Abstract
For many one-way homomorphisms used in cryptography, there exist efficient zero-knowledge proofs of knowledge of a preimage. Examples of such homomorphisms are the ones underlying the Schnorr or the Guillou-Quisquater identification protocols.
In this paper we present, for the first time, efficient zero-knowledge proofs of knowledge for exponentiation \(\psi(x_1) \doteq h_1^{x_1}\) and multi-exponentiation homomorphisms \(\psi(x_1, \ldots, x_l) \doteq h_1^{x_1} \cdot \ldots \cdot h_l^{x_l}\) with h 1, ...,h l ∈ H (i.e., proofs of knowledge of discrete logarithms and representations) where H is a group of hidden order, e.g., an RSA group.
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Bangerter, E., Camenisch, J., Maurer, U. (2005). Efficient Proofs of Knowledge of Discrete Logarithms and Representations in Groups with Hidden Order. In: Vaudenay, S. (eds) Public Key Cryptography - PKC 2005. PKC 2005. Lecture Notes in Computer Science, vol 3386. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30580-4_11
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