Method and apparatus for performing elliptic curve arithmetic
First Claim
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1. A method of performing a cryptographic operation on a point in an elliptic curve cryptosystem using an elliptic curve, said method comprising the steps of:
- c) obtaining information that uniquely identifies said elliptic curve; and
d) performing computations on said point to obtain the result of said cryptographic operation, said computations using said information;
whereby said computations produce an incorrect result if said point is not on said elliptic curve.
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Abstract
A method of performing a cryptographic operation on a point in an elliptic curve cryptosystem using an elliptic carve. The method comprises the steps of obtaining information that uniquely identifies the elliptic curve and performing computations on the point to obtain the result of the cryptographic operation. The computations use the information. The computations produce an incorrect result if the point is not on the elliptic curve.
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Citations
21 Claims
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1. A method of performing a cryptographic operation on a point in an elliptic curve cryptosystem using an elliptic curve, said method comprising the steps of:
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c) obtaining information that uniquely identifies said elliptic curve; and
d) performing computations on said point to obtain the result of said cryptographic operation, said computations using said information;
whereby said computations produce an incorrect result if said point is not on said elliptic curve. - View Dependent Claims (2, 3, 4, 5, 6, 7, 11)
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8. A cryptographic unit for performing a cryptographic operation on a point in an elliptic curve cryptosystem using an elliptic curve, said unit comprising:
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a) storage for information that uniquely identifies said elliptic curve; and
b) a cryptographic module operably coupled to said storage to perform computations on said point to obtain the result of said cryptographic operation, said computations using said information;
whereby said computations produce an incorrect result if said point is not on said elliptic curve. - View Dependent Claims (9, 10, 12, 13, 14)
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15. A computer readable storage medium containing processor instructions for performing a cryptographic operation on a point in an elliptic curve cryptosystem using an elliptic curve, said medium including instructions to:
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c) obtain information that uniquely identifies said elliptic curve; and
d) perform computations on said point to obtain the result of said cryptographic operation, said computations using said information;
whereby said computations produce an incorrect result if said point is not on said elliptic curve. - View Dependent Claims (16, 17, 18, 19, 20, 21)
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Specification