Biblio

Shamir's Secret Sharing Scheme is well established and widely used. It allows a so-called Dealer to split and share a secret k among n Participants such that at least t shares are needed to reconstruct k, where 0 \textbackslashtextbackslashtextless; t ≤ n. Nothing about the secret can be learned from less than t shares. To split secret k, the Dealer generates a polynomial f, whose independent term is k and the coefficients are randomly selected using a uniform distribution. A share is a pair (x, f(x)) where x is also chosen randomly using a uniform distribution. This scheme is useful, for example, to distribute cryptographic keys among different cloud providers and to create multi-factor authentication. The security of Shamir's Secret Sharing Scheme is usually analyzed using a threat model where the Dealer is trusted to split and share secrets as described above. In this paper, we demonstrate that there exists a different threat model where a malicious Dealer can compute shares such that a subset of less than t shares is allowed to reconstruct the secret. We refer to such subsets as hidden sets. We formally define hidden sets and prove lower bounds on the number of possible hidden sets for polynomials of degree t - 1. Yet, we show how to detect hidden sets given a set of n shares and describe how to create hidden sets while sharing a secret using a modification of Shamir's scheme.

A permissioned blockchain platform comes with numerous assurances such as transaction confidentiality and system scalability to several organizations. Most permissioned blockchains rely on a Public-Key Infrastructure (PKI)as cryptographic tools to provide security services such as identity authentication and data confidentiality. Using PKI to validate transactions includes validating digital certificates of endorsement peers which creates an overhead in the system. Because public-key operations are computationally intensive, they limit the scalability of blockchain applications. Due to a large modulus size and expensive modular exponentiation operations, public-key operations such as RSA become slower than polynomial-based schemes, which involve a smaller modulus size and a less smaller number of modular multiplications. For instance, the 2048-bit RSA is approximately 15,728 times slower than a polynomial with a degree of 50 and 128-bit modulus size. In this paper, we propose a lightweight polynomial-based key management scheme in the context of a permissioned blockchain. Our scheme involves computationally less intensive polynomial evaluation operations such as additions and multiplications that result in a faster processing compared with public-key schemes. In addition, our proposed solution reduces the overhead of processing transactions and improves the system scalability. Security and performance analysis are provided in the paper.

In this work NTRU-like cryptosystem NTRU Prime IIT Ukraine, which is created on the basis of existing cryptographic transformations end-to-end encryption type, is considered. The description of this cryptosystem is given and its analysis is carried out. Also, features of its implementation, comparison of the main characteristics and indicators, as well as the definition of differences from existing NTRU-like cryptographic algorithms are presented. Conclusions are made and recommendations are given.