X-only generic mapping function for PACE protocol
AssigneeNXP B.V.
InventorBruce Murray
Life of this patent
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Abstract
A method of calculating the x-coordinate(xM) of a point mapping in an elliptic curve Diffie-Hellman key exchange protocol (EC-DHKF), wherein the point mapping is defined as sG+H, where sG is a point (xS,yS) on an elliptic curve and H is a point (xH,yH) on the elliptic curve, including: computing V=yS2 based upon the elliptic curve and xS; computing W=yH2 based upon the elliptic curve and xH; computing U=sqrt(W·V)mod p, where p is a large prime number; choosing U′=U or U′=p−U such that U′ based upon a characteristic agreed upon by the parties to the EC-DHKF; computing xM based upon V, W, U′, xS, xH, and p.
Claims24
A method of calculating an x-coordinate (xM) of a point mapping in an elliptic curve Diffie-Hellman key exchange protocol (EC-DHKE) between two parties, wherein the point mapping is defined as sG+H, where sG is a point (xs,ys) on an elliptic curve and H is a point (xH,yH) on the elliptic curve, comprising:
- computing V=ys2 based upon the elliptic curve and xs;
- computing W=yH2 based upon the elliptic curve and xH;
- computing U=sqrt(W·V) mod p, where p is a large prime number, wherein sqrt stands for square root;
- choosing U′=U or U′=p−U such that U′ is based upon a characteristic agreed upon by the parties to the EC-DHKE;
- computing xM based upon V, W, U′, xs, xH, and p, wherein the method allows elliptic curve Diffie-Hellmann key exchange for an x-coordinate only implementation in order to establish a connection between the two parties.
A non-transitory machine-readable storage medium encoded with instructions for calculating an x-coordinate (xM) of a point mapping in an elliptic curve Diffie-Hellman key exchange protocol (EC-DHKE) between two parties, wherein the point mapping is defined as sG+H, where sG is a point (xs,ys) on an elliptic curve and H is a point (xH,yH) on the elliptic curve, comprising:
- instructions for computing V=ys2 based upon the elliptic curve and xs;
- instructions for computing W=yH2 based upon the elliptic curve and xH;
- instructions for computing U=sqrt(W·V) mod p, where p is a large prime number, wherein sqrt stands for square root;
- instructions for choosing U′=U or U′=p−U such that U′ is based upon a characteristic agreed upon by the parties to the EC-DHKE;
- instructions for computing xM based upon V, W, U′, xs, xH, and p, wherein executing the instructions allows elliptic curve Diffie-Hellmann key exchange for an x-coordinate only implementation in order to establish a connection between the two parties.
Dependencies are inferred from the claim text.