Reducing elliptic curve logarithms to logarithms in a finite field
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
Designs, Codes and Cryptography - Special issue on towards a quarter-century of public key cryptography
The Relationship Between Breaking the Diffie--Hellman Protocol and Computing Discrete Logarithms
SIAM Journal on Computing
Polynomial Interpolation of the Elliptic Curve and XTR Discrete Logarithm
COCOON '02 Proceedings of the 8th Annual International Conference on Computing and Combinatorics
Efficient Algorithms for Pairing-Based Cryptosystems
CRYPTO '02 Proceedings of the 22nd 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
An Identity Based Encryption Scheme Based on Quadratic Residues
Proceedings of the 8th IMA International Conference on Cryptography and Coding
A One Round Protocol for Tripartite Diffie-Hellman
ANTS-IV Proceedings of the 4th International Symposium on Algorithmic Number Theory
The Weil and Tate Pairings as Building Blocks for Public Key Cryptosystems
ANTS-V Proceedings of the 5th International Symposium on Algorithmic Number Theory
Discrete Applied Mathematics - Special issue: International workshop on coding and cryptography (WCC 2001)
Elliptic Curves Suitable for Pairing Based Cryptography
Designs, Codes and Cryptography
Efficient pairing computation on supersingular Abelian varieties
Designs, Codes and Cryptography
On degrees of polynomial interpolations related to elliptic curve cryptography
WCC'05 Proceedings of the 2005 international conference on Coding and Cryptography
Proceedings of the 7th international conference on Algorithmic Number Theory
ANTS'06 Proceedings of the 7th international conference on Algorithmic Number Theory
Pairing-Based cryptography at high security levels
IMA'05 Proceedings of the 10th international conference on Cryptography and Coding
Pairing-Friendly elliptic curves of prime order
SAC'05 Proceedings of the 12th international conference on Selected Areas in Cryptography
A public key cryptosystem and a signature scheme based on discrete logarithms
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Reducing elliptic curve logarithms to logarithms in a finite field
IEEE Transactions on Information Theory
The Diffie---Hellman problem and generalization of Verheul's theorem
Designs, Codes and Cryptography
Anonymous Signatures Revisited
ProvSec '09 Proceedings of the 3rd International Conference on Provable Security
Inverting the final exponentiation of tate pairings on ordinary elliptic curves using faults
CHES'13 Proceedings of the 15th international conference on Cryptographic Hardware and Embedded Systems
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In many aspects, cryptanalyses of pairing based cryptography consider protocol level security and take difficulties of primitives for granted. In this survey, we consider pairing inversion. At the time this manuscript was written(April 2007), to the best of the author's knowledge, there are neither known feasible algorithms for pairing inversions nor published proofs that the problem is unfeasible.