Secret Sharing for DNA Probability Vectors
Wenkai Zhang, Zhiying Wang
TL;DR
The paper tackles secure secret sharing for DNA storage using composite DNA letters represented as probability vectors. It introduces an asymptotic ramp secret sharing scheme (ARSSS) that operates directly on probability vectors through a cost-efficient mixture operation and a circle-multiplication framework, achieving asymptotic information-theoretic security as the alphabet size grows. The approach eliminates the need to reconstruct each share individually, reducing sequencing costs, and provides both existence proofs and practical generator-matrix constructions, including array-code based extensions for large secrets. Overall, the work extends ramp secret sharing to probabilistic alphabets, enabling efficient, secure storage in DNA-based systems with scalable, multi-vessel shares per secret.
Abstract
Emerging DNA storage technologies use composite DNA letters, where information is represented by a probability vector, leading to higher information density and lower synthesis costs. However, it faces the problem of information leakage in sharing the DNA vessels among untrusted vendors. This paper introduces an asymptotic ramp secret sharing scheme (ARSSS) for secret information storage using composite DNA letters. This innovative scheme, inspired by secret sharing methods over finite fields and enhanced with a modified matrix-vector multiplication operation for probability vectors, achieves asymptotic information-theoretic data security for a large alphabet size. Moreover, this scheme reduces the number of reading operations for DNA samples compared to traditional schemes, and therefore lowers the complexity and the cost of DNA-based secret sharing. We further explore the construction of the scheme, starting with a proof of the existence of a suitable generator, followed by practical examples. Finally, we demonstrate efficient constructions to support large information sizes, which utilize multiple vessels for each secret share rather than a single vessel.