On the Lagarias-Odlyzko algorithm for the subset sum problem
SIAM Journal on Computing
How to prove yourself: practical solutions to identification and signature problems
Proceedings on Advances in cryptology---CRYPTO '86
A digital signature scheme secure against adaptive chosen-message attacks
SIAM Journal on Computing - Special issue on cryptography
An identity-based identification scheme based on discrete logarithms modulo a composite number
EUROCRYPT '90 Proceedings of the workshop on the theory and application of cryptographic techniques on Advances in cryptology
On-line/off-line digital signatures
CRYPTO '89 Proceedings on Advances in cryptology
Signature schemes based on the strong RSA assumption
ACM Transactions on Information and System Security (TISSEC)
An Improved Pseudo-random Generator Based on Discrete Log
CRYPTO '00 Proceedings of the 20th Annual International Cryptology Conference on Advances in Cryptology
A "Paradoxical" Indentity-Based Signature Scheme Resulting from Zero-Knowledge
CRYPTO '88 Proceedings of the 8th Annual International Cryptology Conference on Advances in Cryptology
An Efficient Discrete Log Pseudo Random Generator
CRYPTO '98 Proceedings of the 18th Annual International Cryptology Conference on Advances in Cryptology
EUROCRYPT '02 Proceedings of the International Conference on the Theory and Applications of Cryptographic Techniques: Advances in Cryptology
Efficiency improvements for signature schemes with tight security reductions
Proceedings of the 10th ACM conference on Computer and communications security
An Improved Pseudo-Random Generator Based on the Discrete Logarithm Problem
Journal of Cryptology
Efficient Signature Schemes with Tight Reductions to the Diffie-Hellman Problems
Journal of Cryptology
Generalized Compact Knapsacks, Cyclic Lattices, and Efficient One-Way Functions
Computational Complexity
Trapdoors for hard lattices and new cryptographic constructions
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Solving low density subset sum problems
SFCS '83 Proceedings of the 24th Annual Symposium on Foundations of Computer Science
Unbiased bits from sources of weak randomness and probabilistic communication complexity
SFCS '85 Proceedings of the 26th Annual Symposium on Foundations of Computer Science
Concurrently Secure Identification Schemes Based on the Worst-Case Hardness of Lattice Problems
ASIACRYPT '08 Proceedings of the 14th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
On lattices, learning with errors, random linear codes, and cryptography
Journal of the ACM (JACM)
Short and Stateless Signatures from the RSA Assumption
CRYPTO '09 Proceedings of the 29th Annual International Cryptology Conference on Advances in Cryptology
Fiat-Shamir with Aborts: Applications to Lattice and Factoring-Based Signatures
ASIACRYPT '09 Proceedings of the 15th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Efficient Public Key Encryption Based on Ideal Lattices
ASIACRYPT '09 Proceedings of the 15th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
On diffie-hellman key agreement with short exponents
EUROCRYPT'96 Proceedings of the 15th annual international conference on Theory and application of cryptographic techniques
The exact security of digital signatures-how to sign with RSA and Rabin
EUROCRYPT'96 Proceedings of the 15th annual international conference on Theory and application of cryptographic techniques
Secure hash-and-sign signatures without the random oracle
EUROCRYPT'99 Proceedings of the 17th international conference on Theory and application of cryptographic techniques
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
Lattice-based identification schemes secure under active attacks
PKC'08 Proceedings of the Practice and theory in public key cryptography, 11th international conference on Public key cryptography
Making NTRU as secure as worst-case problems over ideal lattices
EUROCRYPT'11 Proceedings of the 30th Annual international conference on Theory and applications of cryptographic techniques: advances in cryptology
Improved generic algorithms for hard knapsacks
EUROCRYPT'11 Proceedings of the 30th Annual international conference on Theory and applications of cryptographic techniques: advances in cryptology
Pseudorandom knapsacks and the sample complexity of LWE search-to-decision reductions
CRYPTO'11 Proceedings of the 31st annual conference on Advances in cryptology
Generalized compact knapsacks are collision resistant
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part II
An efficient CDH-based signature scheme with a tight security reduction
CRYPTO'05 Proceedings of the 25th annual international conference on Advances in Cryptology
Lattice mixing and vanishing trapdoors: a framework for fully secure short signatures and more
PKC'10 Proceedings of the 13th international conference on Practice and Theory in Public Key Cryptography
On ideal lattices and learning with errors over rings
EUROCRYPT'10 Proceedings of the 29th Annual international conference on Theory and Applications of Cryptographic Techniques
Bonsai trees, or how to delegate a lattice basis
EUROCRYPT'10 Proceedings of the 29th Annual international conference on Theory and Applications of Cryptographic Techniques
Improving efficiency of an ‘on the fly' identification scheme by perfecting zero-knowledgeness
CT-RSA'10 Proceedings of the 2010 international conference on Topics in Cryptology
Efficient collision-resistant hashing from worst-case assumptions on cyclic lattices
TCC'06 Proceedings of the Third conference on Theory of Cryptography
Trapdoors for lattices: simpler, tighter, faster, smaller
EUROCRYPT'12 Proceedings of the 31st Annual international conference on Theory and Applications of Cryptographic Techniques
Lattice signatures without trapdoors
EUROCRYPT'12 Proceedings of the 31st Annual international conference on Theory and Applications of Cryptographic Techniques
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In this paper we present three digital signature schemes with tight security reductions. Our first signature scheme is a particularly efficient version of the short exponent discrete log based scheme of Girault et al. (J. of Cryptology 2006). Our scheme has a tight reduction to the decisional Short Discrete Logarithm problem, while still maintaining the non-tight reduction to the computational version of the problem upon which the original scheme of Girault et al. is based. The second signature scheme we construct is a modification of the scheme of Lyubashevsky (Asiacrypt 2009) that is based on the worst-case hardness of the shortest vector problem in ideal lattices. And the third scheme is a very simple signature scheme that is based directly on the hardness of the Subset Sum problem. We also present a general transformation that converts, what we term lossy identification schemes, into signature schemes with tight security reductions. We believe that this greatly simplifies the task of constructing and proving the security of such signature schemes.