Narrow Results

A secret sharing scheme is a method which allows a dealer to share a secret among a set of participants in such a way that only qualified subsets of participants can recover the secret. The collection of subsets of participants that can reconstruct the secret in this way is called access structure. The rank of an access structure is the maximum cardinality of a minimal qualified subset. A secret sharing scheme is perfect if unqualified subsets of participants obtain no information regarding the secret. The dealer's randomness is the number of random bits required by the dealer to setup a secret sharing scheme. The efficiency of the dealer's randomness is the ratio between the amount of the dealer's randomness and the length of the secret. Because random bits are a natural computational resource, it is important to reduce the amount of randomness used by the dealer to setup a secret sharing scheme. In this paper, we propose some decomposition constructions for perfect secret sharing schemes with access structures of constant rank. Compared with the best previous results, our constructions have some improved upper bounds on the dealer's randomness and on the efficiency of the dealer's randomness.

A cryptology protocol for key distribution using phase and intensity fluctuation is proposed. It provides ways to detect the extent of eavesdropping. Detecting test factors and system design rules are suggested and the performances are analyzed for various signal keyings and cryptofunctions. It has a wide range of implementations, including the use of additive white Gaussian noise, background noise, and polarization modification in wire/wireless and optical communications.

In [D. R. L. Brown, Plactic key agreement (insecure?), J. Math. Cryptol.17(1) (2023) 20220010], a novel cryptographic key exchange technique was proposed using the plactic monoid, based on the apparent difficulty of solving division problems in that monoid. Specifically, given elements $c,b$ in the plactic monoid, the problem is to find $q$ for which $qb=c$, given that such a $q$ exists. In this paper, we introduce a metric on the plactic monoid and use it to give a probabilistic algorithm for solving that problem which is fast for parameter values in the range of interest.

A cryptology protocol for key distribution using phase and intensity fluctuation is proposed. It provides ways to detect the extent of eavesdropping. Detecting test factors and system design rules are suggested and the performances are analyzed for various signal keyings and cryptofunctions. It has a wide range of implementations, including the use of additive white Gaussian noise, background noise, and polarization modification in wire/wireless and optical communications.