# One Time Pad OTP: with modular math, ciphertext reveals modulus always, yes or no?

Assuming that in the OTP scheme, the key has more values than the alphabet, then: using modular math predetermines that the highest possible value in the ciphertext will reveal the modulus used in the scheme.

Therefore, ciphertext reveals highest possible modulus.

Put more simply, given enough ciphertext, ciphertext reveals modulus.

Am I correct?

Edit: clarification: now that I think more about it, the key or its space size in relation to the alphabet size/plaintext size does not even matter. If the One Time Pad uses modular math in its scheme, then the ciphertext reveals the modulus, without exception. Looking for either confirmation or rejection here. Thank you.

• The answer is, of course, "yes", but I'm curious about why you think this is an issue. The modulus is generally a fixed public value, so revealing it compromises nothing. In fact, probably the most common choice for the modulus is 2. – Ilmari Karonen Sep 13 '18 at 21:18
• It's an " issue", llmari, because " one time pad" technology is usually promoted as "not revealing anything extra about the plaintext" . But in practice, OTP reveals alot about the plaintext" , apparently, including the modulus used. If the attacker knows the modulus, the attacker can tailor his/her attack to limit computational resources for that particular modulus. Giving the attacker a huge advantage. Obvious to me, not obvious to you? – EncryptThis Sep 13 '18 at 21:27
• Comments are not for extended discussion; this conversation has been moved to chat. – e-sushi Sep 28 '18 at 23:31

... If the One Time Pad uses modular math in its scheme, then the ciphertext reveals the modulus, without exception... Looking for either confirmation or rejection here...

Rejection.

The publicly available parameters for the scheme reveals the modulus. The modulus is not secret information.

The ciphertext does not "reveal" anything about already-known public information. Proof: The modulus is available even if you possess no ciphertexts.

The modulus being public information has no influence on the security of the scheme.

Proof: The following is the ciphertext that was the result of encrypting one plaintext bit: $1$

The encryption process was done via exclusive-or of the plaintext bit with a random bit. Exclusive-or is addition modulo 2, so the modulus is 2.

There is no algorithm that you can apply to determine whether or not the plaintext message is in fact $0$ or if it is in fact $1$. They are both equally probable.

Your knowledge of the modulus being 2 makes no difference in your ability to recover the plaintext bit from the ciphertext given above.

It's an " issue", llmari, because " one time pad" technology is usually promoted as "not revealing anything extra about the plaintext"

The modulus is not a part of the plaintext message, so this goal is in fact not violated.