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 $d=\operatorname{rank}(Y-Y')$ directions, where $Y$ and $Y'$ 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.