Journal of Cryptology
A course in computational algebraic number theory
A course in computational algebraic number theory
A survey of fast exponentiation methods
Journal of Algorithms
A Family of Jacobians Suitable for Discrete Log Cryptosystems
CRYPTO '88 Proceedings of the 8th Annual International Cryptology Conference on Advances in Cryptology
Optimal Extension Fields for Fast Arithmetic in Public-Key Algorithms
CRYPTO '98 Proceedings of the 18th Annual International Cryptology Conference on Advances in Cryptology
Counting Points on Hyperelliptic Curves over Finite Fields
ANTS-IV Proceedings of the 4th International Symposium on Algorithmic Number Theory
Improving Group Law Algorithms for Jacobians of Hyperelliptic Curves
ANTS-IV Proceedings of the 4th International Symposium on Algorithmic Number Theory
Guide to Elliptic Curve Cryptography
Guide to Elliptic Curve Cryptography
IEEE Transactions on Computers
The Complexity of Certain Multi-Exponentiation Techniques in Cryptography
Journal of Cryptology
Trading Inversions for Multiplications in Elliptic Curve Cryptography
Designs, Codes and Cryptography
Fast elliptic curve arithmetic and improved weil pairing evaluation
CT-RSA'03 Proceedings of the 2003 RSA conference on The cryptographers' track
Efficient doubling on genus two curves over binary fields
SAC'04 Proceedings of the 11th international conference on Selected Areas in Cryptography
Handbook of Elliptic and Hyperelliptic Curve Cryptography, Second Edition
Handbook of Elliptic and Hyperelliptic Curve Cryptography, Second Edition
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We analyze all the cases and propose the corresponding explicit formulae for computing 2D1 + D2 in one step from given divisor classes D1 and D2 on genus 2 hyperelliptic curves defined over prime fields. Compared with naive method, the improved formula can save two field multiplications and one field squaring each time when the arithmetic is performed in the most frequent case. Furthermore, we present a variant which trades one field inversion for fourteen field multiplications and two field squarings by using Montgomery's trick to combine the two inversions. Experimental results show that our algorithms can save up to 13% of the time to perform a scalar multiplication on a general genus 2 hyperelliptic curve over a prime field, when compared with the best known general methods.