How to generate cryptographically strong sequences of pseudo-random bits
SIAM Journal on Computing
A digital signature scheme secure against adaptive chosen-message attacks
SIAM Journal on Computing - Special issue on cryptography
Universal one-way hash functions and their cryptographic applications
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
One-way functions are necessary and sufficient for secure signatures
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
SIAM Journal on Computing
On the limits of nonapproximability of lattice problems
Journal of Computer and System Sciences - 30th annual ACM symposium on theory of computing
Signature schemes based on the strong RSA assumption
ACM Transactions on Information and System Security (TISSEC)
A sieve algorithm for the shortest lattice vector problem
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Optimal Tree-Based One-Time Digital Signature Schemes
STACS '96 Proceedings of the 13th Annual Symposium on Theoretical Aspects of Computer Science
A Digital Signature Based on a Conventional Encryption Function
CRYPTO '87 A Conference on the Theory and Applications of Cryptographic Techniques on Advances in Cryptology
CRYPTO '89 Proceedings of the 9th Annual International Cryptology Conference on Advances in Cryptology
Provably Unforgeable Signatures
CRYPTO '92 Proceedings of the 12th Annual International Cryptology Conference on Advances in Cryptology
On the Efficiency of One-Time Digital Signatures
ASIACRYPT '96 Proceedings of the International Conference on the Theory and Applications of Cryptology and Information Security: Advances in Cryptology
ASIACRYPT '02 Proceedings of the 8th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
On Polynomial-Factor Approximations to the Shortest Lattice Vector Length
SIAM Journal on Discrete Mathematics
Journal of the ACM (JACM)
Bounds on the Efficiency of Generic Cryptographic Constructions
SIAM Journal on Computing
Lattices that admit logarithmic worst-case to average-case connection factors
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Secure hash-and-sign signatures without the random oracle
EUROCRYPT'99 Proceedings of the 17th international conference on Theory and application of cryptographic techniques
Generalized compact knapsacks are collision resistant
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part II
Efficient collision-resistant hashing from worst-case assumptions on cyclic lattices
TCC'06 Proceedings of the Third conference on Theory of Cryptography
Trapdoors for hard lattices and new cryptographic constructions
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Limits on the Hardness of Lattice Problems in lp Norms
Computational Complexity
Rigorous and Efficient Short Lattice Vectors Enumeration
ASIACRYPT '08 Proceedings of the 14th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Fully homomorphic encryption using ideal lattices
Proceedings of the forty-first annual ACM symposium on Theory of computing
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
Signature Schemes with Bounded Leakage Resilience
ASIACRYPT '09 Proceedings of the 15th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
INDOCRYPT '09 Proceedings of the 10th International Conference on Cryptology in India: Progress in Cryptology
An efficient and parallel Gaussian sampler for lattices
CRYPTO'10 Proceedings of the 30th annual conference on Advances in cryptology
Toward basing fully homomorphic encryption on worst-case hardness
CRYPTO'10 Proceedings of the 30th annual conference on Advances in cryptology
Generic constructions for verifiably encrypted signatures without random oracles or NIZKs
ACNS'10 Proceedings of the 8th international conference on Applied cryptography and network security
One-time signature scheme from syndrome decoding over generic error-correcting codes
Journal of Systems and Software
Improved zero-knowledge identification with lattices
ProvSec'10 Proceedings of the 4th international conference on Provable security
One-time signatures and Chameleon hash functions
SAC'10 Proceedings of the 17th international conference on Selected areas in cryptography
Linearly homomorphic signatures over binary fields and new tools for lattice-based signatures
PKC'11 Proceedings of the 14th international conference on Practice and theory in public key cryptography conference on Public key cryptography
Improving BDD cryptosystems in general lattices
ISPEC'11 Proceedings of the 7th international conference on Information security practice and experience
The geometry of lattice cryptography
Foundations of security analysis and design VI
Fully homomorphic encryption from ring-LWE and security for key dependent messages
CRYPTO'11 Proceedings of the 31st annual 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
Parallel shortest lattice vector enumeration on graphics cards
AFRICACRYPT'10 Proceedings of the Third international conference on Cryptology in Africa
PQCrypto'10 Proceedings of the Third international conference on Post-Quantum Cryptography
Short signatures from weaker assumptions
ASIACRYPT'11 Proceedings of the 17th international conference on The Theory and Application of Cryptology and Information Security
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
NTRUCCA: how to strengthen NTRUEncrypt to chosen-ciphertext security in the standard model
PKC'12 Proceedings of the 15th international conference on Practice and Theory in Public Key Cryptography
Practical lattice-based cryptography: a signature scheme for embedded systems
CHES'12 Proceedings of the 14th international conference on Cryptographic Hardware and Embedded Systems
A ciphertext policy attribute-based encryption scheme without pairings
Inscrypt'11 Proceedings of the 7th international conference on Information Security and Cryptology
On Ideal Lattices and Learning with Errors over Rings
Journal of the ACM (JACM)
Lattice-based completely non-malleable public-key encryption in the standard model
Designs, Codes and Cryptography
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We give a direct construction of digital signatures based on the complexity of approximating the shortest vector in ideal (e.g., cyclic) lattices. The construction is provably secure based on the worst-case hardness of approximating the shortest vector in such lattices within a polynomial factor, and it is also asymptotically efficient: the time complexity of the signing and verification algorithms, as well as key and signature size is almost linear (up to poly-logarithmic factors) in the dimension n of the underlying lattice. Since no sub-exponential (in n) time algorithm is known to solve lattice problems in the worst case, even when restricted to cyclic lattices, our construction gives a digital signature scheme with an essentially optimal performance/security trade-off.