Vernam Cipher and the One-Time Pad

A random key as long as the message. Unconditionally secure under stated conditions, and worthless the moment a pad is reused.

Polyalphabeticdemo

Objectives

State the four conditions the one-time pad requires.
Show that any plaintext of the right length is a possible decryption.
Explain why key length, generation, and distribution keep it impractical.

33%

C = P ⊕ K, with K random, as long as the message, and never reused.

Plaintext

plaintext bytes

57 65 20 68 61 76 65 20 61 20 6D 6F 6C 65 20 61 62 6F 72 74 20 74 68 65 20 64 65 61 6C

pad (random)

ciphertext = plaintext ⊕ pad

Why Shannon called this perfectly secret

Type any message of the same length. There is a pad that turns this exact ciphertext into it, and that pad is exactly as likely as the real one.

Claim the ciphertext says…

pad that produces your claim

check: ciphertext ⊕ that pad

(lengths differ, compared over 0 bytes)

Not hard to break. No information at all. The ciphertext does not narrow the message down, which is what makes this the one cipher here with unconditional security.

And why nobody uses it

Key length	as long as the message: a 1 GB file needs 1 GB of key
Key generation	truly random, not a PRNG. A PRNG makes it a stream cipher instead.
Key distribution	you must already have a secure channel, and if you have one, why encrypt?
Reuse	catastrophic. Use a pad twice and both messages fall out.

step 1/3

CPE 645 / CS 685

Vernam Cipher and the One-Time Pad

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