Question
Consider the prime numbers p = 127 and q = 131 . We want to generate RSA key pairs and make an encryption/decryption scenario of
Consider the prime numbers p = 127 and q = 131 . We want to generate RSA key pairs and make an encryption/decryption scenario of a simple text.
We also give the Euler function (16380) = 3456 for finding multiplicative inverse in question 3).
1) compute n and (n)
2) Choose a value for the public key e.
3) Compute the private key d using the Euler theorem :
a-1 mod m = a (m) - 1 mod m if a and m are coprimes.
4) take the message M = "CRYPTO" and convert it to numbers by changing each character by its alphabet order based on this table
A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z |
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 |
Hint : for example the message 'MONDAY" = 13 15 14 04 01 25
5) Encrypt the message M using RSA and name it the ciphertext C.
6) Decrypt C now using the private ke
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