An Integer Erasure Correction Coding and Its Application for Security Enhancement of Encryption

Abstract

This paper presents a new class of erasure-correcting codes (ECCs) aimed at enhancing cryptographic security of certain encryption schemes. The proposed ECCs employ integer arithmetic to encode and decode data bits and can correct all data bytes, each affected by exactly two erasures. In the enhanced encryption scheme, the ciphertext produced by the initial encryption undergoes further processing. The enhancement leverages specific fragmentation, the proposed ECCs and a simulated noisy channel. For legitimate users, the simulated noisy channel functions as a binary erasure channel, while for an attacker without the secret key, it acts as a channel with random deletions. Security notation and evaluation follow the traditional approach, assessing the attacker’s advantage in distinguishing between two ciphertexts versus random guessing. This evaluation employs dedicated analysis based on information-theoretic findings on the capacity of certain deletion channels and is supported by illustrative numerical examples.