An Approach to the Construction of a Recursive Argument of Polynomial Evaluation in the Discrete Log Setting

Succinct Non-interactive Arguments of Knowledge (SNARks) are receiving a lot of attention as a core privacy-enhancing technology for blockchain applications. Polynomial commitment schemes are important building blocks for the construction of SNARks. Polynomial commitment schemes enable the prover to commit to a secret polynomial of the prover and convince the verifier that the evaluation of the committed polynomial is correct at a public point later. Bünz et al. recently presented a novel polynomial commitment scheme with no trusted setup in Eurocrypt’20. To provide a transparent setup, their scheme is built over an ideal class group of imaginary quadratic fields (or briefly, class group). However, cryptographic assumptions on a class group are relatively new and have, thus far, not been well-analyzed. In this paper, we study an approach to transpose Bünz et al.’s techniques in the discrete log setting because the discrete log setting brings a significant improvement in efficiency and security compared to class groups. We show that the transposition to the discrete log setting can be obtained by employing a proof system for the equality of discrete logarithms over multiple bases. Theoretical analysis shows that the transposition preserves security requirements for a polynomial commitment scheme.

Secure Information Transfer Using Two Keyless Cryptography Methods

In the current paper, some methods of information security protocols based on physical layer security are considered. It is proved that well known Shamir’s protocol can be applied to RSA cryptosystem but not to Rabin, Mac-Ellice and trellis based cryptosystems.The main stream of this paper is a description of key sharing protocol on constant public and noiseless channels (like Internet). It is shown that it is able to provide a high reliability and control of security in terms of Shannon’s information providing nothing-additional requirements to communication channels and without any cryptographic assumptions.