光学加密是现代数字光学的一大重要分支。基于4F系统的双随机相位加密和菲涅尔域的双随机加密是最有代表性的两大经典系统。虽然这2个系统均为线性加密系统，但是目前对于这2个系统的攻击基本上是依靠相位恢复的迭代算法去尝试破解系统密钥从而攻破系统，对利用线性性质直接重构置乱映射的攻击方式鲜有报道。这是由于这两大加密系统除具有线性性质外还具有另外一个被人们忽视的更重要的性质——幺正性。有了幺正性的条件，光学攻击理论可以脱离传统的基于Kerckhoff假设的框架，即原本在攻击中极为重要的公钥信息将成为无关变量，且系统的结构复杂度也不会对算法所需要的算力或者攻击结果产生任何影响，这在传统的迭代算法或者直接计算密钥的攻击方法中是难以实现的。利用两大加密系统的线性和幺正性，从矩阵代数出发，引入量子狄拉克符号以及表象理论，给出对于一般线性幺正系统的子空间投影选择明文攻击方案。以上述两大加密系统作为范例进行阐释，原则上方法适用于已经存在和以后将会出现的任意线性幺正加密系统。
The study of optical encryption algorithm has become an important part of optics research today. Double random phase encoding (DRPE) in 4F system and in Fresnel domain are two typical cryptosystems. In spite of the fact that these two cryptosystems are both linear cryptosystems, the attacks on both systems are usually based on iterative phase retrieve algorithm. These crack algorithms mainly focus on the decipher of the key in the cryptosystem and seldom aim to construct the linear scrambling mapping the whole system stands for. This because one essential nature of these cryptosystems has been neglected for long time, the unitarity. With the condition of unitarity,optical attack theory can be independent from Kerckhoff' s rule and the public knowledge of the cryptosystem become irrelevant to attack algorithm. The complexity of the encryption system will not have any influence on the computation amount and crack result which is not the case in other attack algorithms. Thusly, we proposed a new method of subspace projection optical chosen-plaintext attack based on the linear and unitary nature of DPRE system, and it should fit for any linear unitary optical cryptosystems have been proposed and about to be proposed. We bring Dirac state vector and its representation linear algebra theory into our work for convenience as the Dirac state vector can stands for optical wavefront equally.
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