OID ::= { 
            is18033-2 key-encapsulation-mechanism(2) rsa(4) 
         } 

      The associated parameters for id-kem-rsa have type 
      RsaKemParameters: 

        RsaKemParameters ::= { 
           keyDerivationFunction  KeyDerivationFunction, 
           keyLength              KeyLength 
        } 

      The fields of type RsaKemParameters have the following meanings: 

      *  keyDerivationFunction identifies the underlying key derivation 
      function. For alignment with ANS X9.44, it MUST be KDF2 or KDF3. 
      However, other key derivation functions MAY be used with CMS. 
      Please see B.2.1 for the syntax for KDF2 and KDF3. 

        KeyDerivationFunction ::= AlgorithmIdentifier {{KDFAlgorithms}}  

        KDFAlgorithms ALGORITHM ::= { 
           kdf2 | kdf3, 
           ...  -- implementations may define other methods 
        } 

      *  keyLength is the length in bytes of the key-encrypting key, 
      which depends on the underlying symmetric key-wrapping scheme. 

        KeyLength ::= INTEGER (1..MAX) 
 
 
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     o dem identifies the underlying data encapsulation mechanism. For 
       alignment with ANS X9.44, it MUST be an X9-approved symmetric 
       key-wrapping scheme. (See Note.) However, other symmetric key-
       wrapping schemes MAY be used with CMS. Please see B.2.2 for the 
       syntax for the AES, Triple-DES, and Camellia Key Wraps.  

        DataEncapsulationMechanism ::=  
           AlgorithmIdentifier {{DEMAlgorithms}} 

        DEMAlgorithms ALGORITHM ::= { 
           X9-SymmetricKeyWrappingSchemes, 
           Camellia-KeyWrappingSchemes, 
           ...  -- implementations may define other methods 
        } 

        X9-SymmetricKeyWrappingSchemes ALGORITHM ::= { 
           aes128-Wrap | aes192-Wrap | aes256-Wrap | tdes-Wrap, 
           ...   -- allows for future expansion 
        } 

        Camellia-KeyWrappingSchemes ALGORITHM ::= { 
           Camellia128-Wrap | Camellia192-Wrap | Camellia256-Wrap 
        } 

B.2. Selected Underlying Components 

B.2.1. Key Derivation Functions 

   The object identifier for KDF2 (see [ANS X9.44]) is: 

     id-kdf-kdf2 OID ::= { x9-44-components kdf2(1) } 

   The associated parameters identify the underlying hash function. For 
   alignment with ANS X9.44, the hash function MUST be an ASC X9-
   approved hash function. However, other hash functions MAY be used 
   with CMS. 

     kdf2 ALGORITHM ::= { OID id-kdf-kdf2  PARMS KDF2-HashFunction } 

     KDF2-HashFunction ::= AlgorithmIdentifier {{KDF2-HashFunctions}} 

     KDF2-HashFunctions ALGORITHM ::= { 
        X9-HashFunctions, 
        ...  -- implementations may define other methods 
     } 

 
 
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     X9-HashFunctions ALGORITHM ::= { 
        sha1 | sha224 | sha256 | sha384 | sha512, 
        ...  -- allows for future expansion 
     } 

   The object identifier for SHA-1 is: 

     id-sha1 OID ::= { 
        iso(1) identified-organization(3) oiw(14) secsig(3) 
        algorithms(2) sha1(26) 
     } 

   The object identifiers for SHA-224, SHA-256, SHA-384 and SHA-512 are 

     id-sha224 OID ::= { nistAlgorithm hashAlgs(2) sha224(4) } 
     id-sha256 OID ::= { nistAlgorithm hashAlgs(2) sha256(1) } 
     id-sha384 OID ::= { nistAlgorithm hashAlgs(2) sha384(2) } 
     id-sha512 OID ::= { nistAlgorithm hashAlgs(2) sha512(3) } 

   There has been some confusion over whether the various SHA object 
   identifiers have a NULL parameter, or no associated parameters. As 
   also discussed in [PKCS1], implementations SHOULD generate algorithm 
   identifiers without parameters, and MUST accept algorithm identifiers 
   either without parameters, or with NULL parameters. 

     sha1   ALGORITHM ::= { OID id-sha1   } -- NULLParms MUST be 
     sha224 ALGORITHM ::= { OID id-sha224 } -- accepted for these 
     sha256 ALGORITHM ::= { OID id-sha256 } -- OIDs 
     sha384 ALGORITHM ::= { OID id-sha384 } -- "" 
     sha512 ALGORITHM ::= { OID id-sha512 } -- "" 

   The object identifier for KDF3 (see [ANS X9.44]) is:  

     id-kdf-kdf3 OID ::= { x9-44-components kdf3(2) } 

   The associated parameters identify the underlying hash function. For 
   alignment with the draft ANS X9.44, the hash function MUST be an ASC 
   X9-approved hash function. However, other hash functions MAY be used 
   with CMS. 

     kdf3 ALGORITHM ::= { OID id-kdf-kdf3  PARMS KDF3-HashFunction } 

     KDF3-HashFunction ::= AlgorithmIdentifier { KDF3-HashFunctions } 

     KDF3-HashFunctions ALGORITHM ::= { 
        X9-HashFunctions, 

 
 
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        ...  -- implementations may define other methods 
     } 

B.2.2. Symmetric Key-Wrapping Schemes 

   The object identifiers for the AES Key Wrap depends on the size of 
   the key encrypting key. There are three object identifiers (see [AES-
   WRAP]): 

     id-aes128-Wrap OID ::= { nistAlgorithm aes(1) aes128-Wrap(5) } 
     id-aes192-Wrap OID ::= { nistAlgorithm aes(1) aes192-Wrap(25) } 
     id-aes256-Wrap OID ::= { nistAlgorithm aes(1) aes256-Wrap(45) } 

   These object identifiers have no associated parameters. 

     aes128-Wrap ALGORITHM ::= { OID id-aes128-Wrap } 
     aes192-Wrap ALGORITHM ::= { OID id-aes192-Wrap } 
     aes256-Wrap ALGORITHM ::= { OID id-aes256-Wrap } 

   The object identifier for the Triple-DES Key Wrap (see [3DES-WRAP]) 
   is: 

     id-alg-CMS3DESwrap OBJECT IDENTIFIER ::= { 
        iso(1) member-body(2) us(840) rsadsi(113549) pkcs(1) pkcs-9(9) 
        smime(16) alg(3) 6 
     } 

   This object identifier has a NULL parameter. 

     tdes-Wrap ALGORITHM ::=  
        { OID id-alg-CMS3DESwrap  PARMS NullParms } 

   NOTE: ASC X9 has not yet incorporated AES Key Wrap with Padding [AES-
   WRAP-PAD] in to ANS X9.44. When ASC X9.44 adds AES Key Wrap with 
   Padding, this document will also be updated. 

   The object identifiers for the Camellia Key Wrap depend on the size 
   of the key encrypting key. There are three object identifiers: 

     id-camellia128-Wrap OBJECT IDENTIFIER ::= 
        { iso(1) member-body(2) 392 200011 61 security(1) 
          algorithm(1) key-wrap-algorithm(3) 
          camellia128-wrap(2) } 

 
 
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     id-camellia192-Wrap OBJECT IDENTIFIER ::= 
        { iso(1) member-body(2) 392 200011 61 security(1) 
          algorithm(1) key-wrap-algorithm(3) 
          camellia192-wrap(3) } 

     id-camellia256-Wrap OBJECT IDENTIFIER ::= 
        { iso(1) member-body(2) 392 200011 61 security(1) 
          algorithm(1) key-wrap-algorithm(3) 
          camellia256-wrap(4) } 

   These object identifiers have no associated parameters. 

     camellia128-Wrap ALGORITHM ::= { OID id-camellia128-Wrap } 
     camellia192-Wrap ALGORITHM ::= { OID id-camellia192-Wrap } 
     camellia256-Wrap ALGORITHM ::= { OID id-camellia256-Wrap } 

B.3. ASN.1 module 

   CMS-RSA-KEM 
     { iso(1) member-body(2) us(840) rsadsi(113549) pkcs(1) 
       pkcs-9(9) smime(16) modules(0) cms-rsa-kem(21) } 

   DEFINITIONS ::= 

   BEGIN  

   -- EXPORTS ALL 

   -- IMPORTS None 

   -- Useful types and definitions 

   OID ::= OBJECT IDENTIFIER  -- alias 

   -- Unless otherwise stated, if an object identifier has associated 
   -- parameters (i.e., the PARMS element is specified), the 
   -- parameters field shall be included in algorithm identifier 
   -- values. The parameters field shall be omitted if and only if 
   -- the object identifier does not have associated parameters 
   -- (i.e., the PARMS element is omitted), unless otherwise stated.  

   ALGORITHM ::= CLASS { 
     &id    OBJECT IDENTIFIER  UNIQUE, 
     &Type  OPTIONAL 
   } 
   WITH SYNTAX { OID &id [PARMS &Type] } 

 
 
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   AlgorithmIdentifier { ALGORITHM:IOSet } ::= SEQUENCE { 
     algorithm   ALGORITHM.&id( {IOSet} ), 
     parameters  ALGORITHM.&Type( {IOSet}{@algorithm} ) OPTIONAL 
   } 

   NullParms ::= NULL  

   -- ISO/IEC 18033-2 arc 

   is18033-2 OID ::= { iso(1) standard(0) is18033(18033) part2(2) } 

   -- NIST algorithm arc 

   nistAlgorithm OID ::= { 
     joint-iso-itu-t(2) country(16) us(840) organization(1) 
     gov(101) csor(3) nistAlgorithm(4) 
   } 

   -- PKCS #1 arc  

   pkcs-1 OID ::= { 
     iso(1) member-body(2) us(840) rsadsi(113549) pkcs(1) pkcs-1(1) 
   } 

   -- RSA-KEM Key Transport Algorithm 

   id-rsa-kem OID ::= { 
     iso(1) member-body(2) us(840) rsadsi(113549) pkcs(1) 
     pkcs-9(9) smime(16) alg(3) 14 
   } 

   GenericHybridParameters ::= SEQUENCE { 
     kem  KeyEncapsulationMechanism, 
     dem  DataEncapsulationMechanism 
   } 

   KeyEncapsulationMechanism ::= AlgorithmIdentifier {{KEMAlgorithms}} 

   KEMAlgorithms ALGORITHM ::= { kem-rsa, ... } 

   kem-rsa ALGORITHM ::= { OID id-kem-rsa PARMS RsaKemParameters } 

   id-kem-rsa OID ::= { 
     is18033-2 key-encapsulation-mechanism(2) rsa(4) 
   } 

 
 
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   RsaKemParameters ::= SEQUENCE { 
     keyDerivationFunction  KeyDerivationFunction, 
     keyLength              KeyLength 
   } 

   KeyDerivationFunction ::= AlgorithmIdentifier {{KDFAlgorithms}} 

   KDFAlgorithms ALGORITHM ::= { 
     kdf2 | kdf3, 
     ...  -- implementations may define other methods 
   } 

   KeyLength ::= INTEGER (1..MAX) 

   DataEncapsulationMechanism ::= AlgorithmIdentifier {{DEMAlgorithms}} 

   DEMAlgorithms ALGORITHM ::= { 
     X9-SymmetricKeyWrappingSchemes | 
     Camellia-KeyWrappingSchemes, 
     ...  -- implementations may define other methods 
   } 

   X9-SymmetricKeyWrappingSchemes ALGORITHM ::= { 
     aes128-Wrap | aes192-Wrap | aes256-Wrap | tdes-Wrap, 
     ...   -- allows for future expansion 
   } 

   X9-SymmetricKeyWrappingScheme ::= 
               AlgorithmIdentifier {{ X9-SymmetricKeyWrappingSchemes }} 

   Camellia-KeyWrappingSchemes ALGORITHM ::= { 
     camellia128-Wrap | camellia192-Wrap | camellia256-Wrap, 
     ... -- allows for future expansion 
   } 

   Camellia-KeyWrappingScheme ::= 
                  AlgorithmIdentifier {{ Camellia-KeyWrappingSchemes }} 

   -- Key Derivation Functions 

   id-kdf-kdf2 OID ::= { x9-44-components kdf2(1) } 

 
 
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   -- Base arc 

   x9-44 OID ::= { 
     iso(1) identified-organization(3) tc68(133) country(16) x9(840) 
     x9Standards(9) x9-44(44) 
   } 

   x9-44-components OID ::= { x9-44 components(1) } 

   kdf2 ALGORITHM ::= { OID id-kdf-kdf2  PARMS KDF2-HashFunction } 

   KDF2-HashFunction ::= AlgorithmIdentifier {{ KDF2-HashFunctions }} 

   KDF2-HashFunctions ALGORITHM ::= { 
     X9-HashFunctions, 
     ...  -- implementations may define other methods 
   } 

   id-kdf-kdf3 OID ::= { x9-44-components kdf3(2) } 

   kdf3 ALGORITHM ::= { OID id-kdf-kdf3  PARMS KDF3-HashFunction } 

   KDF3-HashFunction  ::= AlgorithmIdentifier {{ KDF3-HashFunctions }} 

   KDF3-HashFunctions ALGORITHM ::= { 
     X9-HashFunctions, 
     ...  -- implementations may define other methods 
   } 

   -- Hash Functions 

   X9-HashFunctions ALGORITHM ::= { 
     sha1 | sha224 | sha256 | sha384 | sha512, 
     ...  -- allows for future expansion 
   } 

   id-sha1 OID ::= { 
     iso(1) identified-organization(3) oiw(14) secsig(3) 
     algorithms(2) sha1(26) 
   } 

   id-sha224 OID ::= { nistAlgorithm hashAlgs(2) sha256(4) } 

   id-sha256 OID ::= { nistAlgorithm hashAlgs(2) sha256(1) } 

   id-sha384 OID ::= { nistAlgorithm hashAlgs(2) sha384(2) } 

 
 
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   id-sha512 OID ::= { nistAlgorithm hashAlgs(2) sha512(3) } 

   sha1   ALGORITHM ::= { OID id-sha1    } -- NullParms MUST be 

   sha224 ALGORITHM ::= { OID id-sha224  } -- accepted for these  

   sha256 ALGORITHM ::= { OID id-sha256  } -- OIDs  

   sha384 ALGORITHM ::= { OID id-sha384  } -- ""  

   sha512 ALGORITHM ::= { OID id-sha512  } -- ""  

   -- Symmetric Key-Wrapping Schemes  

   id-aes128-Wrap OID ::= { nistAlgorithm aes(1) aes128-Wrap(5)  }  

   id-aes192-Wrap OID ::= { nistAlgorithm aes(1) aes192-Wrap(25) } 

   id-aes256-Wrap OID ::= { nistAlgorithm aes(1) aes256-Wrap(45) } 

   aes128-Wrap ALGORITHM ::= { OID id-aes128-Wrap } 

   aes192-Wrap ALGORITHM ::= { OID id-aes192-Wrap } 

   aes256-Wrap ALGORITHM ::= { OID id-aes256-Wrap } 

   id-alg-CMS3DESwrap OBJECT IDENTIFIER ::= { 
     iso(1) member-body(2) us(840) rsadsi(113549) pkcs(1) pkcs-9(9) 
     smime(16) alg(3) 6 
   } 

   tdes-Wrap ALGORITHM ::= { OID id-alg-CMS3DESwrap  PARMS NullParms } 

   id-camellia128-Wrap OBJECT IDENTIFIER ::= 
     { iso(1) member-body(2) 392 200011 61 security(1) 
       algorithm(1) key-wrap-algorithm(3) 
       camellia128-wrap(2) }  

   id-camellia192-Wrap OBJECT IDENTIFIER ::= 
     { iso(1) member-body(2) 392 200011 61 security(1) 
       algorithm(1) key-wrap-algorithm(3) 
       camellia192-wrap(3) } 

   id-camellia256-Wrap OBJECT IDENTIFIER ::= 
     { iso(1) member-body(2) 392 200011 61 security(1) 
       algorithm(1) key-wrap-algorithm(3) 
       camellia256-wrap(4) } 
 
 
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   camellia128-Wrap ALGORITHM ::= { OID id-camellia128-Wrap } 

   camellia192-Wrap ALGORITHM ::= { OID id-camellia192-Wrap } 

   camellia256-Wrap ALGORITHM ::= { OID id-camellia256-Wrap } 

   END 

 
 
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B.4. Examples 

   As an example, if the key derivation function is KDF3 based on SHA-
   256 and the symmetric key-wrapping scheme is the AES Key Wrap with a 
   128-bit KEK, the AlgorithmIdentifier for the RSA-KEM Key Transport 
   Algorithm will have the following value: 

   SEQUENCE { 
      id-rsa-kem,                                   -- RSA-KEM cipher 
      SEQUENCE {                           -- GenericHybridParameters 
         SEQUENCE {                    -- key encapsulation mechanism 
            id-kem-rsa,                                    -- RSA-KEM 
            SEQUENCE {                            -- RsaKemParameters 
               SEQUENCE {                  -- key derivation function 
                  id-kdf-kdf3,                                -- KDF3 
                  SEQUENCE {                     -- KDF3-HashFunction 
                     id-sha256  -- SHA-256; no parameters (preferred) 
                  }, 
               16                              -- KEK length in bytes 
               }, 
         SEQUENCE {                   -- data encapsulation mechanism 
            id-aes128-Wrap             -- AES-128 Wrap; no parameters 
         } 
      } 
   } 

   This AlgorithmIdentifier value has the following DER encoding (?? 
   indicates the algorithm number which is to be assigned): 

   30 47 
     06 0b 2a 86 48 86 f7 0d 01 09 10 03 0e           -- id-rsa-kem 
     30 38 
        30 29 
           06 07 28 81 8c 71 02 02 04                 -- id-kem-rsa 
           30 1e 
              30 19 
                 06 0a 2b 81 05 10 86 48 09 2c 01 02  -- id-kdf-kdf3 
                 30 0b 
                    06 09 60 86 48 01 65 03 04 02 01  -- id-sha256 
                    02 01 10                          -- 16 bytes 
         30 0b 
            06 09 60 86 48 01 65 03 04 01 05         -- id-aes128-Wrap 

 
 
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   The DER encodings for other typical sets of underlying components are 
   as follows: 

   o KDF3 based on SHA-384, AES Key Wrap with a 192-bit KEK 

      30 47 06 0b 2a 86 48 86 f7 0d 01 09 10 03 0e 30 
      38 30 29 06 07 28 81 8c 71 02 02 04 30 1e 30 19 
      06 0a 2b 81 05 10 86 48 09 2c 01 02 30 0b 06 09 
      60 86 48 01 65 03 04 02 02 02 01 18 30 0b 06 09 
      60 86 48 01 65 03 04 01 19 

   o KDF3 based on SHA-512, AES Key Wrap with a 256-bit KEK 

       30 47 06 0b 2a 86 48 86 f7 0d 01 09 10 03 0e 30 
       38 30 29 06 07 28 81 8c 71 02 02 04 30 1e 30 19 
       06 0a 2b 81 05 10 86 48 09 2c 01 02 30 0b 06 09 
       60 86 48 01 65 03 04 02 03 02 01 20 30 0b 06 09 
       60 86 48 01 65 03 04 01 2d 

   o KDF2 based on SHA-1, Triple-DES Key Wrap with a 128-bit KEK (two-
   key triple-DES) 

       30 45 06 0b 2a 86 48 86 f7 0d 01 09 10 03 0e 30 
       36 30 25 06 07 28 81 8c 71 02 02 04 30 1a 30 15 
       06 0a 2b 81 05 10 86 48 09 2c 01 01 30 07 06 05 
       2b 0e 03 02 1a 02 01 10 30 0d 06 0b 2a 86 48 86 
       f7 0d 01 09 10 03 06 

 
 
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Authors' Addresses 

   James Randall 
   Randall Consulting 
   55 Sandpiper Drive 
   Dover, NH 03820 
   USA 

   Email: jdrandall@comcast.net  

   Burt Kaliski 
   EMC 
   176 South Street 
   Hopkinton, MA 01748 
   USA 

   Email: kaliski_burt@emc.com  

   John Brainard 
   RSA, The Security Division of EMC 
   174 Middlesex Turnpike 
   Bedford, MA  01730 
   USA 

   Email: jbrainard@rsa.com  

   Sean Turner 
   IECA, Inc. 
   3057 Nutley Street, Suite 106 
   Fairfax, VA 22031 
   USA 

   Email: turners@ieca.com 

 
 
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