Abstract
Conventional cryptosystems collapse in face of attacks mounted with quantum computers, and thus research on quantum cryptography mainly focuses on symmetric cryptography, with which it is impossible to create complete quantum digital signatures. To address these issues, assuming the availability of quantum computers capable of performing Grover search, we explore their constructive influence on post-quantum cryptography. In particular, we show how a reasonably small quantum computer can assist in generating secure Courtois–Finiasz–Sendrier (CFS) signatures based on Goppa codes. This could be a step towards a practical implementation of full-fledged cryptosystems in a truly post-quantum scenario.
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