论文标题
格罗弗在西蒙
Grover on SIMON
论文作者
论文摘要
对于具有$ n $ bit秘密密钥的任何对称密钥加密系统，可以在$ o（2^{n/2}）$中恢复该密钥，从而利用Grover搜索算法，从而导致有效的密钥长度为一半。在这个方向上，随后的工作是在AES和其他一些块密码上完成的。另一方面，像西蒙这样的轻量级密码未探索。在此背景下，我们介绍了Grover对Simon的所有变体的搜索算法，并列举了量子资源，以非，CNOT和TOFFOLI GATES实施此类攻击。我们还提供电路的T深度和攻击所需的Qubit数量。我们表明，在Simon $ 2N/MN $上实施Grover所需的量子数为$ O（2nr+Mn）$，其中$ r $是所选的Plaintext-Cipher文本对的数量。我们在IBMQ量子模拟器和14 Qubits处理器中运行了Simon的简化版本。我们发现，在仿真支持理论的地方，实际实施远非远离现实，这是由于大门的不忠和量子的短矫正时间。也已经介绍了所有版本的所有版本的完整代码。
For any symmetric key cryptosystem with $n$-bit secret key, the key can be recovered in $O(2^{n/2})$ exploiting Grover search algorithm, resulting in the effective key length to be half. In this direction, subsequent work has been done on AES and some other block ciphers. On the other hand, lightweight ciphers like SIMON was left unexplored. In this backdrop, we present Grover's search algorithm on all the variants of SIMON and enumerate the quantum resources to implement such attack in terms of NOT, CNOT and Toffoli gates. We also provide the T-depth of the circuits and the number of qubits required for the attack. We show that the number of qubits required for implementing Grover on SIMON $2n/mn$ is $O(2nr+mn)$, where $r$ is the number of chosen plaintext-cipher text pairs. We run a reduced version of SIMON in IBMQ quantum simulator and the 14-qubits processor as well. We found that where simulation supports theory, the actual implementation is far from the reality due to the infidelity of the gates and short decoherence time of the qubits. The complete codes for all version of SIMON have also been presented.
