We investigate the statistics of three kinds records associated with planar random walks, namely diagonal, simultaneous and radial records. The mean numbers these grow as universal power laws time, respective exponents 1/4, 1/3 1/2. study diagonal relies on underlying renewal structure successive hitting times locations translated copies a fixed target. In this sense, work represents two-dimens...

The security of multivariate cryptosystems and digital signature schemes relies on the hardness solving a system polynomial equations over finite field. Polynomial is also currently bottleneck index-calculus algorithms to solve elliptic hyperelliptic curve discrete logarithm problem. complexity closely related cost computing Gröbner bases, since solutions can be reduced finding lexicographic ba...

The article considers the method of optimization Gold’s pseudo-random sequences for communication systems. At same time, peculiarity generation specified is taken into account, namely that they can be generated only with a specific maximum number N (for example, 9, 33, 65, etc.). But in practice, there are often cases when much smaller them needed, i.e. excess PVPs. problem arises, which more a...