Designs, Codes and Cryptography - Special issue on towards a quarter-century of public key cryptography
Some facets of complexity theory and cryptography: A five-lecture tutorial
ACM Computing Surveys (CSUR)
Security of most significant bits of gx2
Information Processing Letters
Signature Schemes Based on 3rd Order Shift Registers
ACISP '01 Proceedings of the 6th Australasian Conference on Information Security and Privacy
CT-RSA '02 Proceedings of the The Cryptographer's Track at the RSA Conference on Topics in Cryptology
Informatics - 10 Years Back. 10 Years Ahead.
The Weil and Tate Pairings as Building Blocks for Public Key Cryptosystems
ANTS-V Proceedings of the 5th International Symposium on Algorithmic Number Theory
Number-theoretic constructions of efficient pseudo-random functions
Journal of the ACM (JACM)
On the complexity of the discrete logarithm and Diffie-Hellman problems
Journal of Complexity - Special issue on coding and cryptography
Generic Groups, Collision Resistance, and ECDSA
Designs, Codes and Cryptography
Blind sales in electronic commerce
ICEC '04 Proceedings of the 6th international conference on Electronic commerce
Transformations of two cryptographic problems in terms of matrices
ACM SIGSAM Bulletin
Fast generators for the Diffie-Hellman key agreement protocol and malicious standards
Information Processing Letters
Quantum cryptography: A survey
ACM Computing Surveys (CSUR)
A provably secure short signature scheme based on discrete logarithms
Information Sciences: an International Journal
A secure double auction protocol against false bids
Decision Support Systems
Multisignatures Using Proofs of Secret Key Possession, as Secure as the Diffie-Hellman Problem
SCN '08 Proceedings of the 6th international conference on Security and Cryptography for Networks
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
Secure remote user access over insecure networks
Computer Communications
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
Interpolation of the elliptic curve Diffie-Hellman mapping
AAECC'03 Proceedings of the 15th international conference on Applied algebra, algebraic algorithms and error-correcting codes
A CCA2 secure key encapsulation scheme based on 3rd order shift registers
ACISP'03 Proceedings of the 8th Australasian conference on Information security and privacy
A signature scheme as secure as the Diffie-Hellman problem
EUROCRYPT'03 Proceedings of the 22nd international conference on Theory and applications of cryptographic techniques
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
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
IWCC'11 Proceedings of the Third international conference on Coding and cryptology
Short signature scheme based on discrete logarithms
WAIM'05 Proceedings of the 6th international conference on Advances in Web-Age Information Management
Relationships between diffie-hellman and “index oracles”
SCN'04 Proceedings of the 4th international conference on Security in Communication Networks
How to generate universally verifiable signatures in ad-hoc networks
MADNES'05 Proceedings of the First international conference on Secure Mobile Ad-hoc Networks and Sensors
Security analysis of the strong diffie-hellman problem
EUROCRYPT'06 Proceedings of the 24th annual international conference on The Theory and Applications of Cryptographic Techniques
Abstract models of computation in cryptography
IMA'05 Proceedings of the 10th international conference on Cryptography and Coding
IMA'05 Proceedings of the 10th international conference on Cryptography and Coding
Self-correctors for cryptographic modules
IMACC'11 Proceedings of the 13th IMA international conference on Cryptography and Coding
Mathematical and Computer Modelling: An International Journal
Polynomial approximation of bilinear Diffie--Hellman maps
Finite Fields and Their Applications
Factoring Polynomials over Special Finite Fields
Finite Fields and Their Applications
Algebraic curves and cryptography
Finite Fields and Their Applications
Pairing'07 Proceedings of the First international conference on Pairing-Based Cryptography
Hi-index | 0.00 |
Both uniform and nonuniform results concerning the security of the Diffie--Hellman key-exchange protocol are proved. First, it is shown that in a cyclic group G of order |G|=\prod{p_i^{e_i}}$, where all the multiple prime factors of |G| are polynomial in log|G|, there exists an algorithm that reduces the computation of discrete logarithms in G to breaking the Diffie--Hellman protocol in G and has complexity $\sqrt{\max\{\nu(p_i)\}}\cdot(\log|G|)^{O(1)}$, where $\nu(p)$ stands for the minimum of the set of largest prime factors of all the numbers d in the interval $[p-2\sqrt{p}+1,p+2\sqrt{p}+1]$. Under the unproven but plausible assumption that $\nu(p)$ is polynomial in log p, this reduction implies that the Diffie--Hellman problem and the discrete logarithm problem are polynomial-time equivalent in G. Second, it is proved that the Diffie--Hellman problem and the discrete logarithm problem are equivalent in a uniform sense for groups whose orders belong to certain classes: there exists a polynomial-time reduction algorithm that works for all those groups. Moreover, it is shown that breaking the Diffie--Hellman protocol for a small but nonnegligible fraction of the instances is equally difficult as breaking it for all instances. Finally, efficient constructions of groups are described for which the algorithm reducing the discrete logarithm problem to the Diffie--Hellman problem is efficiently constructible.