A young engineer designs a simple cipher based on Shannon's concept of a product cipher. The...
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A young engineer designs a simple cipher based on Shannon's concept of a "product cipher". The ciphertext output, y, is generated by applying an affine cipher to the plaintext, x, to produce an intermediate result, z, and then applying another affine cipher to the immediate result, z, to produce the ciphertext output, y. This is represented mathematically as follows: y=a2z + b mod n z = aix + b mod n The pairs (a, bi) and (a2, b2) form the key. (a) Determine an expression for the number of distinct mappings from plaintext to ciphertext in terms of n. HINT: It could be that the cipher can be simplified from its two step process. (b) Comment on the usefulness of the approach used in the cipher. A young engineer designs a simple cipher based on Shannon's concept of a "product cipher". The ciphertext output, y, is generated by applying an affine cipher to the plaintext, x, to produce an intermediate result, z, and then applying another affine cipher to the immediate result, z, to produce the ciphertext output, y. This is represented mathematically as follows: y=a2z + b mod n z = aix + b mod n The pairs (a, bi) and (a2, b2) form the key. (a) Determine an expression for the number of distinct mappings from plaintext to ciphertext in terms of n. HINT: It could be that the cipher can be simplified from its two step process. (b) Comment on the usefulness of the approach used in the cipher.
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a Lets analyze the mappings from the plaintext x to the intermediate result z and then to the ciphertext y The equation y a2z b2 mod n and z a1x b1 mod n can be combined to form a single affine cipher equation y a2a1x b1 b2 mod n Expanding the equation further we get y a2a1x a2b1 b2 mod n Therefore the combined key for the simple cipher is a2a1 a2b1 b2 The number of distinct mappings from plaintext to ciphertext can be expressed as n2 since there are n choices for each coefficient in the combined key b This approach in the cipher ... View the full answer
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