Title :
On the Nonlinearity of Exponential Welch Costas Functions
Author :
Drakakis, Konstantinos ; Requena, Verónica ; McGuire, Gary
Author_Institution :
Sch. of Electr., Electron. & Mech. Eng., Univ. Coll. Dublin, Dublin, Ireland
fDate :
3/1/2010 12:00:00 AM
Abstract :
We study the nonlinearity of the exponential Welch Costas functions, using the Fourier transform on Z m. These functions have been proposed for use in nonbinary cryptosystems. High nonlinearity is required to ensure resistance to linear cryptanalysis. We prove some properties of the nonlinearity of these functions, and we suggest a plausible connection of the nonlinearity to the class number of a quadratic field.
Keywords :
Fourier transforms; cryptography; Fourier transform; exponential Welch Costas functions; linear cryptanalysis; nonbinary cryptosystems; quadratic fields; Cryptography; Fourier transforms; Almost perfect nonlinear (APN) functions; Walsh transform; Welch Costas permutations; class number; nonlinearity;
Journal_Title :
Information Theory, IEEE Transactions on
DOI :
10.1109/TIT.2009.2039164
