Rivest-Shamir-Adleman (RSA) encryption algorithm which is based on the combination of prime factorization, Euler's totient function, Euler's totient theorem and Extended Euclidean Algorithm
(EEA) is used to compute the private key for decryption process.
The key result of this study is that this Euclidean algorithm
offers an easy and quantitative interpretation of nucleotide skew data of virus genomes.
When the two numbers of GCD are very long, Euclidean algorithm
will take longer time to compute GCD.
Chapter 3 uses the Euclidean algorithm
to find the reduced form of factions through prime factorization, prove certain divisibility shortcuts, and prove the fundamental theorem of arithmetic.
 This is often computed using the extended Euclidean algorithm
. Using the pseudo code in the Modular integers section, inputs a and n correspond to e and [phi](n), respectively.
One could use the same argument that Feinstein uses to "prove" that it is impossible to determine in polynomial-time whether this equation has a solution, when in fact one can use the Euclidean algorithm
to determine this information in polynomial-time.
Zhou, "A method for blind recognition of convolution code based on euclidean algorithm
," in Proceedings of the 3rd International Conference on Wireless Communications, Networking and Mobile Computing (WiCOM '07), pp.
where the inverse was computed using the Euclidean algorithm
in the ring of integers modulo p.
The Euclidean algorithm
for finding the greatest common divisor is applicable.
This type of modular multiplication is closely related to the Euclidean algorithm
that determines the greatest common divisor between two integers by a process of successive division by the remainder from the previous operation.
The extended Euclidean algorithm
may be used to calculate it.
Errors have been corrected in the third edition and parts of the Fast Euclidean Algorithm
chapter have been refreshed.