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INTERNET-DRAFT                                       ECC Keys in the DNS
Expires: May 2002                                          November 2001

                     Elliptic Curve KEYs in the DNS
                     -------- ----- ---- -- --- ---

                         Richard C. Schroeppel
                          Donald Eastlake 3rd

Status of This Document

   This draft is intended to be become a Proposed Standard RFC.
   Distribution of this document is unlimited. Comments should be sent
   to the DNS mailing list <namedroppers@internic.com> or to the

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

   The list of Internet-Draft Shadow Directories can be accessed at


   A standard method for storing elliptic curve cryptographic keys in
   the Domain Name System is described which utilizes DNS KEY resource

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   The assistance of Hilarie K. Orman in the production of this document
   is greatfully acknowledged.

Table of Contents

      Status of This Document....................................1

      Table of Contents..........................................2

      1. Introduction............................................3
      2. Elliptic Curve KEY Resource Records.....................3
      3. The Elliptic Curve Equation.............................9
      4. How do I Compute Q, G, and Y?..........................10
      5. Performance Considerations.............................11
      6. Security Considerations................................11
      7. IANA Considerations....................................11


      Authors' Addresses........................................14
      Expiration and File Name..................................14

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1. Introduction

   The Domain Name System (DNS) is the global hierarchical replicated
   distributed database system for Internet addressing, mail proxy, and
   other information. The DNS has been extended to include digital
   signatures and cryptographic keys as described in [RFC 2535].  Thus
   the DNS can now be secured and used for key distribution.

   This document describes how to store elliptic curve cryptographic
   (ECC) keys in the DNS so they can be used for a variety of security
   purposes.  A DNS elliptic curve SIG resource record is not defined.
   Familiarity with ECC cryptography is assumed [Menezes].

   The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
   document are to be interpreted as described in [RFC 2119].

2. Elliptic Curve KEY Resource Records

   Elliptic curve public keys are stored in the DNS as KEY RRs using
   algorithm number 4 (see [RFC 2535]).  The structure of the RDATA
   portion of this RR is as shown below.  The first 4 octets, including
   the flags, protocol, and algorithm fields are common to all KEY RRs.
   The remainder is the "public key" part of the KEY RR.

   The period of key validity is not in the KEY RR but is indicated by
   the SIG RR(s) which signs and authenticates the KEY RR(s) at that
   domain name and class.

   The research world continues to work on the issue of which is the
   best elliptic curve system, which finite field to use, and how to
   best represent elements in the field.  So, we have defined
   representations for every type of finite field, and every type of
   elliptic curve.  The reader should be aware that there is a unique
   finite field with a particular number of elements, but many possible
   representations of that field and its elements.  If two different
   representations of a field are given, they are interconvertible with
   a tedious but practical precomputation, followed by a fast
   computation for each field element to be converted.  It is perfectly
   reasonable for an algorithm to work internally with one field
   representation, and convert to and from a different external

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                            1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 3 3
        0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
       |           KEY flags           |    protocol   |  algorithm=4  |
       |S M -FMT- A B Z|
       |       LP      |
       |                        P (length determined from LP)       .../
       |       LF      |
       |                        F (length determined from LF)       .../
       |             DEG               |
       |             DEGH              |
       |             DEGI              |
       |             DEGJ              |
       |             TRDV              |
       |S|     LH      |
       |                        H (length determined from LH)       .../
       |S|     LK      |
       |                        K (length determined from LK)       .../
       |       LQ      |
       |                        Q (length determined from LQ)       .../
       |       LA      |
       |                        A (length determined from LA)       .../
       |             ALTA              |
       |       LB      |
       |                        B (length determined from LB)       .../
       |       LC      |
       |                        C (length determined from LC)       .../

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       |       LG      |
       |                        G (length determined from LG)       .../
       |       LY      |
       |                        Y (length determined from LY)       .../

   SMFMTABZ is a flags octet as follows:

        S = 1 indicates that the remaining 7 bits of the octet selects
           one of 128 predefined choices of finite field, element
           representation, elliptic curve, and signature parameters.
           MFMTABZ are omitted, as are all parameters from LP through G.
           LY and Y are retained.

        If S = 0, the remaining parameters are as in the picture and
           described below.

        M determines the type of field underlying the elliptic curve.

        M = 0 if the field is a GF[2^N] field;

        M = 1 if the field is a (mod P) or GF[P^D] field with P>2.

        FMT is a three bit field describing the format of the field

        FMT = 0  for a (mod P) field.
            > 0  for an extension field, either GF[2^D] or GF[P^D].
                The degree D of the extension, and the field polynomial
                must be specified.  The field polynomial is always monic
                (leading coefficient 1.)

        FMT = 1  The field polynomial is given explicitly; D is implied.

        If FMT >=2, the degree D is given explicitly.

           = 2  The field polynomial is implicit.
           = 3  The field polynomial is a binomial.  P>2.
           = 4  The field polynomial is a trinomial.
           = 5  The field polynomial is the quotient of a trinomial by a
                short polynomial.  P=2.
           = 6  The field polynomial is a pentanomial.  P=2.

        Flags A and B apply to the elliptic curve parameters.

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        A = 1 When P>=5, the curve parameter A is negated.  If P=2, then
              A=1 indicates that the A parameter is special.  See the
              ALTA parameter below, following A.  The combination A=1,
              P=3 is forbidden.

        B = 1 When P>=5, the curve parameter B is negated.  If P=2 or 3,
              then B=1 indicates an alternate elliptic curve equation is
              used.  When P=2 and B=1, an additional curve parameter C
              is present.

        The Z bit SHOULD be set to zero on creation of KEY RR and MUST
           be ignored when processing a KEY RR (when S=0).

   Most of the remaining parameters are present in some formats and
   absent in others.  The presence or absence of a parameter is
   determined entirely by the flags.  When a parameter occurs, it is in
   the order defined by the picture.

   Of the remaining parameters, PFHKQABCGY are variable length.  When
   present, each is preceded by a one-octet length field as shown in the
   diagram above.  The length field does not include itself.  The length
   field may have values from 0 through 110.  The parameter length in
   octets is determined by a conditional formula:  If LL<=64, the
   parameter length is LL.  If LL>64, the parameter length is 16 times
   (LL-60).  In some cases, a parameter value of 0 is sensible, and MAY
   be represented by an LL value of 0, with the data field omitted.  A
   length value of 0 represents a parameter value of 0, not an absent
   parameter.  (The data portion occupies 0 space.) There is no
   requirement that a parameter be represented in the minimum number of
   octets; high-order 0 octets are allowed at the front end.  Parameters
   are always right adjusted, in a field of length defined by LL.  The
   octet-order is always most-significant first, least-significant last.
   The parameters H and K may have an optional sign bit stored in the
   unused high-order bit of their length fields.

   LP defines the length of the prime P.  P must be an odd prime.  The
   parameters LP,P are present if and only if the flag M=1.  If M=0, the
   prime is 2.

   LF,F define an explicit field polynomial.  This parameter pair is
   present only when FMT = 1.  The length of a polynomial coefficient is
   ceiling(log2 P) bits.  Coefficients are in the numerical range [0,P-
   1].  The coefficients are packed into fixed-width fields, from higher
   order to lower order.  All coefficients must be present, including
   any 0s and also the leading coefficient (which is required to be 1).
   The coefficients are right justified into the octet string of length
   specified by LF, with the low-order "constant" coefficient at the
   right end.  As a concession to storage efficiency, the higher order
   bits of the leading coefficient may be elided, discarding high-order
   0 octets and reducing LF.  The degree is calculated by determining

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   the bit position of the left most 1-bit in the F data (counting the
   right most bit as position 0), and dividing by ceiling(log2 P).  The
   division must be exact, with no remainder.  In this format, all of
   the other degree and field parameters are omitted.  The next
   parameters will be LQ,Q.

   If FMT>=2, the degree of the field extension is specified explicitly,
   usually along with other parameters to define the field polynomial.

   DEG is a two octet field that defines the degree of the field
   extension.  The finite field will have P^DEG elements.  DEG is
   present when FMT>=2.

   When FMT=2, the field polynomial is specified implicitly.  No other
   parameters are required to define the field; the next parameters
   present will be the LQ,Q pair.  The implicit field poynomial is the
   lexicographically smallest irreducible (mod P) polynomial of the
   correct degree.  The ordering of polynomials is by highest-degree
   coefficients first -- the leading coefficient 1 is most important,
   and the constant term is least important.  Coefficients are ordered
   by sign-magnitude:  0 < 1 < -1 < 2 < -2 < ...  The first polynomial
   of degree D is X^D (which is not irreducible).  The next is X^D+1,
   which is sometimes irreducible, followed by X^D-1, which isn't.
   Assuming odd P, this series continues to X^D - (P-1)/2, and then goes
   to X^D + X, X^D + X + 1, X^D + X - 1, etc.

   When FMT=3, the field polynomial is a binomial, X^DEG + K.  P must be
   odd.  The polynomial is determined by the degree and the low order
   term K.  Of all the field parameters, only the LK,K parameters are
   present.  The high-order bit of the LK octet stores on optional sign
   for K; if the sign bit is present, the field polynomial is X^DEG - K.

   When FMT=4, the field polynomial is a trinomial, X^DEG + H*X^DEGH +
   K.  When P=2, the H and K parameters are implicitly 1, and are
   omitted from the representation.  Only DEG and DEGH are present; the
   next parameters are LQ,Q.  When P>2, then LH,H and LK,K are
   specified.  Either or both of LH, LK may contain a sign bit for its

   When FMT=5, then P=2 (only).  The field polynomial is the exact
   quotient of a trinomial divided by a small polynomial, the trinomial
   divisor.  The small polynomial is right-adjusted in the two octet
   field TRDV.  DEG specifies the degree of the field.  The degree of
   TRDV is calculated from the position of the high-order 1 bit.  The
   trinomial to be divided is X^(DEG+degree(TRDV)) + X^DEGH + 1.  If
   DEGH is 0, the middle term is omitted from the trinomial.  The
   quotient must be exact, with no remainder.

   When FMT=6, then P=2 (only).  The field polynomial is a pentanomial,
   with the degrees of the middle terms given by the three 2-octet

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INTERNET-DRAFT                                       ECC Keys in the DNS

   values DEGH, DEGI, DEGJ.  The polynomial is X^DEG + X^DEGH + X^DEGI +
   X^DEGJ + 1.  The values must satisfy the inequality DEG > DEGH > DEGI
   > DEGJ > 0.

        DEGH, DEGI, DEGJ  are two-octet fields that define the degree of
           a term in a field polynomial.   DEGH is present when FMT = 4,
           5, or 6.  DEGI and DEGJ are present only when FMT = 6.

        TRDV is a two-octet right-adjusted binary polynomial of degree <
           16.  It is present only for FMT=5.

        LH and H define the H parameter, present only when FMT=4 and P
           is odd.  The high bit of LH is an optional sign bit for H.

        LK and K define the K parameter, present when FMT = 3 or 4, and
           P is odd.  The high bit of LK is an optional sign bit for K.

   The remaining parameters are concerned with the elliptic curve and
   the signature algorithm.

        LQ defines the length of the prime Q.  Q is a prime > 2^159.

   In all 5 of the parameter pairs LA+A,LB+B,LC+C,LG+G,LY+Y, the data
   member of the pair is an element from the finite field defined
   earlier.  The length field defines a long octet string. Field
   elements are represented as (mod P) polynomials of degree < DEG, with
   DEG or fewer coefficients.  The coefficients are stored from left to
   right, higher degree to lower, with the constant term last.  The
   coefficients are represented as integers in the range [0,P-1].  Each
   coefficient is allocated an area of ceiling(log2 P) bits.  The field
   representation is right-justified; the "constant term" of the field
   element ends at the right most bit.  The coefficients are fitted
   adjacently without regard for octet boundaries.  (Example: if P=5,
   three bits are used for each coefficient.  If the field is GF[5^75],
   then 225 bits are required for the coefficients, and as many as 29
   octets may be needed in the data area.  Fewer octets may be used if
   some high-order coefficients are 0.) If a flag requires a field
   element to be negated, each non-zero coefficient K is replaced with
   P-K.  To save space, 0 bits may be removed from the left end of the
   element representation, and the length field reduced appropriately.
   This would normally only happen with A,B,C, because the designer
   chose curve parameters with some high-order 0 coefficients or bits.

   If the finite field is simply (mod P), then the field elements are
   simply numbers (mod P), in the usual right-justified notation.  If
   the finite field is GF[2^D], the field elements are the usual right-
   justified polynomial basis representation.

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INTERNET-DRAFT                                       ECC Keys in the DNS

        LA,A is the first parameter of the elliptic curve equation.
           When P>=5, the flag A = 1 indicates A should be negated (mod
           P).  When P=2 (indicated by the flag M=0), the flag A = 1
           indicates that the parameter pair LA,A is replaced by the two
           octet parameter ALTA.  In this case, the parameter A in the
           curve equation is x^ALTA, where x is the field generator.
           Parameter A often has the value 0, which may be indicated by
           LA=0 (with no A data field), and sometimes A is 1, which may
           be represented with LA=1 and a data field of 1, or by setting
           the A flag and using an ALTA value of 0.

        LB,B is the second parameter of the elliptic curve equation.
           When P>=5, the flag B = 1 indicates B should be negated (mod
           P).  When P=2 or 3, the flag B selects an alternate curve

        LC,C is the third parameter of the elliptic curve equation,
           present only when P=2 (indicated by flag M=0) and flag B=1.

        LG,G defines a point on the curve, of order Q.  The W-coordinate
           of the curve point is given explicitly; the Z-coordinate is

        LY,Y is the user's public signing key, another curve point of
           order Q.  The W-coordinate is given explicitly; the Z-
           coordinate is implicit.  The LY,Y parameter pair is always

3. The Elliptic Curve Equation

   (The coordinates of an elliptic curve point are named W,Z instead of
   the more usual X,Y to avoid confusion with the Y parameter of the
   signing key.)

   The elliptic curve equation is determined by the flag octet, together
   with information about the prime P.  The primes 2 and 3 are special;
   all other primes are treated identically.

   If M=1, the (mod P) or GF[P^D] case, the curve equation is Z^2 = W^3
   + A*W + B.  Z,W,A,B are all numbers (mod P) or elements of GF[P^D].
   If A and/or B is negative (i.e., in the range from P/2 to P), and
   P>=5, space may be saved by putting the sign bit(s) in the A and B
   bits of the flags octet, and the magnitude(s) in the parameter

   If M=1 and P=3, the B flag has a different meaning: it specifies an
   alternate curve equation, Z^2 = W^3 + A*W^2 + B.  The middle term of
   the right-hand-side is different.  When P=3, this equation is more

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INTERNET-DRAFT                                       ECC Keys in the DNS

   commonly used.

   If M=0, the GF[2^N] case, the curve equation is Z^2 + W*Z = W^3 +
   A*W^2 + B.  Z,W,A,B are all elements of the field GF[2^N].  The A
   parameter can often be 0 or 1, or be chosen as a single-1-bit value.
   The flag B is used to select an alternate curve equation, Z^2 + C*Z =
   W^3 + A*W + B.  This is the only time that the C parameter is used.

4. How do I Compute Q, G, and Y?

   The number of points on the curve is the number of solutions to the
   curve equation, + 1 (for the "point at infinity").  The prime Q must
   divide the number of points.  Usually the curve is chosen first, then
   the number of points is determined with Schoof's algorithm.  This
   number is factored, and if it has a large prime divisor, that number
   is taken as Q.

   G must be a point of order Q on the curve, satisfying the equation

        Q * G  =  the point at infinity (on the elliptic curve)

   G may be chosen by selecting a random [RFC 1750] curve point, and
   multiplying it by (number-of-points-on-curve/Q).  G must not itself
   be the "point at infinity"; in this astronomically unlikely event, a
   new random curve point is recalculated.

   G is specified by giving its W-coordinate.  The Z-coordinate is
   calculated from the curve equation.  In general, there will be two
   possible Z values.  The rule is to choose the "positive" value.

   In the (mod P) case, the two possible Z values sum to P.  The smaller
   value is less than P/2; it is used in subsequent calculations.  In
   GF[P^D] fields, the highest-degree non-zero coefficient of the field
   element Z is used; it is chosen to be less than P/2.

   In the GF[2^N] case, the two possible Z values xor to W (or to the
   parameter C with the alternate curve equation).  The numerically
   smaller Z value (the one which does not contain the highest-order 1
   bit of W (or C)) is used in subsequent calculations.

   Y is specified by giving the W-coordinate of the user's public
   signature key.  The Z-coordinate value is determined from the curve
   equation.  As with G, there are two possible Z values; the same rule
   is followed for choosing which Z to use.

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INTERNET-DRAFT                                       ECC Keys in the DNS

   During the key generation process, a random [RFC 1750] number X must
   be generated such that 1 <= X <= Q-1.  X is the private key and is
   used in the final step of public key generation where Y is computed

        Y = X * G (as points on the elliptic curve)

   If the Z-coordinate of the computed point Y is wrong (i.e., Z > P/2
   in the (mod P) case, or the high-order non-zero coefficient of Z >
   P/2 in the GF[P^D] case, or Z sharing a high bit with W(C) in the
   GF[2^N] case), then X must be replaced with Q-X.  This will
   correspond to the correct Z-coordinate.

5. Performance Considerations

   Elliptic curve signatures use smaller moduli or field sizes than RSA
   and DSA.  Creation of a curve is slow, but not done very often.  Key
   generation is faster than RSA or DSA.

   DNS implementations have been optimized for small transfers,
   typically less than 512 octets including DNS overhead. Larger
   transfers will perform correctly and and extensions have been
   standardized to make larger transfers more efficient [RFC 2671].
   However, it is still advisable at this time to make reasonable
   efforts to minimize the size of KEY RR sets stored within the DNS
   consistent with adequate security.  Keep in mind that in a secure
   zone, an authenticating SIG RRset will also be returned.

6. Security Considerations

   Many of the general security consideration in [RFC 2535] apply.  Some
   specific key generation considerations are given above.  Of course,
   the elliptic curve key stored in the DNS for an entity should not be
   trusted unless it has been obtain via a trusted DNS resolver that
   vouches for its security or unless the application using the key has
   done a similar authentication.

7. IANA Considerations

   Assignment of meaning to the remaining ECC KEY flag bits or to values
   of ECC fields outside the ranges for which meaning in defined in this
   document requires an IETF consensus as defined in [RFC 2434].

   This specification uses algorithm number 4 for DNS elliptic curve KEY

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   RRs that was reserved for this purpose in RFC 2535.  An elliptic
   curve (algorithm = 4) SIG RR is not defined and is reserved.

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   [RFC 1034] - P. Mockapetris, "Domain names - concepts and
   facilities", 11/01/1987.

   [RFC 1035] - P. Mockapetris, "Domain names - implementation and
   specification", 11/01/1987.

   [RFC 1750] - D. Eastlake, S. Crocker, J. Schiller, "Randomness
   Recommendations for Security", 12/29/1994.

   [RFC 2119] - S. Bradner, "Key words for use in RFCs to Indicate
   Requirement Levels", March 1997.

   [RFC 2434] - T. Narten, H. Alvestrand, "Guidelines for Writing an
   IANA Considerations Section in RFCs", October 1998.

   [RFC 2535] -  D. Eastlake,"Domain Name System Security Extensions",
   March 1999.

   [RFC 2671] -  P. Vixie, "Extension Mechanisms for DNS (EDNS0)",
   August 1999.

   [Schneier] - Bruce Schneier, "Applied Cryptography: Protocols,
   Algorithms, and Source Code in C", 1996, John Wiley and Sons

   [Menezes] - Alfred Menezes, "Elliptic Curve Public Key
   Cryptosystems", 1993 Kluwer.

   [Silverman] - Joseph Silverman, "The Arithmetic of Elliptic Curves",
   1986, Springer Graduate Texts in mathematics #106.

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Authors' Addresses

   Rich Schroeppel
   500 S. Maple Drive
   Woodland Hills, UT 84653 USA

   Telephone:   1-801-423-7998(h)
   Email:       rcs@cs.arizona.edu

   Donald E. Eastlake 3rd
   155 Beaver Street
   Milford, MA 01757 USA

   Telephone:   +1 508-634-2066(h)
                +1 508-261-5434(w)
   FAX:         +1 508-261-4447(w)
   EMail:       Donald.Eastlake@motorola.com

Expiration and File Name

   This draft expires in May 2002.

   Its file name is draft-ietf-dnsext-ecc-key-01.txt.

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