# Silas Richelson @ IDC on An Algebraic Approach to Non-Malleability

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In their seminal work on non-malleability, Dolev, Dwork and Naor, showed how to construct a non-malleable commitment protocol with logarithmically-many "rounds"/"slots", the idea being that any adversary may successfully maul in some slots but would fail in at least one. Since then new ideas have been introduced, ultimately resulting in constant-round protocols based on any one-way function. Yet, in spite of this remarkable progress,
each of the known constructions leaves something to be desired.

In this paper we propose a novel technique that allows us to to construct a non-malleable protocol with only a single slot", and to improve in at least one aspect over each of the previously proposed protocols. Two direct byproducts of our new ideas are a four round non-malleable commitment and a four round non-malleable zero-knowledge argument, the latter being optimal in terms of round complexity. The protocols are based on the existence of one-way functions and admit very efficient instantiations via standard homomorphic commitments and sigma protocols.

Our analysis relies on algebraic reasoning, and makes novel use of error correcting codes in order to ensure that committers' tags differ in many coordinates. One way of viewing our construction is as a method for combining many atomic sub-protocols in a way that simultaneously amplifies soundness and non-malleability, thus requiring much weaker guarantees to begin with, and resulting in a protocol which is much trimmer in complexity compared to the existing ones.

Joint work with Vipul Goyal, Alon Rosen and Margarita Vald
.

Date and Time:
Sunday, April 6, 2014 - 14:00 to 15:30
Speaker:
Silas Richelson