How to prove yourself: practical solutions to identification and signature problems
Proceedings on Advances in cryptology---CRYPTO '86
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
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
The shortest vector problem in L2 is NP-hard for randomized reductions (extended abstract)
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
On the complexity of computing short linearly independent vectors and short bases in a lattice
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
A sieve algorithm for the shortest lattice vector problem
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
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 Identification Scheme Based on Permuted Kernels (Extended Abstract)
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
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
On Polynomial-Factor Approximations to the Shortest Lattice Vector Length
SIAM Journal on Discrete Mathematics
New lattice based cryptographic constructions
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Hardness of Approximating the Shortest Vector Problem in Lattices
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
On lattices, learning with errors, random linear codes, and cryptography
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Worst-Case to Average-Case Reductions Based on Gaussian Measures
SIAM Journal on Computing
Efficient reductions among lattice problems
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
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 new paradigm for public key identification
IEEE Transactions on Information Theory - Part 1
Sampling methods for shortest vectors, closest vectors and successive minima
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
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
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
Zero-Knowledge Protocols for NTRU: Application to Identification and Proof of Plaintext Knowledge
ProvSec '09 Proceedings of the 3rd International Conference on Provable Security
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
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
Adaptively secure identity-based identification from lattices without random oracles
SCN'10 Proceedings of the 7th international conference on Security and cryptography for networks
Improved zero-knowledge identification with lattices
ProvSec'10 Proceedings of the 4th international conference on Provable security
PKC'11 Proceedings of the 14th international conference on Practice and theory in public key cryptography conference on Public key cryptography
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
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
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
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
Fully anonymous attribute tokens from lattices
SCN'12 Proceedings of the 8th international conference on Security and Cryptography for Networks
Classical hardness of learning with errors
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
On Ideal Lattices and Learning with Errors over Rings
Journal of the ACM (JACM)
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There is an inherent difficulty in building 3-move ID schemes based on combinatorial problems without much algebraic structure. A consequence of this, is that most standard ID schemes today are based on the hardness of number theory problems. Not having schemes based on alternate assumptions is a cause for concern since improved number theoretic algorithms or the realization of quantum computing would make the known schemes insecure. In this work, we examine the possibility of creating identification protocols based on the hardness of lattice problems. We construct a 3-move identification scheme whose security is based on the worst-case hardness of the shortest vector problem in all lattices, and also present a more efficient version based on the hardness of the same problem in ideal lattices.