A modular exponentiation is one of the most important operations in public-key cryptography. However, it takes much time because the modular exponen-tiation deals with very large operands as 512-bit integers. The modular exponentiation is composed of repetition of modular multiplications. Therefore, we can reduce the execution time of it by reducing the execution time of each modular multiplica...

Introduction. Let L be a complete, orthocomplemented lattice. We say that L is a dimension lattice if L is weakly modular and there is an equivalence relation on L satisfying the axioms A,B,C, and D' of Loomis [5]. We say that L is locally finite if every element of L is the join of finite elements. If L is a dimension lattice in which every element is finite, then L is modular. Conversely, Kap...