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Bit-sliced binary normal basis multiplication

Billy Brumley, Dan Page, Bit-sliced binary normal basis multiplication. Symposium on Computer Arithmetic (ARITH), pp. 205–212. August 2011. No electronic version available.


The performance of many cryptographic primitives is reliant on efficient algorithms and implementation techniques for arithmetic in binary fields. While dedicated hardware support for said arithmetic is an emerging trend, the study of software-only implementation techniques remains important for legacy or non-equipped processors. One such technique is that of software-based bit-slicing. In the context of binary fields, this is an interesting option since there is extensive previous work on bit-oriented designs for arithmetic in hardware; such designs are intuitively well suited to bit-slicing in software. In this paper we harness previous work, using it to investigate bit-sliced, software-only implementation arithmetic for binary fields, over a range of practical field sizes and using a normal basis representation. We apply our results to demonstrate significant performance improvements for a stream cipher, and over the frequently employed Ning-Yin approach to normal basis implementation in software.

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