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Versions: 00 01

   Internet Draft                                   Ari Singer, NTRU
   Document: draft-ietf-pkix-pkalgs-supp-01.txt     William Whyte, NTRU
   Expires: September 2002                          March 2002


              Supplemental Algorithms and Identifiers for the
                 Internet X.509 Public Key Infrastructure
                        Certificate and CRL Profile
                   <draft-ietf-pkix-pkalgs-supp-01.txt>


Status of this Memo

   This document is an Internet-Draft and is in full conformance
   with all provisions of Section 10 of RFC 2026 [RFC2026].

   Internet-Drafts are working documents of the Internet Engineering
   Task Force (IETF), its areas, and its working groups.  Note that
   other groups may also distribute working documents as Internet-
   Drafts.

   Internet-Drafts are draft documents valid for a maximum of six
   months and may be updated, replaced, or obsoleted by other documents
   at any time.  It is inappropriate to use Internet-Drafts as
   reference material or to cite them other than as "work in progress."

   The list of current Internet-Drafts can be accessed at
        http://www.ietf.org/ietf/1id-abstracts.txt
   The list of Internet-Draft Shadow Directories can be accessed at
        http://www.ietf.org/shadow.html.

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
   [RFC2119].


Abstract

   This document specifies algorithm identifiers and ASN.1 encoding
   formats for digital signatures and subject public keys, including
   NTRUSign digital signatures and NTRUEncrypt and NTRUSign subject
   public keys used in the Internet X.509 Public Key Infrastructure
   (PKI).  Digital signatures are used to sign certificates and
   certificate revocation lists (CRLs).  Certificates include the
   public key of the named subject.  This document is intended to be a
   companion to draft-ietf-pkix-ipki-pkalgs-05.txt [PKIX-ALGS] and may
   be merged with that document in future revisions if approved by the
   PKIX working group.


Table of Contents


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   Status of this Memo................................................1
   Conventions used in this document..................................1
   Abstract...........................................................1
   1. Overview........................................................3
   2. Algorithm Support...............................................3
   2.1 Signature Algorithms...........................................4
   2.1.1 NTRUSign Signature Algorithm.................................4
   2.2 Subject Public Key Algorithms..................................6
   2.2.1 NTRUEncrypt Keys.............................................6
   2.2.2 NTRUSign Keys...............................................12
   3. ASN.1 Module...................................................15
   4. Security Considerations........................................21
   5. Intellectual Property Rights...................................21
   6. Acknowledgements...............................................21
   7. References.....................................................22
   Authors' Addresses................................................23

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1. Overview

   This document specifies algorithm identifiers and ASN.1 encoding
   formats for digital signatures and subject public keys used in the
   Internet X.509 Public Key Infrastructure (PKI).  This specification
   supplements RFC 2459 [RFC2459], "Internet Public Key Infrastructure:
   X.509 Certificate and CRL Profile".  Implementations of this
   specification must also conform to RFC 2459 [RFC2459].  This
   document is being written concurrently with the PKIX public key
   algorithms Internet Draft [PKIX-ALGS] (the latest version as of this
   writing is draft-ietf-pkix-ipki-pkalgs-05.txt).  It is intended that
   when this document is completed and approved by the PKIX working
   group that it be merged with that document.  The format of this
   document is written to approximately match the format of that
   Internet Draft.

   This specification defines the contents of the signatureAlgorithm,
   signatureValue, signature and subjectPubliKeyInfo fields within
   Internet X.509 certificates and CRLs.

   This document does not currently introduce any new one-way hash
   functions, but it specifies the use of SHA-256, SHA-384 and SHA-512
   hash algorithms as defined in the draft of FIPS 180-2 [FIPS180-2] as
   well as the SHA-1 hash algorithm as defined in FIPS 180-1 [FIPS180-
   1] with the NTRUSign signature algorithm.  It is anticipated that
   future revisions will include the algorithm identifiers and ASN.1
   encoding of the FIPS 180-2 hash algorithms.

   This specification describes the encoding of digital signatures
   generated with the following cryptographic algorithms;
        * NTRUSign Signature Scheme (NTRUSign).

   It is anticipated that future revisions of this document will
   include the extended version of the Digital Signature Algorithm
   (DSA) [FIPS186-2], which has not yet been published.  In addition,
   it is anticipated that the document will include the algorithm
   identifiers and ASN.1 encoding of pre-existing algorithms (e.g. RSA)
   when used in conjunction with the FIPS 180-2 hash algorithms.

   This document specifies the contents of the subjectPublicKeyInfo
   field in Internet X.509 certificates.  For each algorithm, the
   appropriate alternatives for the keyUsage extension are provided.
   This specification describes encoding formats for public keys used
   with the following cryptographic algorithms:
        * NTRUEncrypt Encryption Scheme (NTRUEncrypt)
        * NTRUSign Signature Scheme (NTRUSign)

2. Algorithm Support

   This section describes cryptographic algorithms that may be used
   with the Internet X.509 Certificate and CRL Profile.  In particular,
   it describes the NTRUSign digital signature algorithm, which may be
   used to sign certificates and CRLs.  In addition, this section
   identifies OIDs and ASN.1 encoding for NTRUSign and NTRUEncrypt

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   public keys contained in a certificate.  It is anticipated that
   additional algorithms, such as the extended version of DSA, will be
   included in future revisions.

   Conforming CAs and application are not required to support the
   algorithms or algorithm identifiers described in this section.
   However, conforming CAs and applications that use the algorithms
   identified here MUST support them as specified.

2.1 Signature Algorithms

   Certificates and CRLs conforming to RFC 2459 [RFC2459] may be signed
   with any public key signature algorithm.  The certificate or CRL
   indicates the algorithm through an algorithm identifier, which
   appears in the signatureAlgorithm field within the Certificate or
   CertificateList.  An algorithm identifier consists of an OID and
   (optionally) associated parameters.  This section describes OIDs and
   parameter encoding for NTRUSign.

   Signature algorithms are always used in conjunction with a one-way
   hash function.

   The data to be signed (e.g. the one-way hash function output value)
   is formatted for the signature algorithm to be used.  Then, a
   private key operation (e.g. NTRUSign signature primitive) is
   performed to generate the signature value.  This signature value is
   then ASN.1 encoded as a BIT STRING and included in the Certificate
   or CertificateList in the signature field.

2.1.1 NTRUSign Signature Algorithm

   The NTRUSign signature algorithm was invented by Hoffstein,
   Howgrave-Graham, Pipher, Silverman and Whyte.  It is defined in
   Efficient Embedded Security Standard (EESS) #1 [EESS#1].  This
   profile defines a single signature algorithm, the NTRUSign signature
   algorithm with the SHA-1, SHA-256, SHA-384 or SHA-512 one-way hash
   function.

   The signature algorithm is implemented using the padding and
   encoding conventions described in EESS #1 [EESS#1].  The message
   digest is computed using the SHA-1 Hash Algorithm [FIPS180-1] or any
   of the SHA-2 algorithms [FIPS180-2] and the message digest is
   encoded using the MGF1 mask generation function as specified in Std
   IEEE 1363-2000 [IEEE1363].

   Unlike previously defined public-key signature algorithms, the
   object identifier for the NTRUSign signature algorithm does not
   specify the hash function.  Rather, the parameter field in the
   AlgorithmIdentifier contains an indication of the hash function as
   well as the encoding methods that are to be used.

   The ASN.1 object identifier used to identify this signature
   algorithm is named id-ntru-EESS1v1-NTRUSign and is given by the
   following ASN.1:

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        ntru OBJECT IDENTIFIER ::=
                {iso(1) identified-organization(3) dod(6) internet(1)
                private(4) enterprises(1) ntruCryptosystems (8342) }

        id-eess1  OBJECT IDENTIFIER ::= {ntru eess(1) 1}

        id-eess1-algs  OBJECT IDENTIFIER ::= {id-eess1 1}

        id-ntru-EESS1v1-NTRUSign  OBJECT IDENTIFIER ::=
                {id-eess1-algs 3}

   When this OID appears in the signatureAlgorithm field or the
   signature field of an X.509 certificate, the encoding SHALL omit the
   parameters field.  That is, the AlgorithmIdentifier shall be a
   SEQUENCE of one component: the OBJECT IDENTIFIER id-ntru-EESS1v1-
   SVSSA.

   The NTRUSign parameters in the subjectPublicKeyInfo field of the
   certificate of the issuer shall apply to the verification of the
   signature.

   When signing, the NTRUSign algorithm generates a signature
   polynomial.  This polynomial SHALL be encoded as an OCTET STRING as
   described in EESS #1 [EESS#1].  The signature SHALL be ASN.1 encoded
   using the following ASN.1 structure:

   NTRUSignSignedData ::= NTRUPublicVector

   NTRUPublicVector ::= CHOICE {
        modQVector        [0] IMPLICIT ModQVector,
        packedModQVector  [1] IMPLICIT PackedModQVector,
        ...}

   ModQVector ::= OCTET STRING

   PackedModQVector ::= OCTET STRING

   The field choices of type NTRUPublicVector have the following
   meanings:

        modQVector is the representation of the NTRUPublicVector in
        unpacked form.  For a polynomial of degree N-1 with
        coefficients reduced mod q, each of the N bytes of the OCTET
        STRING represent integers x in the range 0 <= x < q
        corresponding to the coefficient values of the polynomial from
        lowest degree to highest.

        packedModQVector is the representation of the NTRUPublicVector
        in packed form.  For a polynomial of degree N-1 with
        coefficients reduced mod q, each log_2(q) bits of the OCTET
        STRING represent integers x in the range 0 <= x < q
        corresponding to the coefficient values of the polynomial from
        lowest degree to highest.  The values are concatenated bitwise,

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        without any intermediate padding, and irrespective of the byte
        boundaries. If necessary, zero bits are appended to the packed
        data in order to make the length a multiple of 8 bits.

   Implementations that sign certificates using NTRUSign SHOULD encode
   the signature as a ModQVector.

2.2 Subject Public Key Algorithms

   Certificates conforming to RFC 2459 [RFC2459] may convey a public
   key for any public key algorithm.  The certificate indicates the
   algorithm through an algorithm identifier.  This algorithm
   identifier consists of an OID and optionally associated parameters.

   This section identifies preferred OIDs and parameters for the
   NTRUEncrypt and NTRUSign algorithms.  Conforming CAs MUST use the
   identified OIDs when issuing certificates containing public keys for
   these algorithms.  Conforming applications supporting any of these
   algorithms MUST, at a minimum, recognize the OIDs identified in this
   section.

2.2.1 NTRUEncrypt Keys

   This section identifies the preferred OID and parameter encoding for
   the inclusion of an NTRUEncrypt public key in a certificate.  The
   NTRUEncrypt encryption algorithm is defined in EESS #1 [EESS#1].

   The OID id-ntru-EESS1v1-SVES identifies NTRUEncrypt public keys.

        id-ntru-EESS1v1-SVES  OBJECT IDENTIFIER ::= {id-eess1-algs 1}

   The id-ntru-EESS1v1-SVES OID is intended to be used in the algorithm
   field of a value of type AlgorithmIdentifier.  NTRUEncrypt requires
   use of certain parameters with the public key.  The parameters may
   be implied by context, implicitly included through reference of a
   degree, implicitly included through reference of a standard
   parameter set or explicitly included in the certificate.  The
   parameters associated with id-ntru-EESS1v1-SVES are EESS1v1-SVES-
   Parameters.

   EESS1v1-SVES-Parameters ::= CHOICE {
                degree                  Degree,
                standardNTRUParameters  StandardNTRUParameters,
                explicitNTRUParameters  ExplicitNTRUParameters,
                externalParameters      NULL
                }

   When the parameters are implied by context, the parameters field
   SHALL contain externalParameters, which is a value of the ASN.1 type
   NULL.

   When the parameters are specified by degree, the values are
   restricted to 251, 347 and 503.  For the three permitted choices,
   the parameters are defined to be ees251ep1, ees347ep1 and ees503ep1

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   respectively as defined in EESS #1 [EESS#1].  Specifying the degree
   is the preferred way for transmitting parameter information for the
   scheme when the parameters are not implied by context.

        Degree ::= INTEGER  (251 | 347 | 503, ...)

   When the parameters are specified by reference of a standard, the
   parameters shall consist of an OID chosen from the list
   NTRUParameters.  The current list of NTRUParameters OIDs is:

        StandardNTRUParameters ::= OIDS.&id({NTRUParameters})

        NTRUParameters  OIDS ::= {
                { OID id-ees251ep1 }|
                { OID id-ees347ep1 }|
                { OID id-ees503ep1 },
                ...}

   The above object identifiers are specified by:

        id-eess1-params  OBJECT IDENTIFIER ::= {id-eess1 2}

        id-ees251ep1  OBJECT IDENTIFIER ::= {id-eess1-params 1}
        id-ees347ep1  OBJECT IDENTIFIER ::= {id-eess1-params 2}
        id-ees503ep1  OBJECT IDENTIFIER ::= {id-eess1-params 3}

   When the parameters are explicitly included, they SHALL be encoded
   in the ASN.1 structure ExplicitNTRUParameters:

        ExplicitNTRUParameters ::= SEQUENCE {
                version         Version,
                degree          INTEGER,
                bigModulus      INTEGER,
                smallModulus    SmallModulus,
                mrgm            NTRUMRGMAlgorithmIdentifier,
                db              INTEGER,
                bvgm            NTRUBVGMAlgorithmIdentifier,
                ...}

        Version ::= INTEGER { v0(0) } (v0, ...)

        SmallModulus ::= CHOICE {
                integerValue    INTEGER,
                polynomialValue NTRUGeneralPolynomial
                }

        NTRUGeneralPolynomial ::= SEQUENCE {
                numberOfEntries         INTEGER,
                modulus                 INTEGER,
                coefficients            GeneralVector
                }

        GeneralVector ::= OCTET STRING


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   The fields of type NTRUGeneralPolynomial have the following
   meanings:

        numberOfEntries is the number of coefficients used to represent
        the polynomial - this number is equal to the degree of the
        polynomial plus 1.

        modulus is an upper bound on the value of the coefficients.

        coefficients is the list of numberOfEntries coefficients,
        represented in order from lowest degree to highest degree.  If
        modulus < 257, each coefficient is stored in a single byte.  If
        modulus > 256 and modulus < 2^16, each coefficient is stored in
        two bytes.

   The fields of type SmallModulus have the following meanings:

        integerValue is the value of p if p is an integer.

        polynomialValue is the value of p if p is a polynomial.

   The fields of type ExplicitNTRUParameters have the following
   meanings:

        version is the version number, for compatibility with future
        revisions of this document.  It SHALL be 0 for this version of
        the document.

        degree is the value N.

        bigModulus is the value q.  q will be 256 or less.

        smallModulus is the value p.  It SHALL be represented with the
        SmallModulus type.

        mrgm identifies the message representative generation method
        using an allowed AlgorithmIdentifier.

        db is the size of the random component.

        bvgm identifies the blinding value generation method using an
        allowed AlgorithmIdentifier.

   The ASN.1 for the mrgm used in ExplicitNTRUParameters is specified
   below.

        NTRUMRGMAlgorithmIdentifier ::=
                        AlgorithmIdentifier {{NTRUEESS1v1MRGMs}}

        NTRUEESS1v1MRGMs ALGORITHM ::= {
                {OID id-mrgm-ntru-1 PARMS NTRUMRGM1-params},
                ...}

        id-eess1-encodingMethods  OBJECT IDENTIFIER ::= {id-eess1 3}

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        id-mrgm-ntru-1  OBJECT IDENTIFIER ::=
                {id-eess1-encodingMethods 1}

        NTRUMRGM1-params ::= NTRUHashAlgorithmIdentifier

        NTRUHashAlgorithmIdentifier ::=
                        AlgorithmIdentifier {{NTRUEESS1v1Hashes}}

   The identifier id-mrgm-ntru-1 identifies the message representative
   generation method MRGM-NTRU1, defined in EESS #1 [EESS#1].  The
   parameters identify the hashing mechanism using an allowed
   AlgorithmIdentifier.

        NTRUEESS1v1Hashes ALGORITHM ::= {
                {OID id-sha1    PARMS NULL}|
                {OID id-sha256  PARMS NULL }|
                {OID id-sha384  PARMS NULL }|
                {OID id-sha512  PARMS NULL },
                ...}

   These identifiers identify the one-way hash algorithms SHA-1
   [FIPS180-1] and SHA-2 [TBD].

   The ASN.1 for the bvgm used in ExplicitNTRUParameters is specified
   below.

        NTRUBVGMAlgorithmIdentifier ::=
                        AlgorithmIdentifier {{NTRUEESS1v1BVGMs}}

        NTRUEESS1v1BVGMs ALGORITHM ::= {
                {OID id-bvgm-ntru-1 PARMS NTRUBVGM1-params}|
                {OID id-bvgm-ntru-2 PARMS NTRUBVGM2-params},
                ...}

        id-bvgm-ntru-1  OBJECT IDENTIFIER ::=
                {id-eess1-encodingMethods 2}

        NTRUBVGM1-params ::= SEQUENCE {
                c       INTEGER,
                prng    NTRUPRNGAlgorithmIdentifier,
                dr      INTEGER
                }

        id-bvgm-ntru-2  OBJECT IDENTIFIER ::=
                {id-eess1-encodingMethods 3}

        NTRUBVGM2-params ::= SEQUENCE {
                c       INTEGER,
                prng    NTRUPRNGAlgorithmIdentifier,
                dr1     INTEGER,
                dr2     INTEGER,
                dr3     INTEGER
                }

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   The identifier id-bvgm-ntru-1 identifies blinding value generation
   method BVGM-NTRU1, defined in EESS #1 [EESS#1].  The identifier id-
   bvgm-ntru-2 identifies blinding value generation method BVGM-NTRU2,
   defined in EESS #1 [EESS#1].

   The fields of type NTRUBVGM1-params have the following meanings:

        c is the random polynomial generation constant used to select
        the polynomial r.

        prng identifies the pseudo-random number generation algorithm
        using an allowed AlgorithmIdentifier.

        dr is the number of 1s in the blinding value r.

   The fields of type NTRUBVGM2-params have the following meanings:

        c is the random polynomial generation constant used to select
        the polynomial r.

        prng identifies the pseudo-random number generation algorithm
        using an allowed AlgorithmIdentifier.

        dr1 is the number of 1s in the blinding value component r1.

        dr2 is the number of 1s in the blinding value component r2.

        dr3 is the number of 1s in the blinding value component r3.

   The allowed pseudo-random number generation algorithms are defined
   by:

        NTRUPRNGAlgorithmIdentifier ::=
                        AlgorithmIdentifier {{NTRUEESS1v1PRNGs}}

        NTRUEESS1v1PRNGs ALGORITHM ::= {
                NTRUMGFAlgorithms,
                ...}


   This identifies the pseudo-random number generation algorithm to be
   used when generating blinding values.  The only allowed algorithms
   are MGF1 (see [IEEE 1363]) using SHA-1 [FIPS180-1] or SHA-2
   [FIPS180-2].

        NTRUMGFAlgorithms ALGORITHM ::= {
                {OID id-mgf1 PARMS MGF1Parameters},
                ...}

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


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        id-mgf1  OBJECT IDENTIFIER ::= {pkcs-1 8}

        MGF1Parameters ::= AlgorithmIdentifier {{NTRUEESS1v1Hashes}}

   The NTRUEncrypt public key MUST be encoded using the ASN.1 type
   NTRUPublicKey.

        NTRUPublicKey ::= SEQUENCE {
                publicKeyVector         NTRUPublicVector,  -- h
                ntruKeyExtensions       NTRUKeyExtensions OPTIONAL
                }

        NTRUKeyExtensions ::=
                SEQUENCE SIZE(1..MAX) OF NTRUKeyExtension

        NTRUKeyExtension ::= CHOICE {
                keyID           [0] IMPLICIT INTEGER,
                ...}

   The fields of the type NTRUPublicKey have the following meanings:

        publicKeyVector is the polynomial h.  If the NTRUPublicVector
        is a ModQVector, each coefficient will be represented by one
        byte starting with the lowest degree and going to the highest.
        If the NTRUPublicVector is a PackedModQVector, this is the
        OCTET STRING representing h obtained using RE2BSP and then
        BS2OSP as defined in EESS #1 [EESS#1].  All coefficients up to
        X^(N-1) SHALL be explicitly included in publicKeyVector.
        Representing the NTRUEncrypt public key as a ModQVector is the
        preferred method.

        ntruKeyExtensions is provided for future extensibility.  Only
        one extension is currently defined.

   The fields of the type NTRUKeyExtension have the following meanings:

        keyID can be used to associate a unique key identifier with the
        key.

   If the keyUsage extension is present in an end entity certificate
   that conveys an NTRUEncrypt public key, any combination of the
   following values MAY be present:

        keyEncipherment;
        dataEncipherment;

   If the keyUsage extension is present in a CA certificate that
   conveys an NTRUEncrypt public key, any combination of the following
   values MAY be present:

        keyEncipherment; and
        dataEncipherment.


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2.2.2 NTRUSign Keys

   This section identifies the preferred OID and parameter encoding for
   the inclusion of an NTRUSign public key in a certificate.  The
   NTRUSign signature algorithm is defined in EESS #1 [EESS#1].

   The OID id-ntru-EESS1v1-SVSSA identifies NTRUSign public keys.

        id-ntru-EESS1v1-NTRUSign  OBJECT IDENTIFIER ::=
                {id-eess1-algs 3}

   The id-ntru-EESS1v1-NTRUSign OID is intended to be used in the
   algorithm field of a value of type AlgorithmIdentifier.  NTRUSign
   requires use of certain parameters with the public key.  The
   parameters may be implied by context (e.g. they may be inherited
   from the issuer), implicitly included through reference of a degree,
   implicitly included through reference of a standard parameter set or
   explicitly included in the certificate.  The parameters associated
   with id-ntru-EESS1v1-NTRUSign are EESS1v1-NTRUSign-Parameters.

        EESS1v1-NTRUSign-Parameters ::= CHOICE {
                degree                  Degree,
                standardNTRUSignParameters
                                        StandardNTRUSignParameters,
                explicitNTRUSignParameters
                                        ExplicitNTRUSignParameters,
                externalParameters      NULL
                }

   When the parameters are implied by context, the parameters field
   SHALL contain externalParameters, which is the ASN.1 value NULL.

   When the parameters are specified by degree, the value is restricted
   to 251.  For the permitted choice, the parameters are defined to be
   ees251sp2 as defined in EESS #1 [EESS#1].  Specifying the degree is
   the preferred way for transmitting parameter information for the
   scheme when the parameters are not implied by context.

   When the parameters are specified by reference of a standard, the
   parameters shall consist of an OID chosen from the list
   NTRUSignParameters.  The current list of NTRUSignParameters OIDs is:

        StandardNTRUSignParameters ::= OIDS.&id({NTRUSignParameters})

        NTRUSignParameters  OIDS ::= {
                { OID id-ees251sp2 },
                ...}

   The above object identifier is specified by:

        id-ees251sp2  OBJECT IDENTIFIER ::= {id-eess1-params 7}

   When the parameters are explicitly included, they SHALL be encoded
   in the ASN.1 structure ExplicitNTRUSignParameters:

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        ExplicitNTRUSignParameters ::= SEQUENCE {
                version                 Version,
                degree                  INTEGER,
                bigModulus              INTEGER,
                normBound               INTEGER,
                messageRandLength       INTEGER,
                hash                    NTRUSignHashAlgIdentifier,
                mrgm                    NTRUSignMRGMAlgIdentifier,
                ...}


   The fields of type ExplicitNTRUSignParameters have the following
   meanings:

        version is the version number, for compatibility with future
        revisions of this document.  It SHALL be 0 for this version of
        the document.

        degree is the value N.

        bigModulus is the value q.  q will be 256 or less.

        normBound is the maximum norm of the signature

        messageRandLength is the length of the randomization padding
        appended to the message digest before generating the message
        representative

        hash identifies the hash algorithm used using an allowed
        AlgorithmIdentifier.

        mrgm identifies the message representative generation method
        using an allowed AlgorithmIdentifier.

   The AlgorithmIdentifiers for the field hash of
   ExplicitNTRUSignParameters are chosen from the set
   NTRUEESS1v1Hashes, which is defined in section 2.2.1.

        NTRUSignHashAlgIdentifier ::=
                        AlgorithmIdentifier {{NTRUEESS1v1Hashes}}

   The AlgorithmIdentifiers for the field mrgm of
   ExplicitNTRUSignParameters are specified below.

        NTRUSignMRGMAlgIdentifier ::=
                        AlgorithmIdentifier {{NTRUSignEESS1v1MRGMs}}

        NTRUSignEESS1v1MRGMs ALGORITHM ::= {
                {OID id-mrgm-ntrusign-1 PARMS NTRUSignMRGM1-params}|
                {OID id-mrgm-ntrusign-2 PARMS NTRUSignMRGM2-params},
                ...}

        id-mrgm-ntrusign-1  OBJECT IDENTIFIER ::=

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                {id-eess1-encodingMethods 6}

        NTRUSignMRGM1-params ::= NTRUSignPRNGAlgIdentifier

        id-mrgm-ntrusign-2  OBJECT IDENTIFIER ::=
                {id-eess1-encodingMethods 7}

        NTRUSignMRGM2-params ::= SEQUENCE {
                c               INTEGER,
                numGroups       INTEGER,
                numElements     INTEGER,
                prng            NTRUSignPRNGAlgIdentifier
                }

        NTRUSignPRNGAlgIdentifier ::=
                        AlgorithmIdentifier {{NTRUEESS1v1PRNGs}}

   The identifier id-mrgm-ntrusign-2 identifies the message
   representative generation method MRGM-NTRUSign1, defined in EESS #1
   [EESS#1].  The identifier id-mrgm-ntrusign-2 identifies the message
   representative generation method MRGM-NTRUSign2, defined in EESS #1
   [EESS#1].

   The fields of type NTRUSignMRGM1-params have the following meanings:

        NTRUSignPRNGAlgIdentifier is the pseudo-random number
        generation method using an allowed AlgorithmIdentifier

   The fields of type NTRUSignMRGM2-params have the following meanings:

        c is the random polynomial generation constant used to select
        the message representative.

        numGroups is the number of factors combined to form the message
        representative.

        numElements is the number of non-zero coefficients in each
        factor of the message representative

        prng identifies the pseudo-random number generation method
        using an allowed AlgorithmIdentifier.

   The allowed pseudo-random number generation algorithms are chosen
   from the set NTRUEESS1v1PRNGs, which is defined in section 2.2.1.

   The NTRUSign public key MUST be encoded using the ASN.1 type
   NTRUSignPublicKey.

        NTRUSignPublicKey ::= SEQUENCE {
                publicKeyVector         NTRUPublicVector,  -- h
                ntruSignKeyExtensions  NTRUSignKeyExtensions OPTIONAL
                }

        NTRUSignKeyExtensions ::=

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                SEQUENCE SIZE(1..MAX) OF NTRUSignKeyExtension

        NTRUSignKeyExtension ::= CHOICE {
                keyID           [0] IMPLICIT INTEGER,
                ...}

   The fields of the type NTRUSignPublicKey have the following
   meanings:

        publicKeyVector is the polynomial h.  If the NTRUPublicVector
        is a ModQVector, each coefficient will be represented by one
        byte starting with the lowest degree and going to the highest.
        If the NTRUPublicVector is a PackedModQVector, this is the
        OCTET STRING representing h obtained using RE2BSP and then
        BS2OSP as defined in EESS #1 [EESS#1].  All coefficients up to
        X^(N-1) SHALL be explicitly included in publicKeyVector.
        Representing the NTRUSign public key as a ModQVector is the
        preferred method.

        ntruSignKeyExternsions is provided for future extensibility.
        Only one extension is currently defined.

   The fields of the type NTRUSignKeyExtension have the following
   meanings:

        keyID can be used to associate a unique key identifier with the
        key.

   If the keyUsage extension is present in an end entity certificate
   that conveys an NTRUSign public key, any combination of the
   following values MAY be present:

        digitalSignature;
        nonRepudiation;

   If the keyUsage extension is present in a CA certificate that
   conveys an NTRUSign public key, any combination of the following
   values MAY be present:

        digitalSignature;
        nonRepudiation;
        keyCertSign; and
        cRLSign.

3. ASN.1 Module

   PKIXAlgorithmOIDTBD -- {TBD} --

   DEFINITIONS EXPLICIT TAGS ::= BEGIN

   -- EXPORTS ALL; --

   -- IMPORTS None; --


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   -- Supporting definitions

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

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

        OIDS ::= ALGORITHM

   -- Informational object identifiers

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

        id-mgf1  OBJECT IDENTIFIER ::= {pkcs-1 8}

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

        id-sha256       OBJECT IDENTIFIER ::=
                {joint-iso-itu-t(2) country(16) us(840) organization(1)
                gov(101) csor(3) nistalgorithm(4) hashalgs(2) 1}

        id-sha384       OBJECT IDENTIFIER ::=
                {joint-iso-itu-t(2) country(16) us(840) organization(1)
                gov(101) csor(3) nistalgorithm(4) hashalgs(2) 2}

        id-sha512       OBJECT IDENTIFIER ::=
{joint-iso-itu-t(2) country(16) us(840) organization(1) gov(101)
csor(3) nistalgorithm(4) hashalgs(2) 3}

   -- NTRU Object Identifiers

        ntru OBJECT IDENTIFIER ::=
                {iso(1) identified-organization(3) dod(6) internet(1)
                private(4) enterprises(1) ntruCryptosystems (8342) }

        id-eess1  OBJECT IDENTIFIER ::= {ntru eess(1) 1}

        id-eess1-algs  OBJECT IDENTIFIER ::= {id-eess1 1}
        id-eess1-params  OBJECT IDENTIFIER ::= {id-eess1 2}
        id-eess1-encodingMethods  OBJECT IDENTIFIER ::= {id-eess1 3}

   -- OID for NTRUSign Algorithm and Public Key


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        id-ntru-EESS1v1-NTRUSign  OBJECT IDENTIFIER ::=
                {id-eess1-algs 3}

   -- OID for NTRUSign Parameter Set

        id-ees251sp2  OBJECT IDENTIFIER ::= {id-eess1-params 7}

   -- OIDs for NTRUSign Encoding Methods

        id-mrgm-ntrusign-1  OBJECT IDENTIFIER ::=
                {id-eess1-encodingMethods 6}

        id-mrgm-ntrusign-2  OBJECT IDENTIFIER ::=
                {id-eess1-encodingMethods 7}

   -- OID for NTRUEncrypt Algorithm and Public Key

        id-ntru-EESS1v1-SVES  OBJECT IDENTIFIER ::=
             {id-eess1-algs 1}

   -- OIDs for NTRUEncrypt Parameter Sets

        id-ees251ep1  OBJECT IDENTIFIER ::= {id-eess1-params 1}
        id-ees347ep1  OBJECT IDENTIFIER ::= {id-eess1-params 2}
        id-ees503ep1  OBJECT IDENTIFIER ::= {id-eess1-params 3}

   -- OIDs for NTRUEncrypt Encoding Methods

        id-mrgm-ntru-1  OBJECT IDENTIFIER ::=
                {id-eess1-encodingMethods 1}

        id-bvgm-ntru-1  OBJECT IDENTIFIER ::=
                {id-eess1-encodingMethods 2}

        id-bvgm-ntru-2  OBJECT IDENTIFIER ::=
                {id-eess1-encodingMethods 3}

-- General Types

        NTRUPublicVector ::= CHOICE {
                modQVector        [0] IMPLICIT ModQVector,
                packedModQVector  [1] IMPLICIT PackedModQVector,
                ...}

        ModQVector ::= OCTET STRING

        PackedModQVector ::= OCTET STRING

        NTRUGeneralPolynomial ::= SEQUENCE {
                numberOfEntries         INTEGER,
                modulus                 INTEGER,
                coefficients            GeneralVector
                }


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        GeneralVector ::= OCTET STRING

        SmallModulus ::= CHOICE {
                integerValue    INTEGER,
                polynomialValue NTRUGeneralPolynomial
                }

        Degree ::= INTEGER  (251 | 347 | 503, ...)

        Version ::= INTEGER { v0(0) } (v0, ...)

        NTRUEESS1v1Hashes ALGORITHM ::= {
                {OID id-sha1    PARMS NULL}|
                {OID id-sha256  PARMS NULL }|
                {OID id-sha384  PARMS NULL }|
                {OID id-sha512  PARMS NULL },
                ...}

        NTRUEESS1v1PRNGs ALGORITHM ::= {
                NTRUMGFAlgorithms,
                ...}

        NTRUMGFAlgorithms ALGORITHM ::= {
                {OID id-mgf1 PARMS MGF1Parameters},
                ...}

                MGF1Parameters ::= AlgorithmIdentifier
        {{NTRUEESS1v1Hashes}}

   -- Encoding for NTRUSign Signatures

        NTRUSignSignedData ::= NTRUPublicVector

   -- Encoding for NTRUSign Public Keys

        NTRUSignPublicKey ::= SEQUENCE {
                publicKeyVector         NTRUPublicVector,  -- h
                ntruSignKeyExtensions   NTRUSignKeyExtensions OPTIONAL
                }

        NTRUSignKeyExtensions ::=
                SEQUENCE SIZE(1..MAX) OF NTRUSignKeyExtension

        NTRUSignKeyExtension ::= CHOICE {
                keyID           [0] IMPLICIT INTEGER,
                ...}

        EESS1v1-NTRUSign-Parameters ::= CHOICE {
                degree                  Degree,
                standardNTRUSignParameters
                                        StandardNTRUSignParameters,
                explicitNTRUSignParameters
                                        ExplicitNTRUSignParameters,
                externalParameters      NULL

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               Supplemental Algorithms and Identifiers     March 2002

                }

        StandardNTRUSignParameters ::= OIDS.&id({NTRUSignParameters})

        NTRUSignParameters  OIDS ::= {
                { OID id-ees251sp2 },
                ...}

        ExplicitNTRUSignParameters ::= SEQUENCE {
                version                 Version,
                degree                  INTEGER,
                bigModulus              INTEGER,
                normBound               INTEGER,
                messageRandLength       INTEGER,
                hash                    NTRUSignHashAlgIdentifier,
                mrgm                    NTRUSignMRGMAlgIdentifier,
                ...}

        NTRUSignHashAlgIdentifier ::=
                        AlgorithmIdentifier {{NTRUEESS1v1Hashes}}

        NTRUSignMRGMAlgIdentifier ::=
                        AlgorithmIdentifier {{NTRUSignEESS1v1MRGMs}}

        NTRUSignEESS1v1MRGMs ALGORITHM ::= {
                {OID id-mrgm-ntrusign-1 PARMS NTRUSignMRGM1-params}|
                {OID id-mrgm-ntrusign-2 PARMS NTRUSignMRGM2-params},
                ...}

        NTRUSignMRGM1-params ::= NTRUSignPRNGAlgIdentifier

        NTRUSignMRGM2-params ::= SEQUENCE {
                c               INTEGER,
                numGroups       INTEGER,
                numElements     INTEGER,
                prng            NTRUSignPRNGAlgIdentifier
                }

        NTRUSignPRNGAlgIdentifier ::=
                        AlgorithmIdentifier {{NTRUEESS1v1PRNGs}}

   -- Encoding for NTRUEncrypt Public Keys

        NTRUPublicKey ::= SEQUENCE {
                publicKeyVector         NTRUPublicVector,  -- h
                ntruKeyExtensions       NTRUKeyExtensions OPTIONAL
                }

        NTRUKeyExtensions ::=
                SEQUENCE SIZE(1..MAX) OF NTRUKeyExtension

        NTRUKeyExtension ::= CHOICE {
                keyID           [0] IMPLICIT INTEGER,
                ...}

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        EESS1v1-SVES-Parameters ::= CHOICE {
                degree                  Degree,
                standardNTRUParameters  StandardNTRUParameters,
                explicitNTRUParameters  ExplicitNTRUParameters,
                externalParameters      NULL
                }

        StandardNTRUParameters ::= OIDS.&id({NTRUParameters})

        NTRUParameters  OIDS ::= {
                { OID id-ees251ep1 }|
                { OID id-ees347ep1 }|
                { OID id-ees503ep1 },
                ...}

        ExplicitNTRUParameters ::= SEQUENCE {
                version         Version,
                degree          INTEGER,
                bigModulus      INTEGER,
                smallModulus    SmallModulus,
                mrgm           NTRUMRGMAlgorithmIdentifier,
                db             INTEGER,
                bvgm           NTRUBVGMAlgorithmIdentifier,
                ...}

        NTRUMRGMAlgorithmIdentifier ::=
                        AlgorithmIdentifier {{NTRUEESS1v1MRGMs}}

        NTRUBVGMAlgorithmIdentifier ::=
                        AlgorithmIdentifier {{NTRUEESS1v1BVGMs}}

        NTRUEESS1v1MRGMs ALGORITHM ::= {
                {OID id-mrgm-ntru-1 PARMS NTRUMRGM1-params},
                ...}

        NTRUMRGM1-params ::= NTRUHashAlgorithmIdentifier

        NTRUHashAlgorithmIdentifier ::=
                        AlgorithmIdentifier {{NTRUEESS1v1Hashes}}

        NTRUEESS1v1BVGMs ALGORITHM ::= {
                {OID id-bvgm-ntru-1 PARMS NTRUBVGM1-params}|
                {OID id-bvgm-ntru-2 PARMS NTRUBVGM2-params},
                ...}

        NTRUBVGM1-params ::= SEQUENCE {
                c       INTEGER,
                prng    NTRUPRNGAlgorithmIdentifier,
                dr      INTEGER
                }

        NTRUBVGM2-params ::= SEQUENCE {
                c       INTEGER,

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               Supplemental Algorithms and Identifiers     March 2002

                prng    NTRUPRNGAlgorithmIdentifier,
                dr1     INTEGER,
                dr2     INTEGER,
                dr3     INTEGER
                }

   NTRUPRNGAlgorithmIdentifier ::= AlgorithmIdentifier
                                {{NTRUEESS1v1PRNGs}}

   END -- PKIXAlgorithmOIDTBD --

4. Security Considerations

   This document is entirely concerned with security mechanisms.  It is
   based on the Internet X.509 Public Key Infrastructure Certificate
   and CRL Profile [RFC 2459], IEEE P1363.1 [P1363.1] and EESS #1
   [EESS#1] and the appropriate security considerations from those
   documents apply.

5. Intellectual Property Rights

   NTRU Cryptosystems, Inc. has been granted U.S. Patent No. 6,081,597,
   which covers aspects of the NTRUEncrypt public-key encryption
   scheme, and has applied for a patent (or patents) that covers the
   NTRUSign public-key signature scheme.  In addition, NTRU
   Cryptosystems may have applied for additional patent coverage on
   implementation techniques related to the use of NTRUEncrypt or
   NTRUSign.  This and any additional patent information will be sent
   to the IETF.

   The IETF takes no position regarding the validity or scope of any
   intellectual property or other rights that might be claimed to
   pertain to the implementation or use of the technology described in
   this document or the extent to which any license under such rights
   might or might not be available; neither does it represent that it
   has made any effort to identify any such rights. Information on the
   IETF's procedures with respect to rights in standards-track and
   standards-related documentation can be found in BCP-11. Copies of
   claims of rights made available for publication and any assurances
   of licenses to be made available, or the result of an attempt made
   to obtain a general license or permission for the use of such
   proprietary rights by implementers or users of this specification
   can be obtained from the IETF Secretariat.

   The IETF invites any interested party to bring to its attention any
   copyrights, patents or patent applications, or other proprietary
   rights, which may cover technology that may be required to implement
   the techniques in this document.  Please address the information to
   the IETF Executive Director.

6. Acknowledgements

   The authors would like to thank Phil Griffin for his considerable
   aid in the formulation of the ASN.1 structures for this document.

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               Supplemental Algorithms and Identifiers     March 2002


7. References

   [EESS#1] Efficient Embedded Security Standards (EESS) #1:
   Implementation Aspects of NTRU and NTRUSign, Draft Version 4, March
   2002, Consortium for Efficient Embedded Security Standards,
   Available at http://www.ceesstandards.org.

   [FIPS180-1]  FIPS PUB 180-1, Secure Hash Standard, Federal
   Information Processing Standards Publication 180-1, U.S. Department
   of Commerce/National Institute of Standards and Technology, National
   Technical Information Service, Springfield, Virginia, April 17, 1995
   (supersedes FIPS PUB 180).  Available at
   http://www.itl.nist.gov/div897/pubs/fip180-1.htm.

   [FIPS180-2] Draft FIPS PUB 180-2, Secure Hash Standard, Federal
   Information Processing Standards Publication 180-2, U.S. Department
   of Commerce/National Institute of Standards and Technology, National
   Technical Information Service, Springfield, Virginia, May 30, 2001
   (draft available at http://csrc.nist.gov/encryption/shs/dfips-180-
   2.pdf)

   [FIPS186-2] FIPS PUB 186-2, Digital Signature Standard, Federal
   Information Processing Standards Publication 186-2, U.S. Department
   of Commerce/National Institute of Standards and Technology, National
   Technical Information Service, Springfield, Virginia, 2000.
   Available at http://csrc.nist.gov/publications/fips/fips186-
   2/fips186-2.pdf

   [IEEE1363] IEEE Std 1363-2000: IEEE Standard Specifications for
   Public-Key Cryptography, IEEE Computer Society, New York, NY, August
   2000, Institute of Electrical and Electronics Engineers

   [P1363.1] IEEE Draft Standard P1363.1 D2: IEEE Standard
   Specifications for Public-Key Cryptographic Techniques Based on Hard
   Problems over Lattices, Draft 2, May 2001, Available at
   http://grouper.ieee.org/groups/1363.

   [PKIX-ALGS] L. Bassham, R. Housley, W. Polk, "Algorithms and
   Identifiers for the Internet X.509 Public Key Infrastructure
   Certificate and CRL Profile", draft-ietf-pkix-pkalgs-05.txt, October
   2001

   [RFC2026] S. Bradner, "The Internet Standards Process", IETF RFC
   2026, October 1996

   [RFC2119] S. Bradner, "Key Words for Use in RFCs to Indicate
   Requirement Levels", IETF RFC 2119, March 1997

   [RFC2459] R. Housley, W. Ford, W. Polk and D. Solo, "Internet X.509
   Public Key Infrastructure Certificate and CRL Profile", IETF RFC
   2459, January 1999



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                   NTRU Algorithms and Identifiers      February 2002

Authors' Addresses

   Ari Singer
   NTRU
   5 Burlington Woods           Phone:  1-781-418-2500
   Burlington, MA  01803, USA   Email:  asinger@ntru.com

   William Whyte
   NTRU
   5 Burlington Woods           Phone:  1-781-418-2500
   Burlington, MA  01803, USA   Email:  wwhyte@ntru.com

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