Secret Sharing with Certified Deletion

TL;DR

This paper introduces secret sharing with certified deletion, enabling secure quantum-based secret sharing that remains safe even if an adversary eventually collects all shares, by verifying and destroying quantum shares.

Contribution

It systematically studies secret sharing with certified deletion, proposing constructions for no-signaling and adaptive security, and generalizes quantum entropy extraction techniques.

Findings

Constructed a no-signaling certified deletion scheme for any access structure.

Developed a threshold scheme with adaptive certified deletion.

Generalized XOR extractor for high-rate seedless quantum entropy extraction.

Abstract

Secret sharing allows a user to split a secret into many shares so that the secret can be recovered if, and only if, an authorized set of shares is collected. Although secret sharing typically does not require any computational hardness assumptions, its security does require that an adversary cannot collect an authorized set of shares. Over long periods of time where an adversary can benefit from multiple data breaches, this may become an unrealistic assumption. We initiate the systematic study of secret sharing with certified deletion in order to achieve security even against an adversary that eventually collects an authorized set of shares. In secret sharing with certified deletion, a (classical) secret is split into quantum shares which can be verifiably destroyed. We define two natural notions of security: no-signaling security and adaptive security. Next, we show how to construct (i) a secret sharing scheme with no-signaling certified deletion for any monotone access structure, and (ii) a threshold secret sharing scheme with adaptive certified deletion. Our first construction uses Bartusek and Khurana's (CRYPTO 2023) 2-out-of-2 secret sharing scheme with certified deletion as a building block, while our second construction is built from scratch and requires several new technical ideas. For example, we significantly generalize the ``XOR extractor'' of Agarwal, Bartusek, Khurana, and Kumar (EUROCRYPT 2023) in order to obtain high rate seedless extraction from certain quantum sources of entropy.