Apparatus and method to compute in Jacobian of hyperelliptic...

Details Apparatus and method to compute in Jacobian of hyperelliptic... Apparatus and method to compute in Jacobian of hyperelliptic...

2006-02-21

2006-02-21

Mai, Tan V. (Department: 2193)

Electrical computers: arithmetic processing and calculating

Electrical digital calculating computer

Particular function performed

Reexamination Certificate

active

07003537

ABSTRACT:
To implement an operation in Jacobian with improved computation complexity, the sum is computed of a divisor D1=g.c.d. (a1(x),y−b1(x)) and a divisor D2=g.c.d. (a2(x),y−b2(x)) on Jacobian of a hyperelliptic curve y2+y=f(x) defined over GF(2n) by: storing a1(x), a2(x), b1(x) and b2(x); and calculating q(x)=s1(b1(x)+b2(x)) mod a2(x) by using s1(x) in s1(x)a1(x)+s2(x)a2(x)=1 in case of GCD(a1(x),a2(x))=1 where GCD denotes a greatest common polynomial. Thus, a new function q(x) is provided so as to reduce the entire computational complexity and the hardware size. Moreover, in the case of D1=D2, a1(x) and b1(x) is stored; and q(x)=Q(b12(x)+f(x) mod a12(x), a1(x)) where Q(A,B) is a quotient of A/B is calculated.

REFERENCES:
patent: 6377969 (2002-04-01), Orlando et al.

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