Elliptic curves in cryptography
Elliptic curves in cryptography
Polynomial Interpolation of the Discrete Logarithm
Designs, Codes and Cryptography
Elliptic Curve Public Key Cryptosystems
Elliptic Curve Public Key Cryptosystems
Polynomial Interpolation of the Elliptic Curve and XTR Discrete Logarithm
COCOON '02 Proceedings of the 8th Annual International Conference on Computing and Combinatorics
Efficient Group Signature Schemes for Large Groups (Extended Abstract)
CRYPTO '97 Proceedings of the 17th Annual International Cryptology Conference on Advances in Cryptology
Some Open Issues and New Directions in Group Signatures
FC '99 Proceedings of the Third International Conference on Financial Cryptography
Group Blind Digital Signatures: A Scalable Solution to Electronic Cash
FC '98 Proceedings of the Second International Conference on Financial Cryptography
Discrete Applied Mathematics - Special issue: International workshop on coding and cryptography (WCC 2001)
Untraceable Secret Credentials: Trust Establishment with Privacy
PERCOMW '04 Proceedings of the Second IEEE Annual Conference on Pervasive Computing and Communications Workshops
Discrete Applied Mathematics - Special issue: Coding and cryptography
Publicly verifiable secret sharing
EUROCRYPT'96 Proceedings of the 15th annual international conference on Theory and application of cryptographic techniques
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
Quasi-efficient revocation of group signatures
FC'02 Proceedings of the 6th international conference on Financial cryptography
WCC'05 Proceedings of the 2005 international conference on Coding and Cryptography
Interpolation of functions related to the integer factoring problem
WCC'05 Proceedings of the 2005 international conference on Coding and Cryptography
On degrees of polynomial interpolations related to elliptic curve cryptography
WCC'05 Proceedings of the 2005 international conference on Coding and Cryptography
Practical strong designated verifier signature schemes based on double discrete logarithms
CISC'05 Proceedings of the First SKLOIS conference on Information Security and Cryptology
Security flaws in several group signatures proposed by popescu
ICCSA'05 Proceedings of the 2005 international conference on Computational Science and Its Applications - Volume Part III
Polynomial representations of the Lucas logarithm
Finite Fields and Their Applications
Incomplete Character Sums and Polynomial Interpolation of the Discrete Logarithm
Finite Fields and Their Applications
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The double discrete logarithm has attracted interest as a one-way function in cryptography, in particular in group signature schemes and publicly verifiable secret sharing schemes. We obtain lower bounds on the degrees of polynomials interpolating the double discrete logarithm in multiplicative subgroups of a finite field and in the group of points on an elliptic curve over a finite field, respectively. These results support the assumption of hardness of the double discrete logarithm if the parameters are properly chosen. Similar results for other cryptographic one-way functions including the discrete logarithm, the Diffie-Hellmann mapping and related functions as well as functions related to the integer factoring problem have already been known to the literature. The investigations on the double discrete logarithm in this paper are motivated by these results on other cryptographic functions.