Fast Pseudo-Hadamard Transforms

We prove that the fast pseudo-Hadamard transform (FPHT) over a finite field has a bounded branch number. We shall demonstrate that the transform has an efficient implementation for various platforms compared to an equal dimension MDS code. We prove that when using a CS-Cipher[3] like construction the weight of any 2R trail is bounded for the case of an 8 × 8 transform. We show that the FPHT can also be combined with MDS codes to produce efficient transforms with half of the branch of a comparable sized MDS code. We present the FPHTHASH one-way hash function which is constructed using a 32×32 FPHT which produces a 256-bit digest and processes the input at 24 cycles per byte with ISO C source code on an AMD Athlon XP processor.