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Analysis on Boolean Function in a Restricted (Biased) Domain.
- Source :
-
IEEE Transactions on Information Theory . Feb2020, Vol. 66 Issue 2, p1219-1231. 13p. - Publication Year :
- 2020
-
Abstract
- Boolean functions are usually studied under the assumption that each input bit is considered independent and identically distributed. However, in the case of some stream ciphers, a keystream bit is generated by using a nonlinear Boolean function with inputs from a restricted domain. At Eurocrypt 2016, one such stream cipher (FLIP) has been proposed, where a Boolean function on $n$ variables was exploited with inputs of weight $\frac {n}{2}$ only. Recently, Carlet et al. studied several properties of such functions and obtained certain bounds on linear approximations of direct sum in the restricted domain. In this paper, we observe that for a direct sum like $f=f_{1}+f_{2}$ , the inputs to each sub-function $f_{1}$ , $f_{2}$ do not follow a uniform distribution in the restricted domain. In this regard, we study the properties of the Boolean functions by considering a general probability distribution on the inputs. We further obtain several bounds related to the biases of direct sums. Finally, we obtain a lower bound on the bias of the nonlinear filter function of FLIP. Our results provide a general framework to study security parameters of ciphers over restricted domain. [ABSTRACT FROM AUTHOR]
- Subjects :
- *BOOLEAN functions
*STREAM ciphers
*NONLINEAR functions
*CIPHERS
Subjects
Details
- Language :
- English
- ISSN :
- 00189448
- Volume :
- 66
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- IEEE Transactions on Information Theory
- Publication Type :
- Academic Journal
- Accession number :
- 141381278
- Full Text :
- https://doi.org/10.1109/TIT.2019.2932739