Usage Limits on AEAD Algorithms

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Table of Contents

1. Introduction

An Authenticated Encryption with Associated Data (AEAD) algorithm provides confidentiality and integrity. [RFC5116] specifies an AEAD as a function with four inputs - secret key, nonce, plaintext, and optional associated data - that produces ciphertext output and error code indicating success or failure. The ciphertext is typically composed of the encrypted plaintext bytes and an authentication tag.¶

The generic AEAD interface does not describe usage limits. Each AEAD algorithm does describe limits on its inputs, but these are formulated as strict functional limits, such as the maximum length of inputs, which are determined by the properties of the underlying AEAD composition. Degradation of the security of the AEAD as a single key is used multiple times is not given a thorough treatment.¶

These limits might also be influenced by the number of "users" of a given key. In the traditional setting, there is one key shared between a two parties. Any limits on the maximum length of inputs or encryption operations apply to that single key. The attacker's goal is to break security (confidentiality or integrity) of that specific key. However, in practice, there are often many users with independent keys. In this "multi-user" setting, the attacker is assumed to have done some offline work to help break security of single key (or user), where the attacker cannot choose which key is attacked. As a result, AEAD algorithm limits may depend on offline work and the number of users. However, given that a multi-user attacker does not target any specific user, acceptable advantages may differ from that of the single-user setting.¶

The number of times a single pair of key and nonce can be used might also be relevant to security. For some algorithms, such as AEAD_AES_128_GCM or AEAD_AES_256_GCM, this limit is 1 and using the same pair of key and nonce has serious consequences for both confidentiality and integrity; see [NonceDisrespecting]. Nonce-reuse resistant algorithms like AEAD_AES_128_GCM_SIV can tolerate a limited amount of nonce reuse.¶

It is good practice to have limits on how many times the same key (or pair of key and nonce) are used. Setting a limit based on some measurable property of the usage, such as number of protected messages or amount of data transferred, ensures that it is easy to apply limits. This might require the application of simplifying assumptions. For example, TLS 1.3 specifies limits on the number of records that can be protected, using the simplifying assumption that records are the same size; see Section 5.5 of [TLS].¶

Currently, AEAD limits and usage requirements are scattered among peer-reviewed papers, standards documents, and other RFCs. Determining the correct limits for a given setting is challenging as papers do not use consistent labels or conventions, and rarely apply any simplifications that might aid in reaching a simple limit.¶

The intent of this document is to collate all relevant information about the proper usage and limits of AEAD algorithms in one place. This may serve as a standard reference when considering which AEAD algorithm to use, and how to use it.¶

2. Requirements Notation

The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT", "SHOULD", "SHOULD NOT", "RECOMMENDED", "NOT RECOMMENDED", "MAY", and "OPTIONAL" in this document are to be interpreted as described in BCP 14 [RFC2119] [RFC8174] when, and only when, they appear in all capitals, as shown here.¶

3. Notation

This document defines limitations in part using the quantities below.¶

For each AEAD algorithm, we define the confidentiality and integrity advantage roughly as the advantage an attacker has in breaking the corresponding security property for the algorithm. Specifically:¶

• Confidentiality advantage (CA): The advantage of an attacker succeeding in breaking the confidentiality properties of the AEAD. In this document, the definition of confidentiality advantage is the increase in the probability that an attacker is able to successfully distinguish an AEAD ciphertext from the output of a random function.¶
• Integrity advantage (IA): The probability of an attacker succeeding in breaking the integrity properties of the AEAD. In this document, the definition of integrity advantage is the probability that an attacker is able to forge a ciphertext that will be accepted as valid.¶

Each application requires a different application of limits in order to keep CA and IA sufficiently small. For instance, TLS aims to keep CA below 2^-60 and IA below 2^-57. See [TLS], Section 5.5.¶

4. Calculating Limits

Once an upper bound on CA and IA are determined, this document defines a process for determining two overall limits:¶

• Confidentiality limit (CL): The number of bytes of plaintext and maybe authenticated additional data (AAD) an application can encrypt before giving the adversary a non-negligible CA.¶
• Integrity limit (IL): The number of bytes of ciphertext and maybe authenticated additional data (AAD) an application can process, either successfully or not, before giving the adversary a non-negligible IA.¶

For an AEAD based on a block function, it is common for these limits to be expressed instead in terms of the number of blocks rather than bytes. Furthermore, it might be more appropriate to track the number of messages rather than track bytes. Therefore, the guidance is usually based on the total number of blocks processed (s). To aid in calculating limits for message-based protocols, a formulation of limits that includes a maximum message size (l) is included.¶

All limits are based on the total number of messages, either the number of protected messages (q) or the number of forgery attempts (v); which correspond to CL and IL respectively.¶

Limits are then derived from those bounds using a target attacker probability. For example, given a confidentiality advantage of v * (8l / 2^106) and attacker success probability of p, the algorithm remains secure, i.e., the adversary's advantage does not exceed the probability of success, provided that v <= (p * 2^106) / 8l. In turn, this implies that v <= (p * 2^106) / 8l is the corresponding limit.¶

5. Single-User AEAD Limits

This section summarizes the confidentiality and integrity bounds and limits for modern AEAD algorithms used in IETF protocols, including: AEAD_AES_128_GCM [RFC5116], AEAD_AES_256_GCM [RFC5116], AEAD_AES_128_CCM [RFC5116], AEAD_CHACHA20_POLY1305 [RFC8439], AEAD_AES_128_CCM_8 [RFC6655].¶

The CL and IL values bound the total number of encryption and forgery queries (q and v). Alongside each value, we also specify these bounds.¶

CA <= ((s + q + 1)^2) / 2^129

q + s <= p^(1/2) * 2^(129/2) - 1

q <= (p^(1/2) * 2^(129/2) - 1) / (l + 1)

IA <= 2 * (v * (l + 1)) / 2^128

v <= (p * 2^127) / (l + 1)

CA <= v * ((8 * l) / 2^106)
IA <= v * ((8 * l) / 2^106)

v <= (p * 2^103) / l

CA <= (2l * q)^2 / 2^n
   <= (2l * q)^2 / 2^128

q <= sqrt((p * 2^126) / l^2)

IA <= v / 2^t + (2l * (v + q))^2 / 2^n
   <= v / 2^128 + (2l * (v + q))^2 / 2^128

v + (2l * (v + q))^2 <= p * 2^128

v + q <= p^(1/2) * 2^63 / l

IA <= v / 2^t + (2l * (v + q))^2 / 2^n
   <= v / 2^64 + (2l * (v + q))^2 / 2^128

v * 2^64 + (2l * (v + q))^2 <= p * 2^128

6. Multi-User AEAD Limits

In the public-key, multi-user setting, [MUSecurity] proves that the success probability in attacking one of many independently users is bounded by the success probability of attacking a single user multiplied by the number of users present. Each user is assumed to have an independent and identically distributed key, though some may share nonces with some very small probability. Absent concrete multi-user bounds, this means the attacker advantage in the multi-user setting is the product of the single-user advantage and the number of users.¶

This section summarizes the confidentiality and integrity bounds and limits for the same algorithms as in Section 5, except in the multi-user setting. The CL and IL values bound the total number of encryption and forgery queries (q and v). Alongside each value, we also specify these bounds.¶

CA <= ((v + q) * l)^2 / (u * 2^128)

v + q <= sqrt(p * u * 2^128) / l

CA <= (1 / 2^1024) + ((2 * (v + q)) / 2^256)
        + ((2 * o * (v + q)) / 2^(k + 128))
        + (128 * ((v + q) + ((v + q) * l)) / 2^k)

CA <= (128 * ((v + q) + ((v + q) * l)) / 2^128)

v + q <= (p * 2^128) / (128 * (l + 1))

CA <= ((2 * (v + q)) / 2^256)
        + (128 * ((v + q) + ((v + q) * l)) / 2^256)

v + q <= (p * 2^255) / ((64 * l) + 65)

v <= ((p / u) * 2^106) / 8l
  <= (p * 2^103) / (l * u)

v + q <= (p / u)^(1/2) * 2^63 / l

v * 2^64 + (2l * (v + q))^2 <= (p / u) * 2^128

7. Security Considerations

Many of the formulae in this document depend on simplifying assumptions that are not universally applicable. When using this document to set limits, it is necessary to validate all these assumptions for the setting in which the limits might apply. In most cases, the goal is to use assumptions that result in setting a more conservative limit, but this is not always the case.¶

8. IANA Considerations

This document does not make any request of IANA.¶

Authors' Addresses