# Can I securely refill a one time pad over the same connection?

If you have a channel where you are communicating using a one time key, is it possible to receive additional key over that same connection without compromising security?

Naively sending it through the same encrypted channel would of course consume the pad at the same rate that you refill it, but maybe there's a more clever way?

Presumably brute forcing would yield the dictionary both when run against encrypted data and against the pad used to encypt future messages, since both look like (or are) random data.

• Are you talking about the one time pad which has a key as long as the message or about symmetric ciphers which have very short key for long messages (ie sending a new short, symmetric key over an already-established channel for subsequent communication)? – SEJPM Mar 8 '17 at 1:21
• @PaulUszak If you send a new pad $O_2$ encrypted with pad $O_1$, and then send plaintext message $M$ encrypted with $O_2$, you can do $C_1 \oplus C_2 = O_1 \oplus O_2 \oplus O_2 \oplus M = O_1 \oplus M$, but then the message would still be encrypted with the one-time pad $O_1$. – knbk Mar 8 '17 at 9:53
• Is xor the only possible operation? For example, cyclically shifting bits in a block at a time a certain number of steps according to the pad should avoid the "cancelling out" issue of xor. Doing both, i.e. shift(pad2, xor(pad, x)) should avoid the issue. This might of course have some other security implication (like eating some aditional entropy for the shift part), but something other than xor should work, right?. – Filip Haglund Mar 8 '17 at 18:22
• Nope, because it is not theoretically possible to get perfect security when the key (stream) is smaller than what is encrypted. So whichever operation you try, you won't get the security promised by a one-time-pad. If it is sufficient security is a different matter. But if you just require sufficient security then a stream cipher would do as well. OTP is generally useful as a theoretical construction, especially in security proofs. – Maarten Bodewes Mar 11 '17 at 1:07
• Quantum key distribution does this specifically now. That's cleverer, but is that what you mean? – Paul Uszak Jul 29 '19 at 12:16