New constructions of pseudorandom codes

TL;DR

This paper explores new constructions and assumptions for pseudorandom error-correcting codes (PRCs), demonstrating their existence under certain cryptographic assumptions and extending their security to space-bounded adversaries.

Contribution

It introduces new assumptions for PRC existence, revisits and broadens previous constructions, and initiates the study of space-bounded security for PRCs.

Findings

PRCs exist under planted hyperloop and Goldreich's PRG assumptions.

The construction can be based on a wider set of assumptions, including a weakened planted XOR.

Secret-key PRCs can be unconditionally secure against space-bounded adversaries.

Abstract

Introduced in [CG24], pseudorandom error-correcting codes (PRCs) are a new cryptographic primitive with applications in watermarking generative AI models. These are codes where a collection of polynomially many codewords is computationally indistinguishable from random for an adversary that does not have the secret key, but anyone with the secret key is able to efficiently decode corrupted codewords. In this work, we examine the assumptions under which PRCs with robustness to a constant error rate exist. 1. We show that if both the planted hyperloop assumption introduced in [BKR23] and security of a version of Goldreich's PRG hold, then there exist public-key PRCs for which no efficient adversary can distinguish a polynomial number of codewords from random with better than $o(1)$ advantage. 2. We revisit the construction of [CG24] and show that it can be based on a wider range of assumptions than presented in [CG24]. To do this, we introduce a weakened version of the planted XOR assumption which we call the weak planted XOR assumption and which may be of independent interest. 3. We initiate the study of PRCs which are secure against space-bounded adversaries. We show how to construct secret-key PRCs of length $O(n)$ which are $\textit{unconditionally}$ indistinguishable from random by $\text{poly}(n)$ time, $O(n^{1.5-\varepsilon})$ space adversaries.