STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
A note on efficient zero-knowledge proofs and arguments (extended abstract)
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
A new identification scheme based on syndrome decoding
CRYPTO '93 Proceedings of the 13th annual international cryptology conference on Advances in cryptology
Cryptographic primitives based on hard learning problems
CRYPTO '93 Proceedings of the 13th annual international cryptology conference on Advances in cryptology
Linear zero-knowledge—a note on efficient zero-knowledge proofs and arguments
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Efficient noise-tolerant learning from statistical queries
Journal of the ACM (JACM)
SIAM Journal on Computing
Minimum Resource Zero-Knowledge Proofs (Extended Abstract)
CRYPTO '89 Proceedings of the 9th Annual International Cryptology Conference on Advances in Cryptology
Honest Verifier vs Dishonest Verifier in Public Cain Zero-Knowledge Proofs
CRYPTO '95 Proceedings of the 15th Annual International Cryptology Conference on Advances in Cryptology
Zero-Knowledge Proofs for Finite Field Arithmetic; or: Can Zero-Knowledge be for Free?
CRYPTO '98 Proceedings of the 18th Annual International Cryptology Conference on Advances in Cryptology
Secure Human Identification Protocols
ASIACRYPT '01 Proceedings of the 7th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
On Defining Proofs of Knowledge
CRYPTO '92 Proceedings of the 12th Annual International Cryptology Conference on Advances in Cryptology
Noise-tolerant learning, the parity problem, and the statistical query model
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
Succinct Non-Interactive Zero-Knowledge Proofs with Preprocessing for LOGSNP
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Zero-knowledge from secure multiparty computation
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
How to Encrypt with the LPN Problem
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part II
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
Cryptography with Constant Input Locality
Journal of Cryptology
On the Amortized Complexity of Zero-Knowledge Protocols
CRYPTO '09 Proceedings of the 29th Annual International Cryptology Conference on Advances in Cryptology
Fast Cryptographic Primitives and Circular-Secure Encryption Based on Hard Learning Problems
CRYPTO '09 Proceedings of the 29th Annual International Cryptology Conference on Advances in Cryptology
Efficient non-interactive proof systems for bilinear groups
EUROCRYPT'08 Proceedings of the theory and applications of cryptographic techniques 27th annual international conference on Advances in cryptology
Improved zero-knowledge identification with lattices
ProvSec'10 Proceedings of the 4th international conference on Provable security
A zero-knowledge identification scheme based on the q-ary syndrome decoding problem
SAC'10 Proceedings of the 17th international conference on Selected areas in cryptography
Efficient authentication from hard learning problems
EUROCRYPT'11 Proceedings of the 30th Annual international conference on Theory and applications of cryptographic techniques: advances in cryptology
Pseudorandom knapsacks and the sample complexity of LWE search-to-decision reductions
CRYPTO'11 Proceedings of the 31st annual conference on Advances in cryptology
Authenticating pervasive devices with human protocols
CRYPTO'05 Proceedings of the 25th annual international conference on Advances in Cryptology
Algebraic geometric secret sharing schemes and secure multi-party computations over small fields
CRYPTO'06 Proceedings of the 26th annual international conference on Advances in Cryptology
Multiparty computation with low communication, computation and interaction via threshold FHE
EUROCRYPT'12 Proceedings of the 31st Annual international conference on Theory and Applications of Cryptographic Techniques
On the inherent intractability of certain coding problems (Corresp.)
IEEE Transactions on Information Theory
Revisiting lightweight authentication protocols based on hard learning problems
Proceedings of the sixth ACM conference on Security and privacy in wireless and mobile networks
Proof of plaintext knowledge for code-based public-key encryption revisited
Proceedings of the 8th ACM SIGSAC symposium on Information, computer and communications security
Solving the learning parity with noise's open question
Information Processing Letters
Zero-knowledge using garbled circuits: how to prove non-algebraic statements efficiently
Proceedings of the 2013 ACM SIGSAC conference on Computer & communications security
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We construct a perfectly binding string commitment scheme whose security is based on the learning parity with noise (LPN) assumption, or equivalently, the hardness of decoding random linear codes. Our scheme not only allows for a simple and efficient zero-knowledge proof of knowledge for committed values (essentially a Σ-protocol), but also for such proofs showing any kind of relation amongst committed values, i.e., proving that messages m0,…,mu, are such that m0=C(m1,…,mu) for any circuit C. To get soundness which is exponentially small in a security parameter t, and when the zero-knowledge property relies on the LPN problem with secrets of length ℓ, our 3 round protocol has communication complexity ${\mathcal O}(t|C|\ell\log(\ell))$ and computational complexity of ${\mathcal O}(t|C|\ell)$ bit operations. The hidden constants are small, and the computation consists mostly of computing inner products of bit-vectors.