I have heard some people say that the Poly1305 authenticator is a "nuclear" MAC i.e. it is information-theoretically secure. After reading the paper I see it is based on the Wegman-Carter MAC which is supposedly the natural authentication pairing with the one-time pad cipher.
Is it true though that Poly1305 is really an information-theoretically secure MAC? Here is an excerpt from the paper:
This paper introduces and analyzes Poly1305-AES, a state-of-the-art secret-key message-authentication code suitable for a wide variety of applications.
Poly1305-AES computes a 16-byte authenticator Poly1305r(m, AESk(n)) of a variable-length message m, using a 16-byte AES key k, a 16-byte additional key r, and a 16-byte nonce n. Section 2 of this paper presents the complete definition of Poly1305-AES.
Poly1305-AES has several useful features:
- Guaranteed security if AES is secure. The security gap is small, even for long-term keys; the only way for an attacker to break Poly1305-AES is to break AES. Assume, for example, that messages are packets up to 1024 bytes; that the attacker sees 264 messages authenticated under a Poly1305-AES key; that the attacker attempts a whopping 275 forgeries; and that the attacker cannot break AES with a probability above δ. Then, with probability at least 0.999999−δ, all of the 275 forgeries are rejected.
- Cipher replaceability. If anything does go wrong with AES, users can switch from Poly1305-AES to Poly1305-AnotherFunction, with an identical security guarantee. All the effort invested in the non-AES part of Poly1305-AES can be reused; the non-AES part of Poly1305-AES cannot be broken.
So it appears Poly1305 is only secure if AES is secure. So in theory if I do not like AES I can swap it out for something else like ChaCha20 (as many have done e.g. SSH and TLS 1.3). However then the authentication is still only as secure as ChaCha20 which in itself is not information-theoretically secure. So then, what if I need an authentication tag that will remain secure for a long period of time (100+ years) and even resist cryptanalysis indefinitely?
I understand the point of the Poly1305 is to re-use the keys for many messages as long as the nonce changes each time. However, assume a hypothetical system which has many one-time pads generated by a HWRNG and they are pre-shared between two parties via a physical exchange. The key material for each message is divided up as follows:
- 92 byte key for encrypting the 92 byte message using XOR $\oplus$
- 16 byte Poly1305 encryption key $k$ (formerly the AES key)
- 16 byte Poly1305 additional key $r$
- 16 byte Poly1305 nonce $n$
So in this scenario the $k$, $r$ and $n$ are unique and truly random per message sent. So per one-time pad encrypted and authenticated message it uses up 140 bytes of true random data. Now given that this construction creates the Poly1305 tag:
Can the AES$_k$($n$) portion be simply replaced with $k$ $\oplus$ $n$? In other words, encrypt the nonce with a one-time pad. Will this remain theoretically secure indefinitely?