Stabilizer-Public-Key Authentication: Long Stabilizer Public Keys Resist Finite-Copy Forgery Attacks

Abstract

We propose an information-theoretic authentication protocol based on a finite supply of long quadratic-stabilizer public-key states over an odd-prime field, where the effective key length after one signature exposure is the residual dimension $r=n-\ell$. A computationally unbounded adversary observes one valid classical signature and may jointly process $N$ public-key copies, while verification uses one additional independent copy. We show that, conditioned on the exposed signature, the security problem reduces to a partial-prediction game for a uniform stabilizer ensemble on these $r$ residual qudits, with a partial query along $d=\mathrm{rank}(Y-Y^{\prime })$ directions, where $Y$ and $Y^{\prime }$ denote the honestly signed and target-forged messages, respectively. Surprisingly, although the target requires only partial information, there is no first-order reduction in the required copy rate when $d/r\to \beta \in (0,1]$. The optimal average forgery probability for the specified target tends to zero for $N/r\to \alpha <1$ and to one for $\alpha >1$, revealing a sharp threshold at $\alpha =1$. Thus, long stabilizer public keys resist finite-copy forgery attacks under a single-signature-exposure model whenever the adversarial copy rate remains below one.

Revised the title, abstract, introduction, and related discussion to clarify the distinction from and division of roles with the paper arXiv:2609.13923. The technical results are unchanged