A quick exponentiation algorithm for 3×3 block upper triangular matrices

Block upper triangular matrices with elements in Zp have very interesting properties for many applications. Some of them involve powers of this type of matrices with very large exponents requiring specific exponentiation algorithms to compute them efficiently. In this paper, we analyze quick exponentiation in block upper triangular matrices of size 3×3 blocks as an extension of the quick exponentiation in block upper triangular matrices of 2×2 blocks.