Dave thought he had invented a novel system: a combination of RSA and Vigenere.

Question

Dave thought he had invented a novel system: a combination of RSA and Vigenere. He took each character of the message (with space = 00, a = 01, b = 02, z = 26) and encrypted it using RSA seperately; the first letter using an encryption exponent e1, the second letter using an encryption exponent e2 and so on up to e10 when the same e's were used again in order. Dave published n and the exponents ej, 1-j-10. The modulus n was the same in all cases and just to make sure he used a super industrial grade pair of primes that gave an n with 1,000 digits. In addition, since the plaintexts were small he chose large exponents; each ej was a prime with at least 500 digits. Of course each letter produced a ciphertext c of roughly 1, 000 digits, and so the transmission was much longer, but to Dave that wasn't as important as security Was this a good idea, or did it just make extra computation over using a large message blocksize (which given the size of the modulus could have been up to 1, 000 digits or 500 characters) and a (much) smaller exponent e? Or is it worse and actually cryptographically insecure?

Explanation / Answer

In case of Security it is a good idea as that is much imprtant for Dave other than any Memory uses but overall if we see the solution he did can be optimized in case of Memory used concerns.

Blocksize for message to encrypt can be use a bit small, that will reduce the memory used , time spent and the security will be good as well in that case using RSA encryption method only.

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