Fast Probabilistic Algorithms for Verification of Polynomial Identities
Journal of the ACM (JACM)
The Relationship Between Breaking the Diffie--Hellman Protocol and Computing Discrete Logarithms
SIAM Journal on Computing
Towards the Equivalence of Breaking the Diffie-Hellman Protocol and Computing Discrete Algorithms
CRYPTO '94 Proceedings of the 14th 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
Lower bounds for discrete logarithms and related problems
EUROCRYPT'97 Proceedings of the 16th annual international conference on Theory and application of cryptographic techniques
On Black-Box Ring Extraction and Integer Factorization
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part II
Pairing '08 Proceedings of the 2nd international conference on Pairing-Based Cryptography
On the Equivalence of Generic Group Models
ProvSec '08 Proceedings of the 2nd International Conference on Provable Security
Breaking RSA Generically Is Equivalent to Factoring
EUROCRYPT '09 Proceedings of the 28th Annual International Conference on Advances in Cryptology: the Theory and Applications of Cryptographic Techniques
On the Analysis of Cryptographic Assumptions in the Generic Ring Model
ASIACRYPT '09 Proceedings of the 15th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Domain extension of public random functions: beyond the birthday Barrier
CRYPTO'07 Proceedings of the 27th annual international cryptology conference on Advances in cryptology
Black-box extension fields and the inexistence of field-homomorphic one-way permutations
ASIACRYPT'07 Proceedings of the Advances in Crypotology 13th international conference on Theory and application of cryptology and information security
New constructions of public-key encryption schemes from conjugacy search problems
Inscrypt'10 Proceedings of the 6th international conference on Information security and cryptology
On the CCA1-security of Elgamal and Damgård's Elgamal
Inscrypt'10 Proceedings of the 6th international conference on Information security and cryptology
On related-secret pseudorandomness
TCC'10 Proceedings of the 7th international conference on Theory of Cryptography
On the instantiability of hash-and-sign RSA signatures
TCC'12 Proceedings of the 9th international conference on Theory of Cryptography
Optimal randomized comparison based algorithms for collision
MFCS'07 Proceedings of the 32nd international conference on Mathematical Foundations of Computer Science
Efficient two-move blind signatures in the common reference string model
ISC'12 Proceedings of the 15th international conference on Information Security
Group homomorphic encryption: characterizations, impossibility results, and applications
Designs, Codes and Cryptography
Black-box obfuscation for d-CNFs
Proceedings of the 5th conference on Innovations in theoretical computer science
Hi-index | 0.00 |
Computational security proofs in cryptography, without unproven intractability assumptions, exist today only if one restricts the computational model. For example, one can prove a lower bound on the complexity of computing discrete logarithms in a cyclic group if one considers only generic algorithms which can not exploit the properties of the representation of the group elements. We propose an abstract model of computation which allows to capture such reasonable restrictions on the power of algorithms. The algorithm interacts with a black-box with hidden internal state variables which allows to perform a certain set of operations on the internal state variables, and which provides output only by allowing to check whether some state variables satisfy certain relations. For example, generic algorithms correspond to the special case where only the equality relation, and possibly also an abstract total order relation, can be tested. We consider several instantiation of the model and different types of computational problems and prove a few known and new lower bounds for computational problems of interest in cryptography, for example that computing discrete logarithms is generically hard even if an oracle for the decisional Diffie-Hellman problem and/or other low degree relations were available.