Published: June 23, 2013
Author(s)
Joan Boyar (University of Southern Denmark), Magnus Find (University of Southern Denmark), Rene Peralta (NIST)
Conference
Name: 8th International Conference on Algorithms and Complexity (CIAC 2013)
Dates: 05/22/2013 - 05/24/2013
Location: Barcelona, Spain
Citation: Algorithms and Complexity, vol. 7878, pp. 61-72
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, 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.
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,...
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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, 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.
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Keywords
algebraic degree; annihilator immunity; collision-free; multiplicative complexity; nonlinearity measures; one-wayness; SHA-3
Control Families
None selected
