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Efficient Hyperelliptic Curve Cryptosystems Using Theta Divisors
Masanobu KATAGI Toru AKISHITA Izuru KITAMURA Tsuyoshi TAKAGI
Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Vol.E89A
No.1
pp.151160 Publication Date: 2006/01/01
Online ISSN: 17451337
DOI: 10.1093/ietfec/e89a.1.151
Print ISSN: 09168508 Type of Manuscript: Special Section PAPER (Special Section on Cryptography and Information Security) Category: Elliptic Curve Cryptography Keyword: hyperelliptic curve cryptosystem, scalar multiplication, theta divisor, window method,
Full Text: PDF(287.7KB)>>
Summary:
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 sidechannel 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 windowbased method using theta divisors that is secure against sidechannel attacks. It is not obvious how to construct a base point D such that all precomputed points are theta divisors. We present an explicit algorithm for generating such divisors.

