TY - GEN

T1 - Speeding up the arithmetic on hyperelliptic Koblitz curves of genus two

AU - Günther, C.

AU - Lange, T.

AU - Stein, A.

PY - 2001

Y1 - 2001

N2 - Koblitz, Solinas, and others investigated a family of elliptic curves which admit faster cryptosystem computations.In this paper, we generalize their ideas to hyperelliptic curves of genus 2.We consider the following two hyperelliptic curves C a : v 2 + uv = u 5 + au 2 + 1 defined over F2 with a = 0, 1, and show how to speed up the arithmetic in the Jacobian JCa(F2n) by making use of the Frobenius automorphism.With two precomputations, we are able to obtain a speed-up by a factor of 5.5 compared to the generic double-and-add-method in the Jacobian.If we allow 6 precomputations, we are even able to speed up by a factor of 7.

AB - Koblitz, Solinas, and others investigated a family of elliptic curves which admit faster cryptosystem computations.In this paper, we generalize their ideas to hyperelliptic curves of genus 2.We consider the following two hyperelliptic curves C a : v 2 + uv = u 5 + au 2 + 1 defined over F2 with a = 0, 1, and show how to speed up the arithmetic in the Jacobian JCa(F2n) by making use of the Frobenius automorphism.With two precomputations, we are able to obtain a speed-up by a factor of 5.5 compared to the generic double-and-add-method in the Jacobian.If we allow 6 precomputations, we are even able to speed up by a factor of 7.

U2 - 10.1007/3-540-44983-3_8

DO - 10.1007/3-540-44983-3_8

M3 - Conference contribution

SN - 3-540-42069-X

T3 - Lecture Notes in Computer Science

SP - 106

EP - 117

BT - Selected areas in cryptography : 7th Annual International Workshop, SAC 2000 Waterloo, Ontario, Canada, August 14–15, 2000 : proceedings

A2 - Stinson, D.R.

A2 - Tavares, S.

PB - Springer

CY - Berlin

ER -