Method for scalarly multiplying points on an elliptic curve
OwnerAnton Kargl, Bernd Meyerinventors
Life of this patent
Estimating the term…
Abstract
A method performs scalar multiplication of points on an elliptic curve by a finite expandable field K of a first field Fp of a p>3 characteristic, wherein said characteristic p has low Hamming weight and the expandable field has a polynomF(X)+Xd−2 of order d in the polynomial representation thereof.
Claims21
1-13. (canceled)
A scalar multiplication method for encrypting a message in a computer, comprising:
- inputting a scalar value;
- inputting message data relating to points on an elliptic curve;
- performing scalar multiplication of the points on the elliptic curve over a finite extension field K of a prime field Fp having a characteristic p>3, wherein
- p is a characteristic having a Hamming weight≦4, and
- K is an extension field in a polynomial representation and has an irreducible polynomial F(X)=Xd−2 of the degree d;
- encrypting the message data based on the scalar multiplication to thereby produce a result;
- and
- outputting the result to a display device, printer, readily accessible memory or another computer on a network.
A scalar multiplication method for decrypting a message in a computer, comprising:
- inputting a scalar value;
- inputting message data related to points on an elliptic curve;
- performing scalar multiplication of the points on the elliptic curve over a finite extension field K of a prime field Fp having a characteristic p>3, wherein
- p is a characteristic having a Hamming weight≦4, and
- K is an extension field in a polynomial representation and has an irreducible polynomial F(X)=Xd−2 of the degree d;
- decrypting the message data based on the scalar multiplication to thereby produce a result;
- and
- outputting the result to a display device, printer, readily accessible memory or another computer on a network.
A scalar multiplication method for a computer-operated cryptography process, comprising:
- inputting a scalar value;
- inputting message data related to points on an elliptic curve;
- performing scalar multiplication of the points on the elliptic curve over a finite extension field K of a prime field Fp having a characteristic p>3, wherein
- p is a characteristic having a Hamming weight≦4, and
- K is an extension field in a polynomial representation and has an irreducible polynomial F(X)=Xd−2 of the degree d;
- generating a signature from the message data based on the scalar multiplication to thereby produce a result;
- and
- outputting the result to a display device, printer, readily accessible memory or another computer on a network.
A scalar multiplication method for a computer-operated cryptography process, comprising:
- inputting a scalar value;
- inputting message data related to points on an elliptic curve;
- performing scalar multiplication of the points on the elliptic curve over a finite extension field K of a prime field Fp having a characteristic p>3, wherein
- p is a characteristic having a Hamming weight≦4, and
- K is an extension field in a polynomial representation and has an irreducible polynomial F(X)=Xd−2 of the degree d;
- verifying a signature from the message data based on the scalar multiplication to thereby produce a result;
- and
- outputting the result to a display device, printer, readily accessible memory or another computer on a network.
Dependencies are inferred from the claim text.