Some applications of arithmetic groups in cryptography

Abstract

Abstract In this paper, we will offer a new symmetric-key cryptographic scheme which is based on the existence of exponentially distorted subgroups in arithmetic groups. Aside from this, we will also provide new examples of distorted subgroups in SL n ⁢ ( ℤ ⁢ [ x ] ) {\mathrm{SL}_{n}(\mathbb{Z}[x])} which can be utilized for the same purpose.