Perfect Homomorphic Zero-Knowledge Threshold Schemes over any Finite Abelian Group
SIAM Journal on Discrete Mathematics
Generating hard instances of lattice problems (extended abstract)
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
SIAM Journal on Computing
Finding the closest lattice vector when it's unusually close
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Communications of the ACM
Generating Hard Instances of the Short Basis Problem
ICAL '99 Proceedings of the 26th International Colloquium on Automata, Languages and Programming
CRYPTO '89 Proceedings of the 9th Annual International Cryptology Conference on Advances in Cryptology
A Practical Public Key Cryptosystem Provably Secure Against Adaptive Chosen Ciphertext Attack
CRYPTO '98 Proceedings of the 18th Annual International Cryptology Conference on Advances in Cryptology
Universally Composable Security: A New Paradigm for Cryptographic Protocols
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Chosen-Ciphertext Security from Identity-Based Encryption
SIAM Journal on Computing
Worst-Case to Average-Case Reductions Based on Gaussian Measures
SIAM Journal on Computing
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
Learning a Parallelepiped: Cryptanalysis of GGH and NTRU Signatures
Journal of 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
On lattices, learning with errors, random linear codes, and cryptography
Journal of the ACM (JACM)
An efficient threshold public key cryptosystem secure against adaptive chosen ciphertext attack
EUROCRYPT'99 Proceedings of the 17th international conference on Theory and application of cryptographic techniques
Practical threshold signatures
EUROCRYPT'00 Proceedings of the 19th international conference on Theory and application of cryptographic techniques
An efficient and parallel Gaussian sampler for lattices
CRYPTO'10 Proceedings of the 30th annual conference on 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
Changeable Threshold Signature Scheme Based on Lattice Theory
ICEE '10 Proceedings of the 2010 International Conference on E-Business and E-Government
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
Generating Shorter Bases for Hard Random Lattices
Theory of Computing Systems
Homomorphic signatures for polynomial functions
EUROCRYPT'11 Proceedings of the 30th Annual international conference on Theory and applications of cryptographic techniques: advances in cryptology
Threshold decryption and zero-knowledge proofs for lattice-based cryptosystems
TCC'10 Proceedings of the 7th international conference on Theory of Cryptography
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
Efficient lattice (H)IBE in the standard model
EUROCRYPT'10 Proceedings of the 29th Annual international conference on Theory and Applications of Cryptographic Techniques
Simplified threshold RSA with adaptive and proactive security
EUROCRYPT'06 Proceedings of the 24th annual international conference on The Theory and Applications of Cryptographic Techniques
Efficient threshold encryption from lossy trapdoor functions
PQCrypto'11 Proceedings of the 4th international conference on Post-Quantum Cryptography
Functional encryption for inner product predicates from learning with errors
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
| Hi-index | 0.00 |
We develop secure threshold protocols for two important operations in lattice cryptography, namely, generating a hard lattice Λ together with a "strong" trapdoor, and sampling from a discrete Gaussian distribution over a desired coset of Λ using the trapdoor. These are the central operations of many cryptographic schemes: for example, they are exactly the key-generation and signing operations (respectively) for the GPV signature scheme, and they are the public parameter generation and private key extraction operations (respectively) for the GPV IBE. We also provide a protocol for trapdoor delegation, which is used in lattice-based hierarchical IBE schemes. Our work therefore directly transfers all these systems to the threshold setting. Our protocols provide information-theoretic (i.e., statistical) security against adaptive corruptions in the UC framework, and they are robust against up to ℓ/2 semi-honest or ℓ/3 malicious parties (out of ℓ total). Our Gaussian sampling protocol is both noninteractive and efficient, assuming either a trusted setup phase (e.g., performed as part of key generation) or a sufficient amount of interactive but offline precomputation, which can be performed before the inputs to the sampling phase are known.