TY - GEN

T1 - Efficiently computable distortion maps for supersingular curves

AU - Takashima, Katsuyuki

PY - 2008

Y1 - 2008

N2 - Efficiently computable distortion maps are useful in cryptography. Galbraith-Pujolàs-Ritzenthaler-Smith [6] considered them for supersingular curves of genus 2. They showed that there exists a distortion map in a specific set of efficiently computable endomorphisms for every pair of nontrivial divisors under some unproven assumptions for two types of curves. In this paper, we prove that this result holds using a different method without these assumptions for both curves with r > 5 and r > 19 respectively, where r is the prime order of the divisors. In other words, we solve an open problem in [6]. Moreover, we successfully generalize this result to the case C : Y 2 = X 2g+1 + 1 over for any g s.t. 2g+1 is prime. In addition, we provide explicit bases of Jac C [r] with a new property that seems interesting from the cryptographic viewpoint.

AB - Efficiently computable distortion maps are useful in cryptography. Galbraith-Pujolàs-Ritzenthaler-Smith [6] considered them for supersingular curves of genus 2. They showed that there exists a distortion map in a specific set of efficiently computable endomorphisms for every pair of nontrivial divisors under some unproven assumptions for two types of curves. In this paper, we prove that this result holds using a different method without these assumptions for both curves with r > 5 and r > 19 respectively, where r is the prime order of the divisors. In other words, we solve an open problem in [6]. Moreover, we successfully generalize this result to the case C : Y 2 = X 2g+1 + 1 over for any g s.t. 2g+1 is prime. In addition, we provide explicit bases of Jac C [r] with a new property that seems interesting from the cryptographic viewpoint.

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U2 - 10.1007/978-3-540-79456-1_5

DO - 10.1007/978-3-540-79456-1_5

M3 - Conference contribution

AN - SCOPUS:44649155845

SN - 3540794557

SN - 9783540794554

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 88

EP - 101

BT - Algorithmic Number Theory - 8th International Symposium, ANTS-VIII, Proceedings

T2 - 8th International Symposium on Algorithmic Number Theory, ANTS-VIII

Y2 - 17 May 2008 through 22 May 2008

ER -