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In this paper, the authors analyze four previously published respectively trivial approaches to the task of finding the roots of the error locator polynomial during the decryption operation of code-based encryption schemes. They compare the performance of these algorithms and show that optimizations concerning finite field element representations play a key role for the speed of software implementations. Furthermore, they point out a number of timing attack vulnerabilities that can arise in root-finding algorithms, some aimed at recovering the message, others at the secret permutation.
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