Identity-based cryptosystems and signature schemes
Proceedings of CRYPTO 84 on Advances in cryptology
A course in computational algebraic number theory
A course in computational algebraic number theory
A Non-interactive Public-Key Distribution System
Designs, Codes and Cryptography
Computing ray class groups, conductors and discriminants
Mathematics of Computation
Efficient Implementation of Cryptosystems Based on Non-maximal Imaginary Quadratic Orders
SAC '99 Proceedings of the 6th Annual International Workshop on Selected Areas in Cryptography
The Solution of McCurley's Discrete Log Challenge
CRYPTO '98 Proceedings of the 18th Annual International Cryptology Conference on Advances in Cryptology
Modified Maurer-Yacobi`s scheme and its applications
ASIACRYPT '92 Proceedings of the Workshop on the Theory and Application of Cryptographic Techniques: Advances in Cryptology
Reducing Logarithms in Totally Non-maximal Imaginary Quadratic Orders to Logarithms in Finite Fields
ASIACRYPT '99 Proceedings of the International Conference on the Theory and Applications of Cryptology and Information Security: Advances in Cryptology
An Efficient NICE-Schnorr-Type Signature Scheme
PKC '00 Proceedings of the Third International Workshop on Practice and Theory in Public Key Cryptography: Public Key Cryptography
Selecting Cryptographic Key Sizes
PKC '00 Proceedings of the Third International Workshop on Practice and Theory in Public Key Cryptography: Public Key Cryptography
Non-interactive public-key cryptography
EUROCRYPT'91 Proceedings of the 10th annual international conference on Theory and application of cryptographic techniques
A remark on a non-interactive public-key distribution system
EUROCRYPT'92 Proceedings of the 11th annual international conference on Theory and application of cryptographic techniques
Hidden pairings and trapdoor DDH groups
ANTS'06 Proceedings of the 7th international conference on Algorithmic Number Theory
A New Practical Limited Identity-Based Encryption Scheme
Fundamenta Informaticae
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We present a new non-interactive public key distribution system based on the class group of a non-maximal imaginary quadratic order Cl(Δp). The main advantage of our system over earlier proposals based on (Z/nZ)* [19,21] is that embedding id information into group elements in a cyclic subgroup of the class group is easy (straight-forward embedding into prime ideals suffices) and secure, since the entire class group is cyclic with very high probability. In order to compute discrete logarithms in the class group, the KGC needs to know the prime factorization of Δp = Δ1p2. We present an algorithm for computing discrete logarithms in Cl(Δp) by reducing the problem to computing discrete logarithms in Cl(Δ1) and either Fp* or Fp2*. We prove that a similar reduction works for arbitrary nonmaximal orders, and that it has polynomial complexity if the factorization of the conductor is known.