Four Measures of Nonlinearity [chapter]

Joan Boyar, Magnus Find, René Peralta
2013 Lecture Notes in Computer Science  
Cryptographic applications, such as hashing, block ciphers and stream ciphers, make use of functions which are simple by some criteria (such as circuit implementations), yet hard to invert almost everywhere. A necessary condition for the latter property is to be "sufficiently distant" from linear, and cryptographers have proposed several measures for this distance. In this paper, we show that four common measures, nonlinearity, algebraic degree, annihilator immunity, and multiplicative
more » ... y, are incomparable in the sense that for each pair of measures, µ1, µ2, there exist functions f1, f2 with µ1(f1) > µ1(f2) but µ2(f1) < µ2(f2). We also present new connections between two of these measures. Additionally, we give a lower bound on the multiplicative complexity of collision-free functions.
doi:10.1007/978-3-642-38233-8_6 fatcat:zyyhwj6gtfhs5hzctbqndtehsu