Quantum computers pose a fundamental threat to widely deployed public-key cryptosystems, such as RSA and ECC, by enabling efficient integer factorization using Shor's algorithm. Theoretical resource estimates suggest that 2048-bit RSA keys could be broken using Shor's algorithm with fewer than a million noisy qubits. Although such machines do not yet exist, the availability of smaller, cloud-accessible quantum processors and open-source implementations of Shor's algorithm raises the question of what key sizes can realistically be factored with today's platforms. In this work, we experimentally investigate Shor's algorithm on several cloud-based quantum computers using publicly available implementations. Our results reveal a substantial gap between the capabilities of current quantum hardware and the requirements for factoring cryptographically relevant integers. In particular, we observe that circuit constructions still need to be highly specific for each modulus, and that machine fidelities are unstable, with high and fluctuating error rates.

翻译：量子计算机通过Shor算法实现高效整数分解，对广泛部署的公钥密码体系（如RSA和ECC）构成根本性威胁。理论资源估算表明，使用Shor算法破解2048位RSA密钥仅需不足百万个含噪声量子比特。虽然此类机器尚未问世，但当前可云端访问的小型量子处理器及Shor算法的开源实现引发了一个现实问题：现有平台究竟能分解多大密钥规模？本研究通过公开可用的算法实现，在多个云端量子计算机上对Shor算法进行实验性探究。结果表明，当前量子硬件能力与密码学相关整数分解需求之间存在显著差距。特别值得注意的是，电路构建仍需针对每个模数进行高度定制化设计，且机器保真度不稳定，错误率呈现高位波动特征。