52 research outputs found
A Construction of Bent Functions of n + 2 Variables from a Bent Function of n Variables and Its Cyclic Shifts
We present a method to iteratively construct new bent functions of n + 2 variables from a bent function of n variables and its cyclic shift permutations using minterms of n variables and minterms of 2 variables. In addition, we provide the number of bent functions of n + 2 variables that we can obtain by applying the method here presented, and finally we compare this method with a previous one introduced by us in 2008 and with the Rothaus and Maiorana-McFarland constructions.The work of the first author was partially supported by Spanish Grant MTM2011-24858 of the Ministerio de EconomĂa y Competitividad of the Gobierno de España
On the construction of new bent functions from the max-weight and min-weight functions of old bent functions
Given a bent function f (x) of n variables, its max-weight and min-weight functions are introduced as the Boolean functions f + (x) and f â (x) whose supports are the sets {a â Fn2 | w( f âla) = 2nâ1+2 n 2 â1} and {a â Fn2 | w( f âla) = 2nâ1â2 n 2 â1} respectively, where w( f â la) denotes the Hamming weight of the Boolean function f (x) â la(x) and la(x) is the linear function defined by a â Fn2 . f + (x) and f â (x) are proved to be bent functions. Furthermore, combining the 4 minterms of 2 variables with the max-weight or min-weight functions of a 4-tuple ( f0(x), f1(x), f2(x), f3(x)) of bent functions of n variables such that f0(x) â f1(x) â f2(x) â f3(x) = 1, a bent function of n + 2 variables is obtained. A family of 4-tuples of bent functions satisfying the above condition is introduced, and finally, the number of bent functions we can construct using the method introduced in this paper are obtained. Also, our construction is compared with other constructions of bent functions
Cryptography based on the Hardness of Decoding
This thesis provides progress in the fields of for lattice and coding based cryptography. The first contribution consists of constructions of IND-CCA2 secure public key cryptosystems from both the McEliece and the low noise learning parity with noise assumption. The second contribution is a novel instantiation of the lattice-based learning with errors problem which uses uniform errors
LIPIcs, Volume 261, ICALP 2023, Complete Volume
LIPIcs, Volume 261, ICALP 2023, Complete Volum
Space programs summary no. 37-51, volume 3 for the period April 1 to May 31, 1968. Supporting research and advanced development
Space Programs Summary - supporting research and advanced developmen
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