Lecture Note #11 (Digital Signature) was added. See "Lecture Notes"

Lecture Note was updated. See "Lecture Notes"

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Solve Exercise 1.5, 1.6, 1.7, 1.11 in main text book.

1.5 Use exhaustive key search to decrypt the following ciphertext, which was encrypted using Shift Cipher:
    BEEAKFYDJXUQYHYJIQRYHTYJIQFBQDUYJIIKFUHCQD

1.6 If an encryption function e_K is identical to the decryption function d_K , then the key K is said to be an involutory key. Find all the involutory keys in the Shift Cipher over Z₂₆.

1.7 Determine the number of keys in an Affine Cipher over Z_m for m = 30, 100 and 1225.

1.11 (a) Suppose K = (a, b) is a key in an Affine Cipher over Z_n. Prove that K is an involutory key if and only if a^-1 mod n = a and b(a+1) = 0 (mod n).
(b) Determine all the involutory keys in the Affine Cipher over Z₁₅.
(c) Suppose that n = pq, where p and q are distinct odd primes. Prove that the number of involutory keys in the Affine Cipher over Z_n is n+p+q+1.
 

Lecture Note was updated.

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