Abstract
The RSA public key cryptosystem was among the first algorithms to implement the Diffie-Hellman key exchange protocol. At the core of RSA’s security is the problem of factoring its modulus, a very large integer, into its prime factors. In this study, we show a step-by-step tutorial on how to factor the RSA modulus using Euler’s factorization algorithm, an algorithm that belongs to the class of exact algorithms. The Euler’s factorization algorithm is implemented in Python programming language. In this experiment, we also record the relation between the length of the RSA moduli and its factorization time. As a result, this study shows that the Euler’s factorization algorithm can be used to factor small modulus of RSA, the correlation between the factoring time and the size of RSA modulus is directly proportional, and better selection of some Euler’s parameters may lead to lower factoring time.
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