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A Proof of the Beierle-Kranz-Leander’s Conjecture related to Lightweight Multiplication in $F_{2^n}$
Lightweight cryptography constant multiplication Hamming weight
2019/1/9
Lightweight cryptography is an important tool for building strong security solutions for pervasive devices with limited resources. Due to the stringent cost constraints inherent in extremely large app...
In 2003, Alfred Menezes, Edlyn Teske and Annegret Weng presented a conjecture on properties of the solutions of a type of quadratic equation over the binary extension fields, which had been convinced ...
A conjecture about Gauss sums and bentness of binomial Boolean functions
Boolean functions bent functions Walsh spectrum
2016/12/10
In this note, the polar decomposition of binary fields of even extension degree is used to reduce the evaluation of the Walsh transform of binomial Boolean functions to that of Gauss sums. In the case...
The Fourier Entropy-Influence conjecture holds for a log-density 1 class of cryptographic Boolean functions
Boolean functions Fourier and Walsh-Hadamard transforms entropy
2016/1/26
We consider the Fourier Entropy-Influence (FEI) conjecture in
the context of cryptographic Boolean functions. We show that the FEI conjecture
is true for the functions satisfying the strict avalanch...
A Study of Goldbach's conjecture and Polignac's conjecture equivalence issues
Goldbach's conjecture Polignac's conjecture Equivalent
2014/3/5
The famous Goldbach's conjecture and Polignac's conjecture are two of all unsolved problems in the field of number theory today. As well known, the Goldbach's conjecture and the Polignac's conjecture ...
On a generalized combinatorial conjecture involving addition $\mod 2^k - 1$
foundations / combinatorics addition boolean functions
2012/3/27
In this note, we give a simple proof of the combinatorial conjecture proposed by Tang, Carlet and Tang, based on which they constructed two classes of Boolean functions with many good cryptographic pr...
A general conjecture similar to T-D conjecture and its applications in constructing Boolean functions with optimal algebraic immunity
Boolean function Algebraic immunity Bent function Balancedness Nonlinearity lgebraic degree
2012/3/26
In this paper, we propose two classes of 2k-variable Boolean functions, which have optimal algebraic immunity under the assumption that a general combinatorial conjecture is correct. These functions a...
It is a difficult challenge to find Boolean functions used in stream ciphers
achieving all of the necessary criteria and the research of such functions
has taken a significant delay with respect to ...
Recently, Tu and Deng [1] proposed a combinatorial conjecture on binary string,
on the premise that the conjecture is correct they obtain two classes of Boolean functions which
are both algebraic im...
A Conjecture on Binary String and Its Applications on Constructing Boolean Functions of Optimal Algebraic Immunity
boolean function algebraic immunity bent function
2009/6/15
In this paper, we propose a combinatoric conjecture on binary string, on the premise that
our conjecture is correct we mainly obtain two classes of functions which are both algebraic
immunity optima...
We prove that Lenstra proposition suggesting existence of many counterexamples to Agrawal
conjecture is true in a more general case. At the same time we obtain a strictly ascending chain of subgroups...
Resolving the Simultaneous Resettability Conjecture and a New Non-Black-Box Simulation Strategy
Simultaneous Resettability Conjecture New Non-Black-Box Simulation Strategy resettable zero-knowledge proofs
2009/6/11
Canetti, Goldreich, Goldwasser, and Micali (STOC 2000) introduced the notion of
resettable zero-knowledge proofs, where the protocol must be zero-knowledge even if
a cheating verifier can reset the ...
Goldbach’s Conjecture on ECDSA Protocols
Elliptic curves Digital signature Multi - precision integer
2009/4/8
In this paper, an algorithm on
Goldbach’s conjecture is newly defined for
computing a large even number as a sum of two
primes or a sum of prime and composite. Using the
conjecture, an ECDSA (Elli...