Patent ID: 7003537

Claim:
A cryptographic apparatus for computing the sum of a divisor D 1 =g.c.d. ((a 1 (x)), (y−b 1 (x))) and a divisor D 2 =g.c.d. ((a 2 (x)), (y−b 2 (x))) on Jacobian of a hyperelliptic curve y 2 +y=f(x) defined over GF(2 n ), said apparatus comprising: a storage for storing a 1 (x), a 2 (x), b 1 (x) and b 2 (x); means for calculating q(x)={s 1 (x) (b 1 (x)+b 2 (x))} mod a 2 (x) or q(x)={s 2 (x) (b 1 (x)+b 2 (x))} mod a 1 (x) by using s 1 (x) or s 2 (x) in s 1 (x)a 1 (x)+s 2 (x)a 2 (x)=1 in case of GCD(a 1 (x)), a 2 (x))=1 where GCD denotes a greatest common divisor of two polynomials; and means responsive to said means for calculating for permitting or denying access to a secure environment.