Solving sparse linear equations over finite fields
IEEE Transactions on Information Theory
Use of elliptic curves in cryptography
Lecture notes in computer sciences; 218 on Advances in cryptology---CRYPTO 85
Journal of Cryptology
A family of Jacobians suitable for discrete log cryptosystems
CRYPTO '88 Proceedings on Advances in cryptology
A remark concerning m-divisibility and the discrete logarithm in the divisor class group of curves
Mathematics of Computation
A course in computational algebraic number theory
A course in computational algebraic number theory
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
Algebraic aspects of cryptography
Algebraic aspects of cryptography
A survey of fast exponentiation methods
Journal of Algorithms
Modern computer algebra
On the discrete logarithm in the divisor class group of curves
Mathematics of Computation
A method for obtaining digital signatures and public-key cryptosystems
Communications of the ACM
Handbook of Applied Cryptography
Handbook of Applied Cryptography
Efficient Algorithms for Elliptic Curve Cryptosystems
CRYPTO '97 Proceedings of the 17th Annual International Cryptology Conference on Advances in Cryptology
A Fast Software Implementation for Arithmetic Operations in GF(2n)
ASIACRYPT '96 Proceedings of the International Conference on the Theory and Applications of Cryptology and Information Security: Advances in Cryptology
Secure Hyperelliptic Cryptosystems and Their Performances
PKC '98 Proceedings of the First International Workshop on Practice and Theory in Public Key Cryptography: Public Key Cryptography
ANTS-I Proceedings of the First International Symposium on Algorithmic Number Theory
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
Genus Two Hyperelliptic Curve Coprocessor
CHES '02 Revised Papers from the 4th International Workshop on Cryptographic Hardware and Embedded Systems
High Performance Arithmetic for special Hyperelliptic Curve Cryptosystems of Genus Two
ITCC '04 Proceedings of the International Conference on Information Technology: Coding and Computing (ITCC'04) Volume 2 - Volume 2
Elliptic and hyperelliptic curves on embedded μP
ACM Transactions on Embedded Computing Systems (TECS)
On the performance of hyperelliptic cryptosystems
EUROCRYPT'99 Proceedings of the 17th international conference on Theory and application of cryptographic techniques
An algorithm for solving the discrete log problem on hyperelliptic curves
EUROCRYPT'00 Proceedings of the 19th international conference on Theory and application of cryptographic techniques
Efficient doubling on genus two curves over binary fields
SAC'04 Proceedings of the 11th international conference on Selected Areas in Cryptography
Hyperelliptic curve coprocessors on a FPGA
WISA'04 Proceedings of the 5th international conference on Information Security Applications
Effects of Optimizations for Software Implementations of Small Binary Field Arithmetic
WAIFI '07 Proceedings of the 1st international workshop on Arithmetic of Finite Fields
Explicit Formulas for Real Hyperelliptic Curves of Genus 2 in Affine Representation
WAIFI '07 Proceedings of the 1st international workshop on Arithmetic of Finite Fields
SAC'07 Proceedings of the 14th international conference on Selected areas in cryptography
Group law computations on jacobians of hyperelliptic curves
SAC'11 Proceedings of the 18th international conference on Selected Areas in Cryptography
| Hi-index | 14.98 |
Hyperelliptic curves (HEC) look promising for cryptographic applications, because of their short operand size compared to other public-key schemes. The operand sizes seem well suited for small processor architectures, where memory and speed are constrained. However, the group operation has been believed to be too complex and, thus, HEC have not been used in this context so far. In recent years, a lot of effort has been made to speed up group operation of genus-2 HEC. In this paper, we increase the efficiency of the genus-2 and genus-3 hyperelliptic curve cryptosystems (HECC). For certain genus-3 curves, we can gain almost 80 percent performance for a group doubling. This work not only improves Gaudry and Harley's algorithm [1], but also improves the original algorithm introduced by Cantor [2]. Contrary to common belief, we show that it is also practical for certain curves to use Cantor's algorithm to obtain the highest efficiency for the group operation. In addition, we introduce a general reduction method for polynomials according to Karatsuba. We implemented our most efficient group operations on Pentium and ARM microprocessors.