By Kai-Uwe Schmidt, Arne Winterhof
ISBN-10: 3319123246
ISBN-13: 9783319123240
ISBN-10: 3319123254
ISBN-13: 9783319123257
This publication constitutes the refereed lawsuits of the eighth overseas convention on Sequences and Their purposes, SETA 2014, held in Melbourne, VIC, Australia, in November 2014. The 24 complete papers offered including 2 invited papers have been conscientiously reviewed and chosen from 36 submissions. The papers were equipped in topical sections on Boolean capabilities, excellent sequences, correlation of arrays, relative distinction units, aperiodic correlation, pseudorandom sequences and circulate ciphers, crosscorrelation of sequences, top numbers in sequences, OFDM and CDMA, and frequency-hopping sequences.
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Extra info for Sequences and Their Applications - SETA 2014: 8th International Conference, Melbourne, VIC, Australia, November 24-28, 2014, Proceedings
Example text
1673, 25–32 (2014) 35. : A new method to construct Boolean functions with good cryptographic properties. Inform. Process. Lett. 113(14), 567–571 (2013) 36. : More balanced Boolean functions with optimal algebraic immunity, and good nonlinearity and resistance to fast algebraic attacks. IEEE Trans. Inf. edu/∼klapper/ Abstract. We introduce a new transform on Boolean functions generalizing the Walsh-Hadamard transform. For Boolean functions q and f , the q-transform of f measures the proximity of f to the set of functions obtained from q by change of basis.
At−1 + am−t−1 ), and r−1 h(a) = i=0 ρim (a0 ar a2r ) + m−t−1 ρim (a0 at ). i=0 If t = m/2, then π = 0 and the function is neither semi-bent nor bent. For t = m/2, according to the expression obtained for π(a), we can assume without loss of generality that 0 < t < m/2. Let s = gcd(2t, m). It follows from Theorem 1 of [20, p. 190] that π is a 2s -to-1 mapping since gcd(xt + xm−t , xm +1) = xs +1. This is equivalent to saying that Sw is either an empty set or an s-dimensional affine subspace of GF (2)m .
At−1 + am−t−1 ), and r−1 h(a) = i=0 ρim (a0 ar a2r ) + m−t−1 ρim (a0 at ). i=0 If t = m/2, then π = 0 and the function is neither semi-bent nor bent. For t = m/2, according to the expression obtained for π(a), we can assume without loss of generality that 0 < t < m/2. Let s = gcd(2t, m). It follows from Theorem 1 of [20, p. 190] that π is a 2s -to-1 mapping since gcd(xt + xm−t , xm +1) = xs +1. This is equivalent to saying that Sw is either an empty set or an s-dimensional affine subspace of GF (2)m .