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 -