Efficient Hyperelliptic Curve Cryptosystems Using Theta Divisors

Masanobu KATAGI; Toru AKISHITA; Izuru KITAMURA; Tsuyoshi TAKAGI

doi:10.1093/ietfec/e89-a.1.151

Efficient Hyperelliptic Curve Cryptosystems Using Theta Divisors

Masanobu KATAGI, Toru AKISHITA, Izuru KITAMURA, Tsuyoshi TAKAGI

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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.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E89-A No.1 pp.151-160

Publication Date: 2006/01/01

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Online ISSN: 1745-1337

DOI: 10.1093/ietfec/e89-a.1.151

Type of Manuscript: Special Section PAPER (Special Section on Cryptography and Information Security)

Category: Elliptic Curve Cryptography

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Masanobu KATAGI, Toru AKISHITA, Izuru KITAMURA, Tsuyoshi TAKAGI, "Efficient Hyperelliptic Curve Cryptosystems Using Theta Divisors" in IEICE TRANSACTIONS on Fundamentals, vol. E89-A, no. 1, pp. 151-160, January 2006, doi: 10.1093/ietfec/e89-a.1.151.
Abstract: 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.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1093/ietfec/e89-a.1.151/_p

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@ARTICLE{e89-a_1_151,
author={Masanobu KATAGI, Toru AKISHITA, Izuru KITAMURA, Tsuyoshi TAKAGI, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Efficient Hyperelliptic Curve Cryptosystems Using Theta Divisors},
year={2006},
volume={E89-A},
number={1},
pages={151-160},
abstract={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.},
keywords={},
doi={10.1093/ietfec/e89-a.1.151},
ISSN={1745-1337},
month={January},}

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TY - JOUR
TI - Efficient Hyperelliptic Curve Cryptosystems Using Theta Divisors
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 151
EP - 160
AU - Masanobu KATAGI
AU - Toru AKISHITA
AU - Izuru KITAMURA
AU - Tsuyoshi TAKAGI
PY - 2006
DO - 10.1093/ietfec/e89-a.1.151
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E89-A
IS - 1
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - January 2006
AB - 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.
ER -