[Resource Topic] 2021/624: Group Structure in Correlations and its Applications in Cryptography

Welcome to the resource topic for 2021/624

Title:
Group Structure in Correlations and its Applications in Cryptography

Authors: Guru-Vamsi Policharla, Manoj Prabhakaran, Rajeev Raghunath, Parjanya Vyas

Abstract:

Correlated random variables are a key tool in cryptographic applications like secure multi-party computation. We investigate the power of a class of correlations that we term group correlations: A group correlation is a uniform distribution over pairs (x,y) \in G^2 such that x+y\in S, where G is a (possibly non-abelian) group and S is a subset of G. We also introduce bi-affine correlations and show how they relate to group correlations. We present several structural results, new protocols, and applications of these correlations. The new applications include a completeness result for black-box group computation, perfectly secure protocols for evaluating a broad class of black box ``mixed-groups’’ circuits with bi-affine homomorphism, and new information-theoretic results. Finally, we uncover a striking structure underlying OLE: In particular, we show that OLE over \mathrm{GF}(2^n), is isomorphic to a group correlation over \mathbb{Z}_4^n.

ePrint: https://eprint.iacr.org/2021/624

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