Error Correction Capabilities of Non-Linear Cryptographic Hash Functions

TL;DR

This paper investigates the error correction capabilities of non-linear cryptographic hash functions, demonstrating they can achieve capacity similar to linear codes, with validation through comparisons involving SHA.

Contribution

It proves that systematic random non-linear codes are capacity achieving and shows non-linear hashes can have strong error correction, extending known linear hash properties.

Findings

S-RNLC are capacity achieving in the asymptotic regime

SHA performs comparably to S-RNLC and SRLC in error correction

Non-linear hashes exhibit good error-correcting capabilities

Abstract

Linear hashes are known to possess error-correcting capabilities. However, in most applications, non-linear hashes with pseudorandom outputs are utilized instead. It has also been established that classical non-systematic random codes, both linear and non-linear, are capacity achieving in the asymptotic regime. Thus, it is reasonable to expect that non-linear hashes might also exhibit good error-correcting capabilities. In this paper, we show this to be the case. Our proof is based on techniques from multiple access channels. As a consequence, we show that Systematic Random Non-Linear Codes (S-RNLC) are capacity achieving in the asymptotic regime. We validate our results by comparing the performance of the Secure Hash Algorithm (SHA) with that of Systematic Random Linear Codes (SRLC) and S-RNLC, demonstrating that SHA performs equally.