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 complexity, are incomparable in the sense that for each pair of measures, υ1, υ2, there exist functions f1, f2 with υ1(f1) > υ1(f2) but υ2(f1) < υ2(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.
Proceedings Title: 8th International Conference on Algorithms and Complexity (CIAC 2013)- Springer Lecture Notes in Computer Science
Conference Dates: May 22-24, 2013
Conference Location: Barcelona, -1
Conference Title: 8th International Conference on Algorithms and Complexity (CIAC 2013)
Pub Type: Conferences
nonlinearity measures, annihilator immunity, multiplicative complexity, algebraic degree, collision-free, one-wayness, SHA-3