For example, the cyclic group with 7 elements has the operator addition modulo 7.
4.
Consider the abelian group ( that is, the set with addition modulo 4 ), and its subgroup.
5.
Does this mean that any other 7 element group will have an operator that is isomorphic to addition modulo 7?
6.
The cipher uses only the operations of addition modulo 2 32, exclusive or, and rotation by a fixed number of bits.
7.
Sometimes the elements of I _ c may be defined by a vector addition modulo the simulation space's dimension to realize toroidal topologies:
8.
Unlike basic Nihilist, the additive was added by non-carrying addition ( digit-wise addition modulo 10 ), thus producing a more uniform output which doesn't leak as much information.
9.
Z 3 = { 0, 1, 2 } with addition modulo 3; group element 0 corresponds to the identity permutation e, group element 1 to permutation ( 123 ), and group element 2 to permutation ( 132 ).
10.
The oracle maps the state | x \ rangle | y \ rangle to | x \ rangle | y \ oplus f ( x ) \ rangle, where \ oplus is addition modulo 2 ( see below for details of implementation ).