A Parallel Hardware Architecture for fast Gaussian Elimination over GF(2)

This paper presents a hardware-optimized variant of the well-known Gaussian elimination over GF(2) and its highly efficient implementation. The proposed hardware architecture, we call SMITH1 , can solve any regular and (uniquely solvable) overdetermined linear system of equations (LSE) and is not limited to matrices of a certain structure. Besides solving LSEs, the architecture at hand can also accomplish the related problem of matrix inversion extremely fast. Its average running time for n×n binary matrices with uniformly distributed entries equals 2n (clock cycles) as opposed to about 1 4 n3 in software. The average running time remains very close to 2n for random matrices with densities much greater or lower than 0.5. The architecture has a worst-case time complexity of O(n2 ) and also a space complexity of O(n2 ). With these characteristics the architecture is particularly suited to efficiently solve medium-sized LSEs as they for example appear in the cryptanalysis of certain s...

• Type: Conference
• Year: 2006
• Where: FCCM
• Authors: Andrey Bogdanov, M. C. Mertens
• Keywords: Architecture, Average Running Time, FCCM 2006, Hardware, Time Complexity