Journal article
Fast evaluation of polynomials over binary finite fields and application to side-channel countermeasures
We describe a new technique for evaluating polynomials over binary finite fields. This is useful in the context of anti-DPA countermeasures when an S-box is expressed as a polynomial over a binary finite field. For n-bit S-boxes, our new technique has heuristic complexity O(2n/2/√n) instead of O(2n/2) proven complexity for the Parity-Split method.
We also prove a lower bound of Ω(2n/2/√n) on the complexity of any method to evaluate n-bit S-boxes; this shows that our method is asymptotically optimal. Here, complexity refers to the number of non-linear multiplications required to evaluate the polynomial corresponding to an S-box. In practice, we can evaluate any 8-bit S-box in 10 non-linear multiplications instead of 16 in the Roy–Vivek paper from CHES 2013, and the DES S-boxes in 4 non-linear multiplications instead of 7.
We also evaluate any 4-bit S-box in 2 non-linear multiplications instead of 3. Hence our method achieves optimal complexity for the PRESENT S-box
Language: | English |
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Publisher: | Springer Berlin Heidelberg |
Year: | 2015 |
Pages: | 73-83 |
ISSN: | 21908516 and 21908508 |
Types: | Journal article |
DOI: | 10.1007/s13389-015-0099-9 |
ORCIDs: | 0000-0002-8426-0859 |