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
Counting points on curves over finite fields
Journal of Symbolic Computation
Algebraic aspects of cryptography
Algebraic aspects of cryptography
Mathematics of Computation
On the discrete logarithm in the divisor class group of curves
Mathematics of Computation
Computing discrete logarithms in real quadratic congruence function fields of large genus
Mathematics of Computation
Solving Large Sparse Linear Systems over Finite Fields
CRYPTO '90 Proceedings of the 10th Annual International Cryptology Conference on Advances in Cryptology
The Solution of McCurley's Discrete Log Challenge
CRYPTO '98 Proceedings of the 18th Annual International Cryptology Conference on Advances in Cryptology
Speeding up the Discrete Log Computation on Curves with Automorphisms
ASIACRYPT '99 Proceedings of the International Conference on the Theory and Applications of Cryptology and Information Security: Advances in Cryptology
ANTS-I Proceedings of the First International Symposium on Algorithmic Number Theory
Speeding Up Pollard's Rho Method for Computing Discrete Logarithms
ANTS-III Proceedings of the Third International Symposium on Algorithmic Number Theory
Lower bounds for discrete logarithms and related problems
EUROCRYPT'97 Proceedings of the 16th annual international conference on Theory and application of cryptographic techniques
Counting the number of points on elliptic curves over finite fields: strategies and performances
EUROCRYPT'95 Proceedings of the 14th annual international conference on Theory and application of cryptographic techniques
On the performance of hyperelliptic cryptosystems
EUROCRYPT'99 Proceedings of the 17th international conference on Theory and application of cryptographic techniques
Proceedings of the 2001 international symposium on Symbolic and algebraic computation
Journal of Symbolic Computation - Computer algebra: Selected papers from ISSAC 2001
Compact Representation of Domain Parameters of Hyperelliptic Curve Cryptosystems
ACISP '02 Proceedings of the 7th Australian Conference on Information Security and Privacy
How Secure Are Elliptic Curves over Composite Extension Fields?
EUROCRYPT '01 Proceedings of the International Conference on the Theory and Application of Cryptographic Techniques: Advances in Cryptology
Speeding Up Point Multiplication on Hyperelliptic Curves with Efficiently-Computable Endomorphisms
EUROCRYPT '02 Proceedings of the International Conference on the Theory and Applications of Cryptographic Techniques: Advances in Cryptology
INDOCRYPT '01 Proceedings of the Second International Conference on Cryptology in India: Progress in Cryptology
Speeding up the Scalar Multiplication in the Jacobians of Hyperelliptic Curves Using Frobenius Map
INDOCRYPT '02 Proceedings of the Third International Conference on Cryptology: Progress in Cryptology
Supersingular Curves in Cryptography
ASIACRYPT '01 Proceedings of the 7th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
An Extension of Kedlaya's Point-Counting Algorithm to Superelliptic Curves
ASIACRYPT '01 Proceedings of the 7th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Two Topics in Hyperelliptic Cryptography
SAC '01 Revised Papers from the 8th Annual International Workshop on Selected Areas in Cryptography
Selection of secure hyperelliptic curves of g = 2 based on a subfield
Journal of Computer Science and Technology
Discrete Applied Mathematics - Special issue: International workshop on coding and cryptography (WCC 2001)
On the complexity of the discrete logarithm and Diffie-Hellman problems
Journal of Complexity - Special issue on coding and cryptography
Elliptic and hyperelliptic curves on embedded μP
ACM Transactions on Embedded Computing Systems (TECS)
Pseudoirreducible Polynomials: Probabilistic Irreducibility Testing
Cybernetics and Systems Analysis
IEEE Transactions on Computers
A new cryptography algorithm using cab curves an LDPC for wireless communication systems
MATH'06 Proceedings of the 10th WSEAS International Conference on APPLIED MATHEMATICS
An L (1/3 + ε) Algorithm for the Discrete Logarithm Problem for Low Degree Curves
EUROCRYPT '07 Proceedings of the 26th annual international conference on Advances in Cryptology
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
Extractors for Jacobians of Binary Genus-2 Hyperelliptic Curves
ACISP '08 Proceedings of the 13th Australasian conference on Information Security and Privacy
Pairing '08 Proceedings of the 2nd international conference on Pairing-Based Cryptography
Generating Genus Two Hyperelliptic Curves over Large Characteristic Finite Fields
EUROCRYPT '09 Proceedings of the 28th Annual International Conference on Advances in Cryptology: the Theory and Applications of Cryptographic Techniques
Distributed signcryption scheme on hyperelliptic curve
CNIS '07 Proceedings of the Fourth IASTED International Conference on Communication, Network and Information Security
Extractors for Jacobian of hyperelliptic curves of genus 2 in odd characteristic
Cryptography and Coding'07 Proceedings of the 11th IMA international conference on Cryptography and coding
Efficient doubling on genus two curves over binary fields
SAC'04 Proceedings of the 11th international conference on Selected Areas in Cryptography
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Hardware/software co-design for hyperelliptic curve cryptography (HECC) on the 8051 µP
CHES'05 Proceedings of the 7th international conference on Cryptographic hardware and embedded systems
Group law computations on jacobians of hyperelliptic curves
SAC'11 Proceedings of the 18th international conference on Selected Areas in Cryptography
EUROCRYPT'12 Proceedings of the 31st Annual international conference on Theory and Applications of Cryptographic Techniques
Improving the complexity of index calculus algorithms in elliptic curves over binary fields
EUROCRYPT'12 Proceedings of the 31st Annual international conference on Theory and Applications of Cryptographic Techniques
Isomorphism classes of hyperelliptic curves of genus 3 over finite fields
Finite Fields and Their Applications
Hyperelliptic curves of genus three over finite fields of even characteristic
Finite Fields and Their Applications
Algebraic curves and cryptography
Finite Fields and Their Applications
On polynomial systems arising from a weil descent
ASIACRYPT'12 Proceedings of the 18th international conference on The Theory and Application of Cryptology and Information Security
High-Performance scalar multiplication using 8-dimensional GLV/GLS decomposition
CHES'13 Proceedings of the 15th international conference on Cryptographic Hardware and Embedded Systems
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We present an index-calculus algorithm for the computation of discrete logarithms in the Jacobian of hyperelliptic curves defined over finite fields. The complexity predicts that it is faster than the Rho method for genus greater than 4. To demonstrate the efficiency of our approach, we describe our breaking of a cryptosystem based on a curve of genus 6 recently proposed by Koblitz.