Why does it work?Encryption & decryption inverses

• N=pq, de = 1 mod f(n)

• E(M) = M e mod n = C

• D(C) = C d mod n.

• Assume M and n relatively prime

de = 1 mod f(n) => de = t f(n) +1 for t integer

=> (M e) d mod n = M ed mod n

= M t f(n) +1 mod n

= (Mf(n)) t M mod n

= 1t M mod n by F.L.T.

= M mod n

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