标题： 一种用于奇类型高斯正规基乘法的矩阵分解方法 显示英文标题

标题： A Matrix Decomposition Method for Odd-Type Gaussian Normal Basis Multiplication

摘要： 正常基在许多应用中被使用，因为其实现效率高。 然而，大多数二进制域乘法器的空间复杂度降低技术仅适用于最优正常基或偶类型高斯正常基。 对于k从2到1,000的187个二进制域GF(2^k)使用奇类型高斯正常基。 本文提出了一种减少二进制域GF(2^k)上奇类型高斯正常基乘法器空间复杂度的方法。 该方法的思想源自最优正常基的矩阵分解方法。 结果表明，与之前的工作相比，我们的空间复杂度降低方法在关键路径延迟有很小的权衡情况下，可以减少实现中使用的XOR门的数量。 显示英文摘要

摘要： Normal basis is used in many applications because of the efficiency of the implementation. However, most space complexity reduction techniques for binary field multiplier are applicable for only optimal normal basis or Gaussian normal basis of even type. There are 187 binary fields GF(2^k) for k from 2 to 1,000 that use odd-type Gaussian normal basis. This paper presents a method to reduce the space complexity of odd-type Gaussian normal basis multipliers over binary field GF(2^k). The idea is adapted from the matrix decomposition method for optimal normal basis. The result shows that our space complexity reduction method can reduce the number of XOR gates used in the implementation comparing to previous works with a small trade-off in critical path delay.