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AssigneeSun Microsystems, Inc.
InventorsNils Gura, Hans Eberle, Edouard Goupy
Estimating the term…
A reduction operation is utilized in an arithmetic operation on two binary polynomials X(t) and Y(t) over GF(2), where an irreducible polynomial Mm(t)=tm+am−1tm−1+am−2tm−2+ . . . +a1t+a0, where the coefficients as are equal to either 1 or 0, and m is a field degree. The reduction operation includes partially reducing a result of the arithmetic operation on the two binary polynomials to produce a congruent polynomial of degree less than a chosen integer n, with m≦n. The partial reduction includes using a polynomial M′=(Mm(t)−tm)*tn−m, or a polynomial M″=Mm(t)*tn−m as part of reducing the result to the degree less than n and greater than or equal to m. The integer n can be the data path width of an arithmetic unit performing the arithmetic operation, a multiple of a digit size of a multiplier performing the arithmetic operation, a word size of a storage location, such as a register, or a maximum operand size of a functional unit in which the arithmetic operation is performed.
A method for performing an arithmetic operation on two binary polynomials X(t) and Y(t) over GF(2), where an irreducible polynomial Mm(t)=tm+am−1tm−1+am−2tm−2+ . . . +a1t+a0, where the coefficients ai are equal to either 1 or 0, and m is a field degree, comprising:
A method for performing a multiplication on two binary polynomials X(t) and Y(t) over GF(2), where an irreducible polynomial Mm(t)=tm+am−1tm−1+am−2tm−2+ . . . +a1t+a0, where the coefficients ai are equal to either 1 or 0, and m is a field degree, comprising:
An elliptic curve processing apparatus for performing a multiplication of two elements X(t) and Y(t), over GF(2), where m is a field degree, and Mm(t) is an irreducible polynomial for GF(2m), Mm(t)=tm+am−1tm−1+am−2tm−2+ . . . +a1t+a0, where the coefficients ai are equal to either 1 or 0, and m is a field degree, comprising:
An elliptic curve processing apparatus for performing a squaring operation of an element X(t), over GF(2), where m is a field degree, and Mm(t) is an irreducible polynomial for GF(2m), comprising:
A computer program product encoded on computer readable media comprising:
A computer program product encoded on computer readable media comprising:
A method for performing an arithmetic operation on a first and second binary polynomial X(t) and Y(t) over GF(2), where an irreducible polynomial Mm(t)=tm+am−1tm−1+am−2tm−2+ . . . +a1t+a0, and where the coefficients ai are equal to either 1 or 0, and m is a field degree, the first and second binary polynomials being of degree less than m, the method comprising:
An apparatus for performing an arithmetic operation on a first and second binary polynomial X(t) and Y(t) over GF(2), where an irreducible polynomial Mm(t)=tm+am−1tm−1+am−2tm−2+ . . . +a1t+a0, and where the coefficients ai are equal to either 1 or 0, and m is a field degree, the first and second binary polynomials being of degree less than m, the apparatus comprising:
Dependencies are inferred from the claim text.