TY - GEN
T1 - Efficient algorithms for the construction of hyperelliptic cryptosystems
AU - Okamoto, Tatsuaki
AU - Sakurai, Kouichi
N1 - Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 1992.
PY - 1992
Y1 - 1992
N2 - The jacobian of hyperelliptic curves, including elliptic curves as a special case, offers a good primitive for cryptosystems, since cryptosystems (discrete logarithms) based on the jacobians seem to be more intractable than those based on conventional multiplicative groups. In this paper, we show that the problem to determine the group structure of the jacobian can be characterized to be in NP ∩ co-NP, when the jacobian is a non-degenerate type (“non-half-degenerate”). We also show that the hyperelliptic discrete logarithm can be characterized to be in NP ∩ co-NP, when the group structure is non-half-degenerate. Moreover, we imply the reducibility of the hyperelliptic discrete logarithm to a multiplicative discrete logarithm. The extended Weil pairing over the jacobian is the key tool for these algorithms.
AB - The jacobian of hyperelliptic curves, including elliptic curves as a special case, offers a good primitive for cryptosystems, since cryptosystems (discrete logarithms) based on the jacobians seem to be more intractable than those based on conventional multiplicative groups. In this paper, we show that the problem to determine the group structure of the jacobian can be characterized to be in NP ∩ co-NP, when the jacobian is a non-degenerate type (“non-half-degenerate”). We also show that the hyperelliptic discrete logarithm can be characterized to be in NP ∩ co-NP, when the group structure is non-half-degenerate. Moreover, we imply the reducibility of the hyperelliptic discrete logarithm to a multiplicative discrete logarithm. The extended Weil pairing over the jacobian is the key tool for these algorithms.
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U2 - 10.1007/3-540-46766-1_21
DO - 10.1007/3-540-46766-1_21
M3 - Conference contribution
AN - SCOPUS:33746826979
SN - 9783540551881
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 267
EP - 278
BT - Advances in Cryptology — CRYPTO 1991, Proceedings
A2 - Feigenbaum, Joan
PB - Springer Verlag
T2 - 11th Confrence on Advances in Cryptology, CRYPTO 1991
Y2 - 11 August 1991 through 15 August 1991
ER -