Fast Modular Exponentiation Methods for Public-Key Cryptography

Modular exponentiation (ME) is a complex operation for several public-key cryptosystems (PKCs). Moreover, ME is expensive for resource-constrained devices in terms of computation time and energy consumption, especially when the exponent is large. ME is defined as the task of raising an integer
$x$
to power
$k$
and reducing the result modulo some integer
$n$
. Several methods to calculate ME have been proposed. In this paper, we present the efficient ME methods. We then implement the methods using different security levels of RSA keys on a Raspberry Pi. Finally, we give the fast ME method.