Simulation Security of Scheme II Against BPP^{QNC^d} Adversaries

Computational study of one-time memory security in the quantum random oracle model against bounded-depth quantum adversaries

quant-ph arXiv:2601.13258 Jan 2026

5.96e-8

Lifting bound at lambda=128

4.44e-16

Lifting bound at lambda=256

120

Min lambda for 1e-6 security (d=16)

0.9239

cos(pi/8) POVM rate

Experiments conducted

Problem Overview

Conjecture 5.1 (Stambler, 2026)

The one-time memory Scheme II is simulation-secure in the quantum random oracle model against adversaries in the class BPP^QNC^d for any polynomial depth d. The scheme uses conjugate coding (BB84 encoding) combined with hash-locking via a random oracle and conjunction obfuscation to hide the encoding basis.

Lifting Framework Analysis

Security Bound vs. Adversary Depth (by lambda)

Security Bound vs. lambda (d=16, q=16)

Monte Carlo Simulation Results

Adversary Advantage vs. Depth (lambda_eff=10)

Oracle Query Sweep (d=16, lambda=64)

Component Analysis

Conjunction Obfuscation: Distinguishing Probability

Sequential POVM Bound (k=1 measurement)

Depth Complexity Tradeoff

Light Cone Fraction vs. Depth

Simulation Distance by Depth (lambda_eff=8)

Security Thresholds

Depth d	Queries q	Min lambda (adv < 1e-6)	Min lambda (adv < 1e-9)	Min lambda (adv < 1e-12)

Depth Sweep Results

Depth d	Mean Advantage	Key Accuracy	P(Both Messages)	POVM Bound	Attack Success

POVM Bounds Matrix

n \ k	1	2	4	8	16	32	64	128

Simulation Security of Scheme II Against BPPQNCd Adversaries