Shor algorithm led to the discovery of multiple vulnerabilities in a number of cryptosystems. As a result, post-quantum cryptography attempts to provide cryptographic solutions that can face these attacks, ensuring the security of sensitive data in a future where quantum computers are assumed to exist. Error correcting codes are a source for efficiency when it comes to signatures, especially random ones described in this paper, being quantum-resistant and reaching the Gilbert-Varshamov bound, thus offering a good trade-off between rate and distance. In the light of this discussion, we introduce a signature based on a family of linear error-block codes (LEB), with strong algebraic properties: it is the family of quasi-cyclic LEB codes that we do define algebraically during this work.

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