# Leakage-Resilient Non-Malleable Secret Sharing in Non-compartmentalized Models

## TL;DR

This paper introduces leakage-resilient non-malleable secret sharing schemes in non-compartmentalized models, addressing adversaries with complex corruption and tampering capabilities, and provides constructions for specific tampering families.

## Contribution

It initiates the study of leakage-resilient secret sharing in non-compartmentalized models and constructs schemes resilient to affine and bit-wise independent tampering.

## Key findings

- Achieves constant information ratio in non-adaptive leakage adversaries.
- Provides near-optimal schemes for non-adaptive leakage-resilient secret sharing.
- Constructs leakage-resilient non-malleable schemes for specific tampering families.

## Abstract

Non-malleable secret sharing was recently proposed by Goyal and Kumar in independent tampering and joint tampering models for threshold secret sharing (STOC18) and secret sharing with general access structure (CRYPTO18). The idea of making secret sharing non-malleable received great attention and by now has generated many papers exploring new frontiers in this topic, such as multiple-time tampering and adding leakage resiliency to the one-shot tampering model. Non-compartmentalized tampering model was first studied by Agrawal et.al (CRYPTO15) for non-malleability against permutation composed with bit-wise independent tampering, and shown useful in constructing non-malleable string commitments. We initiate the study of leakage-resilient secret sharing in the non-compartmentalized model. The leakage adversary can corrupt several players and obtain their shares, as in normal secret sharing. The leakage adversary can apply arbitrary affine functions with bounded total output length to the full share vector and obtain the outputs as leakage. These two processes can be both non-adaptive and do not depend on each other, or both adaptive and depend on each other with arbitrary ordering. We construct such leakage-resilient secret sharing schemes and achieve constant information ratio (the scheme for non-adaptive adversary is near optimal). We then explore making the non-compartmentalized leakage-resilient secret sharing also non-malleable against tampering. We consider a tampering model, where the adversary can use the shares obtained from the corrupted players and the outputs of the global leakage functions to choose a tampering function from a tampering family F. We give two constructions of such leakage-resilient non-malleable secret sharing for the case F is the bit-wise independent tampering and, respectively, for the case F is the affine tampering functions.