Perfect correctness of the parallel signing algorithm

Determine whether the many-bit parallel quantum signing algorithm described for OSS can be adapted to achieve perfect correctness—that is, always output a valid signature on any input message—while maintaining the stated efficiency and security guarantees.

Background

The paper’s signing method measures and corrects bits in parallel, using subspace projections and error-correcting codes to achieve high-probability correctness in a small number of rounds. Concurrent work achieved perfect correctness for a related OSS scheme, but the authors did not address perfect correctness for their new parallel algorithm.

They explicitly pose the question of adapting their parallel signing algorithm to be perfectly correct, highlighting both practical and theoretical interest in eliminating any residual signing error.

References

show how to make the OSS construction perfectly correct, which we do not consider. An interesting open question is whether our parallel signing algorithm can be adapted to be perfectly correct

— Unclonable Cryptography in Linear Quantum Memory (2511.04633 - Shmueli et al., 6 Nov 2025) in Concurrent and Independent Work, Perfect correctness