基于箝位矩阵的公钥密码

Public Key Cryptography Based on Clamping Matrix

摘要: 箝位矩阵是一类以一定范围内的非负整数作为构成元素的矩阵，且在运算过程中这些元素始终被钳制在该范围内。构造两组在箝位运算下互逆的方阵，由此生成一对密钥。在一阶矩阵情形下，箝位设计的密码系统只具多项式复杂度的破解强度，当二阶以上时，原先的破解成因不复存在，从而陡然升级为NP复杂度的强度，且随着矩阵阶数的增大而呈指数增强。箝位矩阵的公钥密码具有独特的批处理加解密形式，虽然涉及矩阵乘法，但对每个明文处理单位而言，平均计算占有并不高。和传统的RSA、Elgamal和椭圆密码等基于大素数（或基于由大素数参与构造的有限域）不同，箝位矩阵的公钥密码的密钥获取极其容易，不需要耗费资源作素数检验，而且箝位矩阵的公钥密码系统具有自然的随机性效应，不像RSA需要专门设计的附加随机填充的模式，或者不像Elgamal引入临时性的随机密钥那样的协议交互的设计。由此可以证明，箝位矩阵密码系统具有像离散对数困难性那样的归约到枚举未定矩阵形式的NP复杂度强度。

Abstract: Clamping matrix was a kind of matrix whose elements were non-negative integers within a certain range, and these elements were always clamped within this range during the operation. Be constructed to two sets of square matrices that were mutually inverse under the clamp operation, thereby generating a pair of keys. In the case of a first-order matrix, the clamp-designed cryptosys-tem only had the cracking strength of polynomial complexity. When it was higher than the second order, the original cracking causes no longer exists, so it was suddenly upgraded to the strength of NP-complexity, and with the matrix, it increased exponentially as the order increases. The public key cryptography of the clamping matrix had a unique form of batch encryption and decryption. Although matrix multiplication was involved, the average computational occupancy for each plaintext processing unit was not high. Different from traditional RSA, Elgamal and elliptic ciphers based on large prime numbers (or based on finite fields constructed by large prime numbers), the key acquisition of public key cryptography with a clamping matrix was extremely easy, and it did not need to spend resources for prime number checking. Moreover, the public key cryptosystem of the clamping matrix had a natural randomness effect, unlike RSA which required a specially designed pattern of additional random padding, or the design of protocol interaction like Elgamal introduced a temporary random key. Clamping-matrix cryptosystems could be shown to have NP-complexity strengths like discrete log difficulty reduction to enumerated indeterminate matrix form.