Demonstrating possession of a discrete logarithm without revealing it
Proceedings on Advances in cryptology---CRYPTO '86
Efficient zero-knowledged identification scheme for smart cards
Lecture Notes in Computer Science on Advances in Cryptology-EUROCRYPT'88
The knowledge complexity of interactive proof systems
SIAM Journal on Computing
Efficient Identification and Signatures for Smart Cards
CRYPTO '89 Proceedings of the 9th Annual International Cryptology Conference on Advances in Cryptology
Statistical Zero Knowledge Protocols to Prove Modular Polynomial Relations
CRYPTO '97 Proceedings of the 17th 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
A Statistically-Hiding Integer Commitment Scheme Based on Groups with Hidden Order
ASIACRYPT '02 Proceedings of the 8th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
On diffie-hellman key agreement with short exponents
EUROCRYPT'96 Proceedings of the 15th annual international conference on Theory and application of cryptographic techniques
EUROCRYPT'91 Proceedings of the 10th annual international conference on Theory and application of cryptographic techniques
An improved protocol for demonstrating possession of discrete logarithms and some generalizations
EUROCRYPT'87 Proceedings of the 6th annual international conference on Theory and application of cryptographic techniques
Proving in zero-knowledge that a number is the product of two safe primes
EUROCRYPT'99 Proceedings of the 17th international conference on Theory and application of cryptographic techniques
Efficient proofs of knowledge of discrete logarithms and representations in groups with hidden order
PKC'05 Proceedings of the 8th international conference on Theory and Practice in Public Key Cryptography
On the Portability of Generalized Schnorr Proofs
EUROCRYPT '09 Proceedings of the 28th Annual International Conference on Advances in Cryptology: the Theory and Applications of Cryptographic Techniques
A self-certified and Sybil-free framework for secure digital identity domain buildup
WISTP'08 Proceedings of the 2nd IFIP WG 11.2 international conference on Information security theory and practices: smart devices, convergence and next generation networks
A certifying compiler for zero-knowledge proofs of knowledge based on Σ-protocols
ESORICS'10 Proceedings of the 15th European conference on Research in computer security
On the importance of public-key validation in the MQV and HMQV key agreement protocols
INDOCRYPT'06 Proceedings of the 7th international conference on Cryptology in India
Private client-side profiling with random forests and hidden markov models
PETS'12 Proceedings of the 12th international conference on Privacy Enhancing Technologies
Efficiency limitations of Σ-protocols for group homomorphisms revisited
SCN'12 Proceedings of the 8th international conference on Security and Cryptography for Networks
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At PKC 2005, Bangerter, Camenisch and Maurer proposed an efficient protocol to prove knowledge of discrete logarithms in groups of unknown order. We describe an attack that enables the verifier to recover the full secret with essentially no computing power beyond what is required to run the protocol and after only a few iterations of it. We also describe variants of the attack that apply when some additional simple checks are performed by the prover.