Elliptic Curve Public Key Cryptosystems
Elliptic Curve Public Key Cryptosystems
CRYPTO '00 Proceedings of the 20th 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
A Practical Public Key Cryptosystem Provably Secure Against Adaptive Chosen Ciphertext Attack
CRYPTO '98 Proceedings of the 18th Annual International Cryptology Conference on Advances in Cryptology
ASIACRYPT '00 Proceedings of the 6th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
A One Round Protocol for Tripartite Diffie-Hellman
ANTS-IV Proceedings of the 4th International Symposium on Algorithmic Number Theory
ASIACRYPT '94 Proceedings of the 4th International Conference on the Theory and Applications of Cryptology: Advances in Cryptology
A secure and optimally efficient multi-authority election scheme
EUROCRYPT'97 Proceedings of the 16th annual international conference on Theory and application of cryptographic techniques
Public-key cryptosystems based on cubic finite field extensions
IEEE Transactions on Information Theory
Efficient Algorithms for Pairing-Based Cryptosystems
CRYPTO '02 Proceedings of the 22nd Annual International Cryptology Conference on Advances in Cryptology
Toward Hierarchical Identity-Based Encryption
EUROCRYPT '02 Proceedings of the International Conference on the Theory and Applications of Cryptographic Techniques: Advances in Cryptology
Cryptanalysis of a Pseudorandom Generator Based on Braid Groups
EUROCRYPT '02 Proceedings of the International Conference on the Theory and Applications of Cryptographic Techniques: Advances in Cryptology
Self-Blindable Credential Certificates 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
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
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
Ate Pairing on Hyperelliptic Curves
EUROCRYPT '07 Proceedings of the 26th annual international conference on Advances in Cryptology
Pairing '08 Proceedings of the 2nd international conference on Pairing-Based Cryptography
Pairings on Hyperelliptic Curves with a Real Model
Pairing '08 Proceedings of the 2nd international conference on Pairing-Based Cryptography
Publicly Verifiable Privacy-Preserving Group Decryption
Information Security and Cryptology
Privacy for Private Key in Signatures
Information Security and Cryptology
Improved Implementations of Cryptosystems Based on Tate Pairing
ISA '09 Proceedings of the 3rd International Conference and Workshops on Advances in Information Security and Assurance
CANS '09 Proceedings of the 8th International Conference on Cryptology and Network Security
Pairing-Based Onion Routing with Improved Forward Secrecy
ACM Transactions on Information and System Security (TISSEC)
Pairing'10 Proceedings of the 4th international conference on Pairing-based cryptography
A generalization of Verheul's theorem for some ordinary curves
Inscrypt'10 Proceedings of the 6th international conference on Information security and cryptology
Fast irreducibility testing for XTR using a gaussian normal basis of low complexity
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
On degrees of polynomial interpolations related to elliptic curve cryptography
WCC'05 Proceedings of the 2005 international conference on Coding and Cryptography
Efficient tate pairing computation for elliptic curves over binary fields
ACISP'05 Proceedings of the 10th Australasian conference on Information Security and Privacy
Improved zero value attack on XTR
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
A new two-party identity-based authenticated key agreement
CT-RSA'05 Proceedings of the 2005 international conference on Topics in Cryptology
Efficient hardware for the tate pairing calculation in characteristic three
CHES'05 Proceedings of the 7th international conference on Cryptographic hardware and embedded systems
Closed formulae for the Weil pairing inversion
Finite Fields and Their Applications
Pairing'07 Proceedings of the First international conference on Pairing-Based Cryptography
The importance of the final exponentiation in pairings when considering fault attacks
Pairing'07 Proceedings of the First international conference on Pairing-Based Cryptography
Pairing'07 Proceedings of the First international conference on Pairing-Based Cryptography
The k-BDH assumption family: bilinear map cryptography from progressively weaker assumptions
CT-RSA'13 Proceedings of the 13th international conference on Topics in Cryptology
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We show that finding an efficiently computable injective homomorphism from the XTR subgroup into the group of points over GF(p2) of a particular type of supersingular elliptic curve is at least as hard as solving the Diffie-Hellman problem in the XTR subgroup. This provides strong evidence for a negative answer to the question posed by S. Vanstone and A. Menezes at the Crypto 2000 Rump Session on the possibility of efficiently inverting the MOV embedding into the XTR subgroup. As a side result we show that the Decision Diffie-Hellman problem in the group of points on this type of supersingular elliptic curves is efficiently computable, which provides an example of a group where the Decision Diffie-Hellman problem is simple, while the Diffie-Hellman and discrete logarithm problem are presumably not. The cryptanalytical tools we use also lead to cryptographic applications of independent interest. These applications are an improvement of Joux's one round protocol for tripartite Diffie-Hellman key exchange and a non refutable digital signature scheme that supports escrowable encryption. We also discuss the applicability of our methods to general elliptic curves defined over finite fields.