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This is an article in a series on Cryptography for the Everyday Developer. Follow along to learn the basics of modern cryptography and encryption. Modern cryptography relies heavily on number theory. One of the simplest but most important tools in the number theorist’s toolkit is the Euclidean algorithm. This algorithm, and its extension, the extended Euclidean algorithm, form the basis for practical cryptographic operations such as modular inversion. This blog post walks through both algorithms, with an explanation of why they are important to public key cryptography. ...