Reference : Fast Evaluation of Polynomials over Binary Finite Fields and Application to Side-Chan...
 Document type : Scientific congresses, symposiums and conference proceedings : Paper published in a book Discipline(s) : Engineering, computing & technology : Computer science To cite this reference: http://hdl.handle.net/10993/19541
 Title : Fast Evaluation of Polynomials over Binary Finite Fields and Application to Side-Channel Countermeasures Language : English Author, co-author : Coron, Jean-Sébastien [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Computer Science and Communications Research Unit (CSC) >] Roy, Arnab [University of Luxembourg > Computer Science and Communications Research Unit > > ; Technical University of Denmark > Department of Applied Mathematics and Computer Science] Venkatesh, Srinivas Vivek [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Computer Science and Communications Research Unit (CSC) >] Publication date : 2014 Main document title : Cryptographic Hardware and Embedded Systems – CHES 2014 Editor : Batina, Lejla Robshaw, Matthew Publisher : Springer Collection and collection volume : Lecture Notes in Computer Science, 8731 Pages : 170-187 Peer reviewed : Yes Audience : International ISBN : 978-3-662-44708-6 Event name : 16th Workshop on Cryptographic Hardware and Embedded Systems – CHES 2014 Event date : 23-09-2014 to 26-09-2014 Event country : South Korea Keywords : [en] side-channel countermeasure ; masking ; polynomial evaluation ; finite field Abstract : [en] 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 ${\cal O}(2^{n/2}/\sqrt{n})$ instead of ${\cal O}(2^{n/2})$ proven complexity for the Parity-Split method. We also prove a lower bound of ${\Omega}(2^{n/2}/\sqrt{n})$ 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. Target : Researchers ; Professionals ; Students Permalink : http://hdl.handle.net/10993/19541 DOI : 10.1007/978-3-662-44709-3_10 Other URL : http://eprint.iacr.org/2014/890 Mentions required by the publisher for OA : The final publication is available at www.springerlink.com

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