Identity-based cryptosystems and signature schemes
Proceedings of CRYPTO 84 on Advances in cryptology
Journal of 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
On the discrete logarithm in the divisor class group of curves
Mathematics of Computation
Designs, Codes and Cryptography
Identity-Based Encryption from the Weil Pairing
CRYPTO '01 Proceedings of the 21st Annual International Cryptology Conference on Advances in Cryptology
A Family of Jacobians Suitable for Discrete Log Cryptosystems
CRYPTO '88 Proceedings of the 8th Annual International Cryptology Conference on Advances in Cryptology
An Elliptic Curve Implementation of the Finite Field Digital Signature Algorithm
CRYPTO '98 Proceedings of the 18th Annual International Cryptology Conference on Advances in Cryptology
Evidence that XTR Is More Secure than Supersingular Elliptic Curve Cryptosystems
EUROCRYPT '01 Proceedings of the International Conference on the Theory and Application of Cryptographic Techniques: 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
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
A One Round Protocol for Tripartite Diffie-Hellman
ANTS-IV Proceedings of the 4th International Symposium on Algorithmic Number Theory
Arithmetic on superelliptic curves
Mathematics of Computation
Algebraic Function Fields and Codes
Algebraic Function Fields and Codes
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
The Tate pairing and the discrete logarithm applied to elliptic curve cryptosystems
IEEE Transactions on Information Theory
Efficient Identity Based Signature Schemes Based on Pairings
SAC '02 Revised Papers from the 9th Annual International Workshop on Selected Areas in Cryptography
Efficient Algorithms for Pairing-Based Cryptosystems
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
Short Signatures from the Weil Pairing
ASIACRYPT '01 Proceedings of the 7th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
An Identity-Based Signature from Gap Diffie-Hellman Groups
PKC '03 Proceedings of the 6th International Workshop on Theory and Practice in Public Key Cryptography: Public Key Cryptography
The Weil and Tate Pairings as Building Blocks for Public Key Cryptosystems
ANTS-V Proceedings of the 5th International Symposium on Algorithmic Number Theory
ANTS-V Proceedings of the 5th International Symposium on Algorithmic Number Theory
Hardware Implementation of Finite Fields of Characteristic Three
CHES '02 Revised Papers from the 4th International Workshop on Cryptographic Hardware and Embedded Systems
Montgomery Ladder for All Genus 2 Curves in Characteristic 2
WAIFI '08 Proceedings of the 2nd international workshop on Arithmetic of Finite Fields
A Generalized Brezing-Weng Algorithm for Constructing Pairing-Friendly Ordinary Abelian Varieties
Pairing '08 Proceedings of the 2nd international conference on Pairing-Based Cryptography
Subset-Restricted Random Walks for Pollard rho Method on ${\mathbf{F}_{p^m}}$
Irvine Proceedings of the 12th International Conference on Practice and Theory in Public Key Cryptography: PKC '09
LATINCRYPT'10 Proceedings of the First international conference on Progress in cryptology: cryptology and information security in Latin America
A new method for constructing pairing-friendly abelian surfaces
Pairing'10 Proceedings of the 4th international conference on Pairing-based cryptography
Fully collusion-resistant traitor tracing scheme with shorter ciphertexts
Designs, Codes and Cryptography
An improved two-party identity-based authenticated key agreement protocol using pairings
Journal of Computer and System Sciences
Efficient doubling on genus two curves over binary fields
SAC'04 Proceedings of the 11th international conference on Selected Areas in Cryptography
Deniable authenticated key establishment for internet protocols
Proceedings of the 11th international conference on Security Protocols
Efficient tate pairing computation for elliptic curves over binary fields
ACISP'05 Proceedings of the 10th Australasian conference on Information Security and Privacy
A remark on implementing the weil pairing
CISC'05 Proceedings of the First SKLOIS conference on Information Security and Cryptology
Efficient doubling on genus 3 curves over binary fields
CT-RSA'06 Proceedings of the 2006 The Cryptographers' Track at the RSA conference on Topics in Cryptology
Fast bilinear maps from the tate-lichtenbaum pairing on hyperelliptic curves
ANTS'06 Proceedings of the 7th international conference on Algorithmic Number Theory
A verifiable random function with short proofs and keys
PKC'05 Proceedings of the 8th international conference on Theory and Practice in Public Key Cryptography
Hardware acceleration of the tate pairing in characteristic three
CHES'05 Proceedings of the 7th international conference on Cryptographic hardware and embedded systems
Balancing accountability and privacy using e-cash (extended abstract)
SCN'06 Proceedings of the 5th international conference on Security and Cryptography for Networks
How to solve key escrow and identity revocation in identity-based encryption schemes
ICISS'05 Proceedings of the First international conference on Information Systems Security
Optimal eta pairing on supersingular genus-2 binary hyperelliptic curves
CT-RSA'12 Proceedings of the 12th conference on Topics in Cryptology
Ordinary abelian varieties having small embedding degree
Finite Fields and Their Applications
Counting points on Cab curves using Monsky--Washnitzer cohomology
Finite Fields and Their Applications
Finite Fields and Their Applications
Algebraic curves and cryptography
Finite Fields and Their Applications
Improved Pollard rho method for computing discrete logarithms over finite extension fields
Journal of Computational and Applied Mathematics
New definitions and separations for circular security
PKC'12 Proceedings of the 15th international conference on Practice and Theory in Public Key Cryptography
Pairing'07 Proceedings of the First international conference on Pairing-Based Cryptography
Zeta function and cryptographic exponent of supersingular curves of genus 2
Pairing'07 Proceedings of the First international conference on Pairing-Based Cryptography
Constructing pairing-friendly genus 2 curves with ordinary Jacobians
Pairing'07 Proceedings of the First international conference on Pairing-Based Cryptography
On the minimal embedding field
Pairing'07 Proceedings of the First international conference on Pairing-Based Cryptography
Using SMT solvers to automate design tasks for encryption and signature schemes
Proceedings of the 2013 ACM SIGSAC conference on Computer & communications security
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Frey and Rück gave a method to transform the discrete logarithm problem in the divisor class group of a curve over Fq into a discrete logarithm problem in some finite field extension Fqk. The discrete logarithm problem can therefore be solved using index calculus algorithms as long as k is small. In the elliptic curve case it was shown by Menezes, Okamoto and Vanstone that for supersingular curves one has k ≤ 6. In this paper curves of higher genus are studied. Bounds on the possible values for k in the case of supersingular curves are given which imply that supersingular curves are weaker than the general case for cryptography. Ways to ensure that a curve is not supersingular are also discussed. A constructive application of supersingular curves to cryptography is given, by generalising an identity-based cryptosystem due to Boneh and Franklin. The generalised scheme provides a significant reduction in bandwidth compared with the original scheme.