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