Untraceable RFID tags via insubvertible encryption
Proceedings of the 12th ACM conference on Computer and communications security
XTR +: A Provable Security Public Key Cryptosystem
Computational Intelligence and Security
Arithmetic Operators for Pairing-Based Cryptography
CHES '07 Proceedings of the 9th international workshop on Cryptographic Hardware and Embedded Systems
Revisiting Pairing Based Group Key Exchange
Financial Cryptography and Data Security
Pairing '08 Proceedings of the 2nd international conference on Pairing-Based Cryptography
Pairing Computation on Twisted Edwards Form Elliptic Curves
Pairing '08 Proceedings of the 2nd international conference on Pairing-Based Cryptography
CANS '08 Proceedings of the 7th International Conference on Cryptology and Network Security
The Diffie---Hellman problem and generalization of Verheul's theorem
Designs, Codes and Cryptography
FPGA and ASIC implementations of the ηT pairing in characteristic three
Computers and Electrical Engineering
Efficient non-interactive proof systems for bilinear groups
EUROCRYPT'08 Proceedings of the theory and applications of cryptographic techniques 27th annual international conference on Advances in cryptology
Efficiently computable distortion maps for supersingular curves
ANTS-VIII'08 Proceedings of the 8th international conference on Algorithmic number theory
An analysis of the vector decomposition problem
PKC'08 Proceedings of the Practice and theory in public key cryptography, 11th international conference on Public key cryptography
On the elliptic curves y2=x3-c with embedding degree one
Journal of Computational and Applied Mathematics
A generalization of Verheul's theorem for some ordinary curves
Inscrypt'10 Proceedings of the 6th international conference on Information security and cryptology
An improved two-party identity-based authenticated key agreement protocol using pairings
Journal of Computer and System Sciences
Shorter verifier-local revocation group signatures from bilinear maps
CANS'06 Proceedings of the 5th international conference on Cryptology and Network Security
Side channel attacks and countermeasures on pairing based cryptosystems over binary fields
CANS'06 Proceedings of the 5th international conference on Cryptology and Network Security
Pairing-Based cryptography at high security levels
IMA'05 Proceedings of the 10th international conference on Cryptography and Coding
Optimal eta pairing on supersingular genus-2 binary hyperelliptic curves
CT-RSA'12 Proceedings of the 12th conference on Topics in Cryptology
Efficient pairing computation on ordinary elliptic curves of embedding degree 1 and 2
IMACC'11 Proceedings of the 13th IMA international conference on Cryptography and Coding
Functional re-encryption and collusion-resistant obfuscation
TCC'12 Proceedings of the 9th international conference on Theory of Cryptography
Group to group commitments do not shrink
EUROCRYPT'12 Proceedings of the 31st Annual international conference on Theory and Applications of Cryptographic Techniques
Algebraic curves and cryptography
Finite Fields and Their Applications
Pairing'07 Proceedings of the First international conference on Pairing-Based Cryptography
Shorter IBE and signatures via asymmetric pairings
Pairing'12 Proceedings of the 5th international conference on Pairing-Based Cryptography
Towards asymmetric searchable encryption with message recovery and flexible search authorization
Proceedings of the 8th ACM SIGSAC symposium on Information, computer and communications security
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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 Vanstone and 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 problems are presumably not. So-called distortion maps on groups of points on elliptic curves that play an important role in our cryptanalysis 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 which includes a classification of elliptic curve groups where distortion maps exist.