Introduction to finite fields and their applications
Introduction to finite fields and their applications
Identity-based cryptosystems and signature schemes
Proceedings of CRYPTO 84 on Advances in cryptology
Use of elliptic curves in cryptography
Lecture notes in computer sciences; 218 on Advances in cryptology---CRYPTO 85
Nonsingular plane cubic curves over finite fields
Journal of Combinatorial Theory Series A
Journal of Cryptology
Discrete logarithms in GF(P) using the number field sieve
SIAM Journal on Discrete Mathematics
A remark concerning m-divisibility and the discrete logarithm in the divisor class group of curves
Mathematics of Computation
Factoring with two large primes
Mathematics of Computation
Efficient algorithms for the Riemann-Roch problem and for addition in the Jacobian of a curve
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
Real and imaginary quadratic representations of hyperelliptic function fields
Mathematics of Computation
Elliptic curves in cryptography
Elliptic curves in cryptography
The Relationship Between Breaking the Diffie--Hellman Protocol and Computing Discrete Logarithms
SIAM Journal on Computing
The Xedni Calculus and the Elliptic Curve Discrete LogarithmProblem
Designs, Codes and Cryptography
Analysis of the Xedni Calculus Attack
Designs, Codes and Cryptography
Computing Riemann---Roch spaces in algebraic function fields and related topics
Journal of Symbolic Computation
Identity-Based Encryption from the Weil Pairing
SIAM Journal on Computing
Constructing hyperelliptic curves of genus 2 suitable for cryptography
Mathematics of Computation
Analysis of the Weil Descent Attack of Gaudry, Hess and Smart
CT-RSA 2001 Proceedings of the 2001 Conference on Topics in Cryptology: The Cryptographer's Track at RSA
Efficient Algorithms for Pairing-Based Cryptosystems
CRYPTO '02 Proceedings of the 22nd Annual International Cryptology Conference on Advances in Cryptology
Computing Zeta Functions of Hyperelliptic Curves over Finite Fields of Characteristic 2
CRYPTO '02 Proceedings of the 22nd Annual International Cryptology Conference on Advances in Cryptology
Supersingular Abelian Varieties in Cryptology
CRYPTO '02 Proceedings of the 22nd Annual International Cryptology Conference on Advances in Cryptology
Diffie-Hillman is as Strong as Discrete Log for Certain Primes
CRYPTO '88 Proceedings of the 8th Annual International Cryptology Conference on Advances in Cryptology
Algorithms for Black-Box Fields and their Application to Cryptography (Extended Abstract)
CRYPTO '96 Proceedings of the 16th Annual International Cryptology Conference on Advances in Cryptology
Extending the GHS Weil Descent Attack
EUROCRYPT '02 Proceedings of the International Conference on the Theory and Applications of Cryptographic Techniques: Advances in Cryptology
Elliptic Curve Discrete Logarithms and the Index Calculus
ASIACRYPT '98 Proceedings of the International Conference on the Theory and Applications of Cryptology and Information Security: Advances in Cryptology
Efficient Implementation of Schoof's Algorithm
ASIACRYPT '98 Proceedings of the International Conference on the Theory and Applications of Cryptology and Information Security: Advances in Cryptology
Weil Descent of Elliptic Curves over Finite Fields of Characteristic Three
ASIACRYPT '00 Proceedings of the 6th International Conference on the Theory and Application of Cryptology and Information Security: Advances 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
ASIACRYPT '02 Proceedings of the 8th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
FC '00 Proceedings of the 4th International Conference on Financial Cryptography
Computing in the jacobian of a plane algebraic curve
ANTS-I Proceedings of the First International Symposium on Algorithmic Number Theory
Construction of Secure CabCurves Using Modular Curves
ANTS-IV Proceedings of the 4th International Symposium on Algorithmic Number Theory
A One Round Protocol for Tripartite Diffie-Hellman
ANTS-IV Proceedings of the 4th International Symposium on Algorithmic Number Theory
ANTS-V Proceedings of the 5th International Symposium on Algorithmic Number Theory
The Function Field Sieve Is Quite Special
ANTS-V Proceedings of the 5th International Symposium on Algorithmic Number Theory
Postal Revenue Collection in the Digital Age
FC '00 Proceedings of the 4th International Conference on Financial Cryptography
Arithmetic on superelliptic curves
Mathematics of Computation
Discrete Applied Mathematics - Special issue: International workshop on coding and cryptography (WCC 2001)
Elliptic Curves: Number Theory and Cryptography
Elliptic Curves: Number Theory and Cryptography
Guide to Elliptic Curve Cryptography
Guide to Elliptic Curve Cryptography
Efficient Implementation of Pairing-Based Cryptosystems
Journal of Cryptology
Evidence that XTR Is More Secure than Supersingular Elliptic Curve Cryptosystems
Journal of Cryptology
Short Signatures from the Weil Pairing
Journal of Cryptology
The Weil Pairing, and Its Efficient Calculation
Journal of Cryptology
Advances in Elliptic Curve Cryptography (London Mathematical Society Lecture Note Series)
Advances in Elliptic Curve Cryptography (London Mathematical Society Lecture Note Series)
Building Curves with Arbitrary Small MOV Degree over Finite Prime Fields
Journal of Cryptology
Elliptic Curves Suitable for Pairing Based Cryptography
Designs, Codes and Cryptography
Generating More MNT Elliptic Curves
Designs, Codes and Cryptography
Cryptographic implications of Hess' generalized GHS attack
Applicable Algebra in Engineering, Communication and Computing
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
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
Fast point multiplication on elliptic curves through isogenies
AAECC'03 Proceedings of the 15th international conference on Applied algebra, algebraic algorithms and error-correcting codes
Constructing elliptic curves with prescribed embedding degrees
SCN'02 Proceedings of the 3rd international conference on Security in communication networks
Efficient doubling on genus two curves over binary fields
SAC'04 Proceedings of the 11th international conference on Selected Areas in Cryptography
New directions in cryptography
IEEE Transactions on Information Theory
An improved algorithm for computing logarithms over and its cryptographic significance (Corresp.)
IEEE Transactions on Information Theory
A public key cryptosystem and a signature scheme based on discrete logarithms
IEEE Transactions on Information Theory
Reducing elliptic curve logarithms to logarithms in a finite field
IEEE Transactions on Information Theory
An index calculus algorithm for plane curves of small degree
ANTS'06 Proceedings of the 7th international conference on Algorithmic Number Theory
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Algebraic curves over finite fields are being extensively used in the design of public-key cryptographic schemes. This paper surveys some topics in algebraic curve cryptography, with an emphasis on recent developments in algorithms for the elliptic and hyperelliptic curve discrete logarithm problems, and computational problems in pairing-based cryptography.