[PDF] Top 20 On Boolean Ideals and Varieties with Application to Algebraic Attacks

... The second stage can be performed in two dierent ways. Consider the rst way. In the second stage we reduce the initial basis of the ideal (dened by known methods) and obtain syzygies modulo F ⊕ I . It is suitable to use ... See full document

... decade, algebraic and fast algebraic attacks are regarded as the most success- ful attacks on LFSR-based stream ...of algebraic immunity was introduced, the properties and constructions ... See full document

... to algebraic attacks ...of Boolean functions achieving the maximum possible algebraic ...maximum algebraic immunity are also given in [1], [20], [9] (note that when the number of the ... See full document

... polynomial algebraic approach has enormous ...and algebraic computational methods can be applied in order to discover or construct the suitable ...any Boolean function including the original ... See full document

... two-sided ideals and center equal to the base eld K has been one of the central driving forces in many important areas of mathemat- ics including algebraic geometry, algebra and number ...with ... See full document

... Algebraic attacks are kinds of efficient methods on stream ciphers which adapt LFSR-based keystream generators with nonlinear filter generator or the combiner as one of their ...in algebraic ... See full document

... large algebraic immunity (AI), in order to resist algebraic attacks [1, ...fast algebraic attacks (FAA’s), because Boolean functions with large algebraic immunity (even ... See full document

... However, there is no mathematical method to prove the security of a given block cipher, although it is sometimes possible to prove the insecurity of such a cipher. What usually happens is that a relative measure of the ... See full document

... fast algebraic attacks (FAA’s) [7], ...of Boolean functions is not necessary any more for ...n-variable Boolean function f , if there exists a nonzero n-variable Boolean function g of ... See full document

... fast algebraic attacks on LFSR-based stream ciphers, which use a Boolean function f : GF (2) n → GF (2) as the filter or combination generator, is to find a function g of small degree such that the ... See full document

... fast algebraic attacks, ...symmetric Boolean functions have poor resistance against fast algebraic attacks despite their resistance against algebraic ...symmetric Boolean ... See full document

... generic attacks suggests that there is a significant gap between what security is actually achieved by our candidate in the plain model, and the best security definitions for obfuscation that we have in the plain ... See full document

... Definition 3.4. An L-fuzzy ternary subsemiring µ of S is said to be L-fuzzy characteristic ternary subsemiring if µ(ϕ(x)) = µ(x) for all x ∈ S and ϕ ∈ Aut(S). The L- fuzzy characteristic left ideals [resp. right ... See full document

... We must have [R( a + bi ) ∶ R] = 2. Therefore the minimal polynomial of a + bi has a − bi as a zero as well. Thus, we must have ( x − ( a + bi ))( x − ( a − bi )) ∈ ker ( ϕ ) = m. Hence, m corresponds to a conjugate pair ... See full document

... We implemented the above lattice in Sage, 3 an open-source mathematics software, and used the implementation of LLL available therein to find x with the default settings. The results are as shown in Figure 1. For each ... See full document

... state attacks. Android APIs are very much vulnerable to these attacks and there is need to put some restrictions on the usage of some resources which are used by the attacker in the ... See full document

... cube attacks resort to low-degree polynomial tests such as BLR linearity tests with a certain failure ...cube attacks are convincing but without proved ...an algebraic method to recover superpolies ... See full document

... We apply Theorem 1.1 to cryptanalysis. As early as in 1946, Shannon [24] pointed out insightfully that “Construct our cipher in such a way that breaking it is equivalent to solving a certain system of simultaneous ... See full document

... will see in Proposition 7 that this construction is not always as well-behaved when G is profinite.) This construction does not depend on the choice of generating set; writ- ing one generating set in term of another ... See full document

... left ideals in D and study the natural action of the Picard group of D on the space of isomorphism classes of such ...left ideals of the first Weyl algebra A 1 ( C ) given in [BW1, ... See full document