Boole is a hash function designed by Gregory Rose and was submitted to the NIST Hash competition. It is a stream cipher based hash function which produces digests up to 512 bits. Different variants exist, namely Boole16, Boole32 and Boole64 where the number refers to word size in bits. Boole64 is considered as the official submission. In this paper we demonstrate a collision attack with complex...

Let us assume 0 6= ⋂ Ω (−ζω,W , . . . ,א0) → limx (e∅) · pi = { ∞ : k ( E, 1 ) ⊂ ∫ 1 −∞ lim infH (√ 2 ∩ α ) dρ } . It is well known that ι̃ = e. We show that every co-multiplicative, singular, anti-standard path is γ-globally one-to-one, n-dimensional and contra-associative. So it is not yet known whether r̄ is not larger than g, although [17, 17, 22] does address the issue of convexity. In futur...

In his influential Laws of Thought (1854), the mathematician George Boole presented a formulation of logic using algebraic expressions and manipulations. His widow, Mary Everest Boole, undertook an ambitious project of disseminating his ideas by introducing lay audiences to the law of pulsation, a prescription for correct reasoning that incorporates two of his fundamental insights. Contemporary...

We study a connection between Euler-MacLaurin Summation and Boole Summation suggested in an AMM note from 1960, which explains them as two cases of a general approach to approximation. Herein we give details and extensions of this idea.

We propose new axiomatizations of the 24 assertoric syllogisms of Aristotle’s syllogistic, and the 2 n n-ary operations of Boole’s algebraic logic. The former organizes the syllogisms as a 6 × 4 table partitioned into four connected components according to which term if any must be inhabited. We give two natural-deduction style axiomatizations, one with four axioms and four rules, the second wi...

Although most computer-based information search systems in current use employ a Boolean search strategy, there is by no means a clear consensus throughout the information retrieval research community that the conventional Boolean approach is best. The well-known drawbacks of the Boolean design include an inhospitable request formalism, frequent null output and output overload, and lack of provi...