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
Zero-knowledge proofs of identity
Journal of Cryptology
Witness indistinguishable and witness hiding protocols
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
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
Generating hard instances of lattice problems (extended abstract)
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
A public-key cryptosystem with worst-case/average-case equivalence
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
SIAM Journal on Computing
A sieve algorithm for the shortest lattice vector problem
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
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
A "Paradoxical" Indentity-Based Signature Scheme Resulting from Zero-Knowledge
CRYPTO '88 Proceedings of the 8th Annual International Cryptology Conference on Advances in Cryptology
CRYPTO '89 Proceedings of the 9th Annual International Cryptology Conference on Advances in Cryptology
Provably Secure and Practical Identification Schemes and Corresponding Signature Schemes
CRYPTO '92 Proceedings of the 12th 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
The Composite Discrete Logarithm and Secure Authentication
PKC '00 Proceedings of the Third International Workshop on Practice and Theory 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
New lattice-based cryptographic constructions
Journal of the ACM (JACM)
On lattices, learning with errors, random linear codes, and cryptography
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Lattices that admit logarithmic worst-case to average-case connection factors
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Worst-Case to Average-Case Reductions Based on Gaussian Measures
SIAM Journal on Computing
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
SWIFFT: A Modest Proposal for FFT Hashing
Fast Software Encryption
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
Public-key cryptosystems from the worst-case shortest vector problem: extended abstract
Proceedings of the forty-first annual ACM symposium on Theory of computing
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
EUROCRYPT'08 Proceedings of the theory and applications of cryptographic techniques 27th annual international conference on Advances in cryptology
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
Asymptotically efficient lattice-based digital signatures
TCC'08 Proceedings of the 5th conference on Theory of cryptography
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
A lattice-based threshold ring signature scheme
LATINCRYPT'10 Proceedings of the First international conference on Progress in cryptology: cryptology and information security in Latin America
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
The geometry of lattice cryptography
Foundations of security analysis and design VI
Public-key identification schemes based on multivariate quadratic polynomials
CRYPTO'11 Proceedings of the 31st annual conference on Advances in cryptology
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
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
TCC'12 Proceedings of the 9th international conference on Theory of Cryptography
Tightly-Secure signatures from lossy identification schemes
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
Towards efficient arithmetic for lattice-based cryptography on reconfigurable hardware
LATINCRYPT'12 Proceedings of the 2nd international conference on Cryptology and Information Security in Latin America
On the design of hardware building blocks for modern lattice-based encryption schemes
CHES'12 Proceedings of the 14th international conference on Cryptographic Hardware and Embedded Systems
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 message recovery signature schemes
International Journal of Electronic Security and Digital Forensics
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We demonstrate how the framework that is used for creating efficient number-theoretic ID and signature schemes can be transferred into the setting of lattices. This results in constructions of the most efficient to-date identification and signature schemes with security based on the worst-case hardness of problems in ideal lattices. In particular, our ID scheme has communication complexity of around 65,000 bits and the length of the signatures produced by our signature scheme is about 50,000 bits. All prior lattice-based identification schemes required on the order of millions of bits to be transferred, while all previous lattice-based signature schemes were either stateful, too inefficient, or produced signatures whose lengths were also on the order of millions of bits. The security of our identification scheme is based on the hardness of finding the approximate shortest vector to within a factor of $\tilde{O}(n^2)$ in the standard model, while the security of the signature scheme is based on the same assumption in the random oracle model. Our protocols are very efficient, with all operations requiring $\tilde{O}(n)$ time. We also show that the technique for constructing our lattice-based schemes can be used to improve certain number-theoretic schemes. In particular, we are able to shorten the length of the signatures that are produced by Girault's factoring-based digital signature scheme ([10][11][31]).