The Vernam cipher is a symmetric stream cipher invented by the American engineer Gilbert S. Vernam in 1917. It represents a foundational development in modern cryptography because it introduced the concept of combining plaintext with a random key using the bitwise XOR operation, which became the basis for the one-time pad. Vernam’s design originally targeted teleprinter communication systems, using a punched paper tape to supply the key stream. The cipher is fully reversible: applying the same key to the ciphertext recovers the original plaintext, and using a truly random key of equal length provides perfect secrecy.
In the Vernam cipher, each plaintext letter or bit is combined with a corresponding key value. For alphabetic implementations, letters are often mapped to numbers (A=0, B=1, …, Z=25), then each plaintext number is added modulo 26 to the key number. Decryption simply subtracts the key modulo 26. For instance, to encrypt the word HELLO using a key XMCKL, we convert letters to numbers: H=7, E=4, L=11, L=11, O=14 and X=23, M=12, C=2, K=10, L=11. Adding modulo 26 yields ciphertext numbers 4, 16, 13, 21, 25, corresponding to letters E, Q, N, V, Z. Applying the same key to EQNVZ recovers HELLO.
The key principle of the Vernam cipher is that the keystream must be as long as the message and used only once. When these conditions are met and the key is truly random, the cipher is equivalent to a one-time pad, providing theoretically unbreakable encryption. Vernam’s original patent described a teleprinter system where key material was distributed via punched tape, enabling automated encryption and decryption in real time. This mechanized approach allowed secure communication in military and corporate contexts without relying on human memorization or repetitive keys.
The historical significance of the Vernam cipher lies not only in its immediate application but also in its conceptual innovation. By formalizing a method for combining a plaintext with a random key stream, Vernam laid the groundwork for modern stream ciphers, digital encryption, and secure communication protocols. While practical implementations initially required physical media like tape, today the same principle underlies secure digital systems, including cryptographically secure pseudo-random number generators and symmetric key algorithms.
For example, encrypting HELLO with the key XMCKL produces EQNVZ, demonstrating the straightforward arithmetic of the cipher while highlighting its reliance on the secrecy and randomness of the key. The Vernam cipher exemplifies a core cryptographic insight: when a random, single-use key is combined with plaintext using a reversible operation, perfect secrecy is achievable. This insight continues to influence both theoretical and practical cryptography more than a century after Gilbert S. Vernam introduced the concept.