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Register a new userOn some block ciphers and imprimitive groups
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The group generated by the round functions of a block ciphers is a widely investigated problem. We identify a large class of block ciphers for which such group is easily guaranteed to be primitive. Our class includes the AES and the SERPENT.
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The twin group $T_n$ is a right angled Coxeter group generated by $n- 1$ involutions and having only far commutativity relations. These groups can be thought of as planar analogues of Artin braid groups. In this note, we study some properties of twin groups whose analogues are well-known for Artin braid groups. We give an algorithm for two twins to be equivalent under individual Markov moves. Further, we show that twin groups $T_n$ have $R_infty$-property and are not co-Hopfian for $n ge 3$.
A binary relation on a finite set is called a Hall relation if it contains a permutation of the set. Under the usual relational product, Hall relations form a semigroup which is known to be a block-group, that is, a semigroup with at most one idempotent in each $mathrsfs{R}$-class and each $mathrsfs{L}$-class. Here we show that in a certain sense, the converse is true: every block-group divides a semigroup of Hall relations on a finite set.
We generalize a result of R. Thomas to establish the non-vanishing of the first l2-Betti number for a class of finitely generated groups.
we will present an estimation for the upper-bound of the amount of 16-bytes plaintexts for English texts, which indicates that the block ciphers with block length no more than 16-bytes will be subject to recover plaintext attacks in the occasions of plaintext -known or plaintext-chosen attacks.
We classify the ergodic invariant random subgroups of block-diagonal limits of symmetric groups in the cases when the groups are simple and the associated dimension groups have finite dimensional state spaces. These block-diagonal limits arise as the transformation groups (full groups) of Bratteli diagrams that preserve the cofinality of infinite paths in the diagram. Given a simple full group $G$ admitting only a finite number of ergodic measures on the path-space $X$ of the associated Bratteli digram, we prove that every non-Dirac ergodic invariant random subgroup of $G$ arises as the stabilizer distribution of the diagonal action on $X^n$ for some $ngeq 1$. As a corollary, we establish that every group character $chi$ of $G$ has the form $chi(g) = Prob(gin K)$, where $K$ is a conjugation-invariant random subgroup of $G$.
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