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
Lecture Notes in Computer Science on Advances in Cryptology-EUROCRYPT'88
Zero-knowledge proofs of identity
Journal of Cryptology
The knowledge complexity of interactive proof systems
SIAM Journal on Computing
Witness indistinguishable and witness hiding protocols
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
Fast signature generation with a Fiat Shamir—like scheme
EUROCRYPT '90 Proceedings of the workshop on the theory and application of cryptographic techniques on Advances in cryptology
Random oracles are practical: a paradigm for designing efficient protocols
CCS '93 Proceedings of the 1st ACM conference on Computer and communications security
Special Uses and Sbuses of the Fiat-Shamir Passport Protocol
CRYPTO '87 A Conference on the Theory and Applications of Cryptographic Techniques on Advances in Cryptology
An Improvement of the Fiat-Shamir Identification and Signature Scheme
CRYPTO '88 Proceedings of the 8th 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
On the Length of Cryptographic Hash-Values Used in Identification Schemes
CRYPTO '94 Proceedings of the 14th Annual International Cryptology Conference on Advances in Cryptology
On the security of a practical identification scheme
EUROCRYPT'96 Proceedings of the 15th annual international conference on Theory and application of cryptographic techniques
Security proofs for signature schemes
EUROCRYPT'96 Proceedings of the 15th annual international conference on Theory and application of cryptographic techniques
A New Identification Scheme Based on the Bilinear Diffie-Hellman Problem
ACISP '02 Proceedings of the 7th Australian Conference on Information Security and Privacy
The Representation Problem Based on Factoring
CT-RSA '02 Proceedings of the The Cryptographer's Track at the RSA Conference on Topics in Cryptology
CRYPTO '02 Proceedings of the 22nd Annual International Cryptology Conference on Advances in Cryptology
Identification Protocols Secure against Reset Attacks
EUROCRYPT '01 Proceedings of the International Conference on the Theory and Application of Cryptographic Techniques: Advances in Cryptology
Strong Key-Insulated Signature Schemes
PKC '03 Proceedings of the 6th International Workshop on Theory and Practice in Public Key Cryptography: Public Key Cryptography
On the Security of Beth's Identification Schemes against Active and Concurrent Adversaries
Mathematical Methods in Computer Science
Improved Non-committing Encryption with Applications to Adaptively Secure Protocols
ASIACRYPT '09 Proceedings of the 15th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
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Ong-Schnorr identification and signatures are variants of the Fiat-Shamir scheme with short and fast communication and signatures. This scheme uses secret, keys that are 2t-roots modulo N of the public keys, whereas Fiat-Shamir uses square roots modulo N. Security for particular cases has recently been proved by Micali [M94] and Shoup [ShYG]. We prove that identification and signatures are secure for arbilrary moduli N = pq unless N can easily be factored. The proven security of identification against active impersonation attacks depends on the maximal 2-power 2th that divides either p - 1 or q - 1. We show that signatures are secure against adaptive chosen-message attacks. This proves the security of a very efficient signature scheme.