**Fast Pseudo-Hadamard Transforms**

*Tom St Denis*

**Abstract: **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\cite{CSC} like construction the weight of any $2R$ trail is bounded for the case of an $8 \times 8$ 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 FPHT-HASH one-way hash function which is constructed using a $32 \times 32$ 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.

**Category / Keywords: **secret-key cryptography / Pseudo-Hadamard Transform, Branch Analysis, One-Way Hash Function

**Date: **received 16 Jan 2004, last revised 2 Feb 2004

**Contact author: **tomstdenis at iahu ca

**Available format(s): **PDF | BibTeX Citation

**Note: **Minor typographical errors fixed.

**Version: **20040202:170437 (All versions of this report)

**Short URL: **ia.cr/2004/010

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