A course in computational algebraic number theory
A course in computational algebraic number theory
Generating hard instances of lattice problems (extended abstract)
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Matrix computations (3rd ed.)
A public-key cryptosystem with worst-case/average-case equivalence
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
A Lattice-Based Public-Key Cryptosystem
SAC '98 Proceedings of the Selected Areas in Cryptography
Cryptanalysis of the Goldreich-Goldwasser-Halevi Cryptosystem from Crypto '97
CRYPTO '99 Proceedings of the 19th Annual International Cryptology Conference on Advances in Cryptology
Eliminating Decryption Errors in the Ajtai-Dwork Cryptosystem
CRYPTO '97 Proceedings of the 17th Annual International Cryptology Conference on Advances in Cryptology
Cryptanalysis of the Ajtai-Dwork Cryptosystem
CRYPTO '98 Proceedings of the 18th Annual International Cryptology Conference on Advances in Cryptology
Tensor-Based Trapdoors for CVP and Their Application to Public Key Cryptography
Proceedings of the 7th IMA International Conference on Cryptography and Coding
A Lattice Based Public Key Cryptosystem Using Polynomial Representations
PKC '03 Proceedings of the 6th International Workshop on Theory and Practice in Public Key Cryptography: Public Key Cryptography
NTRU: A Ring-Based Public Key Cryptosystem
ANTS-III Proceedings of the Third International Symposium on Algorithmic Number Theory
Improving Lattice Based Cryptosystems Using the Hermite Normal Form
CaLC '01 Revised Papers from the International Conference on Cryptography and Lattices
On lattices, learning with errors, random linear codes, and cryptography
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Representing hard lattices with O(n log n) bits
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Generalized Compact Knapsacks, Cyclic Lattices, and Efficient One-Way Functions
Computational Complexity
Lossy trapdoor functions and their applications
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Trapdoors for hard lattices and new cryptographic constructions
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Algorithms for quantum computation: discrete logarithms and factoring
SFCS '94 Proceedings of the 35th Annual Symposium on Foundations of Computer Science
SWIFFT: A Modest Proposal for FFT Hashing
Fast Software Encryption
A Framework for Efficient and Composable Oblivious Transfer
CRYPTO 2008 Proceedings of the 28th Annual conference on Cryptology: Advances in Cryptology
Post Quantum Cryptography
H-LLL: using householder inside LLL
Proceedings of the 2009 international symposium on Symbolic and algebraic computation
Fast LLL-type lattice reduction
Information and Computation
EUROCRYPT'97 Proceedings of the 16th annual international conference on Theory and application of cryptographic techniques
Cryptanalysis of the Paeng-Jung-Ha cryptosystem from PKC 2003
PKC'07 Proceedings of the 10th international conference on Practice and theory in public-key cryptography
Multi-bit cryptosystems based on lattice problems
PKC'07 Proceedings of the 10th international conference on Practice and theory in public-key cryptography
A digital signature scheme based on CV P∞
PKC'08 Proceedings of the Practice and theory in public key cryptography, 11th international conference on Public key cryptography
Asymptotically efficient lattice-based digital signatures
TCC'08 Proceedings of the 5th conference on Theory of cryptography
EUROCRYPT'05 Proceedings of the 24th annual international conference on Theory and Applications of Cryptographic Techniques
CRYPTO'06 Proceedings of the 26th annual international conference on Advances in Cryptology
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A prime goal of Lattice-based cryptosystems is to provide an enhanced security assurance by remaining secure with respect to quantum computational complexity, while remaining practical on conventional computer systems. In this paper, we define and analyze a superclass of GGH-style nearly-orthogonal bases for use in private keys, together with a subclass of Hermite Normal Forms for use in Miccianciostyle public keys and discuss their benefits when used in Bounded Distance Decoding cryptosystems in general lattices. We propose efficient methods for the creation of such nearly-orthogonal private bases and "Optimal" Hermite Normal Forms and discuss timing results for these methods. Finally, we propose a class of cryptosystems based on the use of these constructions and provide a fair comparison between this class of cryptosystems and related cryptosystems.