Journal of Cryptology
CRYPTO '99 Proceedings of the 19th Annual International Cryptology Conference on Advances in Cryptology
Timing Attacks on Implementations of Diffie-Hellman, RSA, DSS, and Other Systems
CRYPTO '96 Proceedings of the 16th Annual International Cryptology Conference on Advances in Cryptology
Efficient Elliptic Curve Exponentiation Using Mixed Coordinates
ASIACRYPT '98 Proceedings of the International Conference on the Theory and Applications of Cryptology and Information Security: Advances in Cryptology
Proceedings of the 8th IMA International Conference on Cryptography and Coding
A Combined Timing and Power Attack
PKC '02 Proceedings of the 5th International Workshop on Practice and Theory in Public Key Cryptosystems: Public Key Cryptography
Exceptional Procedure Attackon Elliptic Curve Cryptosystems
PKC '03 Proceedings of the 6th International Workshop on Theory and Practice in Public Key Cryptography: Public Key Cryptography
A Refined Power-Analysis Attack on Elliptic Curve Cryptosystems
PKC '03 Proceedings of the 6th International Workshop on Theory and Practice in Public Key Cryptography: Public Key Cryptography
Improving Group Law Algorithms for Jacobians of Hyperelliptic Curves
ANTS-IV Proceedings of the 4th International Symposium on Algorithmic Number Theory
Resistance against Differential Power Analysis for Elliptic Curve Cryptosystems
CHES '99 Proceedings of the First International Workshop on Cryptographic Hardware and Embedded Systems
A Timing Attack against RSA with the Chinese Remainder Theorem
CHES '00 Proceedings of the Second International Workshop on Cryptographic Hardware and Embedded Systems
Protections against Differential Analysis for Elliptic Curve Cryptography
CHES '01 Proceedings of the Third International Workshop on Cryptographic Hardware and Embedded Systems
Two topics in hyperelliptic cryptography
Two topics in hyperelliptic cryptography
Efficient pairing computation on supersingular Abelian varieties
Designs, Codes and Cryptography
CHES'06 Proceedings of the 8th international conference on Cryptographic Hardware and Embedded Systems
Fast bilinear maps from the tate-lichtenbaum pairing on hyperelliptic curves
ANTS'06 Proceedings of the 7th international conference on Algorithmic Number Theory
Group law computations on jacobians of hyperelliptic curves
SAC'11 Proceedings of the 18th international conference on Selected Areas in Cryptography
Pairing'07 Proceedings of the First international conference on Pairing-Based Cryptography
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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). However, it is expected that HECC still can be improved due to their mathematically rich structure. We consider here the application of degenerate divisors of HECC to scalar multiplication. We investigate the operations of the degenerate divisors in the Harley algorithm and the Cantor algorithm of genus 2. The timings of these operations are reported. We then present a novel efficient scalar multiplication method using the degenerate divisors. This method is applicable to cryptosystems with fixed base point, e.g., ElGamal-type encryption, sender of Diffie-Hellman, and DSA. Using a Xeon processor, we found that the double-and-add-always method using the degenerate base point can achieve about a 20% increase in speed for a 160-bit HECC. However, we mounted an timing attack using the time difference to designate the degenerate divisors. The attack assumes that the secret key is fixed and the base point can be freely chosen by the attacker. Therefore, the attack is applicable to ElGamal-type decryption and single-pass Diffie-Hellman – SSL using a hyperelliptic curve could be vulnerable to the proposed attack. Our experimental results show that one bit of the secret key for a 160-bit HECC can be recovered by calling the decryption oracle 500 times.