(Difficult) One thing about the RSA algorithm that does not quite make sense is how we can use Euler's or Fermat's theorem to calculate the exponent 'e' of a message. In Euler's theorem we could find a to the power of (p-1)(q-1) was congruent to 1 (mod pq) because a was relatively prime to pq, (in this case pq = n) Are there limitations on the message size to ensure that the message will be relatively prime to n? It seems that if we are multiplying together two very large prime numbers, the chance of the message being a multiple of one of the primes seems very unlikely, but it still poses some concerns. If the message was never larger than either of the primes, then this would not be an issue.
(Reflective) As we read about the encryption process of RSA, I wondered how it was implemented given today's technology. Would there be any way to prevent two companies from using the same value of n? If two people shared the same value of n, and n has a unique factoriziation, they would know each other's values for p and q. How could a system be developed to prevent multiple users with the same encryption and decryption methods? Likewise, although it would take a ridiculous amount of inital computations, Eve could create a multiplication table of values of p,q and calculate 'n' for n = pq. Although this list would be enormous, given enough storage capacity, Eve would already know the factors for many values of n, and if she found a system using the same value of n in their encryption, she would effectively have their key for encryption and decryption. Maybe n is large enough to make this impractical for modern technology, but it seems that it might pose a threat if newer methods of storage and compression on computer systems are found.
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