Efficient Hyperelliptic Curve Cryptosystems Using Theta Divisors

Masanobu KATAGI  Toru AKISHITA  Izuru KITAMURA  Tsuyoshi TAKAGI  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E89-A   No.1   pp.151-160
Publication Date: 2006/01/01
Online ISSN: 1745-1337
DOI: 10.1093/ietfec/e89-a.1.151
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Cryptography and Information Security)
Category: Elliptic Curve Cryptography
hyperelliptic curve cryptosystem,  scalar multiplication,  theta divisor,  window method,  

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It has recently been reported that the performance of hyperelliptic curve cryptosystems (HECC) is competitive to that of elliptic curve cryptosystems (ECC). Concerning the security of HECC, the theta divisors play an important role. The scalar multiplication using a random base point is vulnerable to an exceptional procedure attack, which is a kind of side-channel attacks, using theta divisors. In the case of cryptographic protocols of the scalar multiplication using fixed base point, however, the exceptional procedure attack is not applicable. First, we present novel efficient scalar multiplication using theta divisors, which is the positive application of theta divisors on HECC. Second, we develop a window-based method using theta divisors that is secure against side-channel attacks. It is not obvious how to construct a base point D such that all pre-computed points are theta divisors. We present an explicit algorithm for generating such divisors.