In cryptography, the one-time pad is considered unbreakable under which conditions?

• A. The key is truly random, never reused, and kept secret
• B. It relies on public-key cryptography
• C. It requires the factoring of large numbers
• D. It uses a fixed-size key

Answer: (A)

The unbreakability of a one-time pad rests on having a key that is truly random, as long as the message, used only once, and kept secret. When these conditions hold, encryption simply hides the plaintext because the ciphertext is a perfect randomization of the message; without the exact key, every possible plaintext is equally likely, so nothing about the original message can be inferred from the ciphertext. If any condition is violated, secrecy fails: reusing the key across multiple messages creates relationships between ciphertexts that can be exploited to recover the messages, non-random or biased keys introduce patterns that an attacker can detect, and a fixed-size key implies repetition, which also leaks information. Concepts like public-key cryptography or the need to factor large numbers are unrelated to the unconditional secrecy claimed by a proper one-time pad.