Error Correction Capabilities of Non-Linear Cryptographic Hash Functions

• URL: http://arxiv.org/abs/2405.01495v1
• Date: Thu, 2 May 2024 17:26:56 GMT
• Title: Error Correction Capabilities of Non-Linear Cryptographic Hash Functions
• Authors: Alejandro Cohen, Rafael G. L. D'Oliveira,
• Abstract summary: Linear hashes are known to possess error-correcting capabilities. In most applications, non-linear hashes with pseudorandom outputs are utilized instead. We show that non-linear hashes might also exhibit good error-correcting capabilities.
• Score: 56.368766255147555
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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