A note on Mod and generalised Mod classes

A Note on Mod and Generalised Mod Classes

We characterise Mod classes in terms of #P functions, where the membership is determined by co-primality or gcd testing of the function value (Theorem 3.1), instead of residue (mod k) testing. Imposing a restriction on the range of the functions gives a characterisation of the intersection of Mod classes (Theorem 3.2). These intersection classes, which we denote by Mod ∩k P , are interesting be...

A note on closure properties of logspace MOD classes

Structure and Importance of Logspace-MOD-Classes

We reene the techniques of Beigel, Gill, Hertrampf 4] who investigated polynomial time counting classes, in order to make them applicable to the case of logarithmic space. We deene the complexity classes MOD k L and demonstrate their signiicance by proving that all standard problems of linear algebra over the nite rings Z/kZ are complete for these classes. We then deene new complexity classes L...

Computing Mod Without Mod

Encryption algorithms are designed to be difficult to break without knowledge of the secrets or keys. To achieve this, the algorithms require the keys to be large, with some algorithms having a recommend size of 2048-bits or more. However most modern processors only support computation on 64-bits at a time. Therefore standard operations with large numbers are more complicated to implement. One ...

A note on the new basis in the mod 2 Steenrod algebra

‎The Mod $2$ Steenrod algebra is a Hopf algebra that consists of the primary cohomology operations‎, ‎denoted by $Sq^n$‎, ‎between the cohomology groups with $mathbb{Z}_2$ coefficients of any topological space‎. ‎Regarding to its vector space structure over $mathbb{Z}_2$‎, ‎it has many base systems and some of the base systems can also be restricted to its sub algebras‎. ‎On the contrary‎, ‎in ...