The most widely used and tested public-key cryptosystem was originally introduced by Rivest, Shamir and Adleman, and is now referred to as the RSA system. It is based on an amazingly simple number-theoretical (one could even say arithmetical) idea, and yet it has been able to resist all cryptanalytic attacks. The idea is a clever use of the fact that, while it is easy to multiply two large primes, it is extremely difficult to factorize their product. Thus, the product can be publicized and used as the encryption key. The primes themselves cannot be recovered from the product. On the other hand, the primes are needed for decryption. Thus, we have an excellent framework for a public-key cryptosystem. Moreover, the details can be explained very fast — that’s why we called the system “amazingly simple”.
KeywordsPartial Information Discrete Logarithm Chinese Remainder Theorem Modular Exponentiation Generalize Riemann Hypothesis
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