Zero-knowledge proofs of identity
Journal of Cryptology
Public-key cryptosystems provably secure against chosen ciphertext attacks
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
Journal of the ACM (JACM)
Multiple NonInteractive Zero Knowledge Proofs Under General Assumptions
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
A method for obtaining digital signatures and public-key cryptosystems
Communications of the ACM
Foundations of Cryptography: Basic Tools
Foundations of Cryptography: Basic Tools
SIAM Journal on Computing
Reaction Attacks against several Public-Key Cryptosystems
ICICS '99 Proceedings of the Second International Conference on Information and Communication Security
Symmetric Public-Key Encryption
CRYPTO '85 Advances in Cryptology
Eliminating Decryption Errors in the Ajtai-Dwork Cryptosystem
CRYPTO '97 Proceedings of the 17th Annual International Cryptology Conference on Advances in Cryptology
Cryptanalysis of the Ajtai-Dwork Cryptosystem
CRYPTO '98 Proceedings of the 18th Annual International Cryptology Conference on Advances in Cryptology
Universal Hash Proofs and a Paradigm for Adaptive Chosen Ciphertext Secure Public-Key Encryption
EUROCRYPT '02 Proceedings of the International Conference on the Theory and Applications of Cryptographic Techniques: Advances in Cryptology
ASIACRYPT '00 Proceedings of the 6th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
New lattice based cryptographic constructions
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Publicly verifiable secret sharing
EUROCRYPT'96 Proceedings of the 15th annual international conference on Theory and application of cryptographic techniques
Efficient and non-malleable proofs of plaintext knowledge and applications
EUROCRYPT'03 Proceedings of the 22nd international conference on Theory and applications of cryptographic techniques
Fully homomorphic encryption using ideal lattices
Proceedings of the forty-first annual ACM symposium on Theory of computing
Multi-bit cryptosystems based on lattice problems
PKC'07 Proceedings of the 10th international conference on Practice and theory in public-key cryptography
Zero-knowledge protocols for the mceliece encryption
ACISP'12 Proceedings of the 17th Australasian conference on Information Security and Privacy
Proof of plaintext knowledge for code-based public-key encryption revisited
Proceedings of the 8th ACM SIGSAC symposium on Information, computer and communications security
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Ajtai and Dwork proposed a public-key encryption scheme in 1996 which they proved secure under the assumption that the unique shortest vector problem is hard in the worst case. This cryptosystem and its extension by Regev are the only one known for which security can be proved under a worst case assumption, and as such present a particularly interesting case to study. In this paper, we show statistical zero-knowledge protocols for statements of the form “plaintext m corresponds to ciphertext c” and “ciphertext c and c' decrypt to the same value” for the Ajtai-Dwork cryptosystem. We then show a interactive zero-knowledge proof of plaintext knowledge (PPK) for the Ajtai-Dwork cryptosystem, based directly on the security of the cryptosystem rather than resorting to general interactive zero-knowledge constructions. The witness for these proofs is the randomness used in the encryption.