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Abstract
In recent years, methods to securely mask Sboxes against sidechannel attacks by representing them as polynomials over finite binary fields have become quite efficient. A good cost model for this is to count how many nonlinear multiplications are needed. In this work we improve on the current stateoftheart generic method published by Coron–Roy–Vivek at CHES 2014 by working over slightly larger fields than strictly needed. This leads us, for example, to evaluate DES Sboxes with only 3 nonlinear multiplications and, as a result, obtain 25% improvement in the running time for secure software implementations of DES when using three or more shares.
On the theoretical side, we prove a logarithmic upper bound on the number of nonlinear multiplications required to evaluate any dbit Sbox, when ignoring the cost of working in unreasonably large fields. This upper bound is lower than the previous lower bounds proved under the assumption of working over the field F_{2^d}, and we show this bound to be sharp. We also achieve a way to evaluate the AES Sbox using only 3 nonlinear multiplications over F_{2^{16}}.
On the theoretical side, we prove a logarithmic upper bound on the number of nonlinear multiplications required to evaluate any dbit Sbox, when ignoring the cost of working in unreasonably large fields. This upper bound is lower than the previous lower bounds proved under the assumption of working over the field F_{2^d}, and we show this bound to be sharp. We also achieve a way to evaluate the AES Sbox using only 3 nonlinear multiplications over F_{2^{16}}.
Original language  English 

Title of host publication  Cryptographic Hardware and Embedded Systems – CHES 2016 
Subtitle of host publication  18th International Conference, Santa Barbara, CA, USA, August 1719, 2016, Proceedings 
Editors  Benedikt Gierlichs, Axel Y Poschmann 
Publisher  Springer 
Pages  479497 
Number of pages  19 
ISBN (Electronic)  9783662531402 
ISBN (Print)  9783662531396 
DOIs  
Publication status  Published  4 Aug 2016 
Publication series
Name  Lecture Notes in Computer Science 

Publisher  Springer Verlag 
Volume  9813 
ISSN (Print)  03029743 
Keywords
 Sidechannel countermeasure
 Masking
 Probing security
 Block cipher
 oftware implementation
 Polynomial evaluation
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Dive into the research topics of 'Reducing the Number of Nonlinear Multiplications in Masking Schemes'. Together they form a unique fingerprint.Projects
 1 Finished

HEAT: Homomorphic Encryption Applications and Technology
Smart, N. P.
1/01/15 → 31/12/17
Project: Research