Network Working Group F. Günther
Internet-Draft ETH Zurich
Intended status: Informational M. Thomson
Expires: 15 February 2021 Mozilla
C.A. Wood
Cloudflare
14 August 2020
Usage Limits on AEAD Algorithms
draft-irtf-cfrg-aead-limits-00
Abstract
An Authenticated Encryption with Associated Data (AEAD) algorithm
provides confidentiality and integrity. Excessive use of the same
key can give an attacker advantages in breaking these properties.
This document provides simple guidance for users of common AEAD
functions about how to limit the use of keys in order to bound the
advantage given to an attacker. It considers limits in both single-
and multi-user settings.
Discussion Venues
This note is to be removed before publishing as an RFC.
Source for this draft and an issue tracker can be found at
https://github.com/chris-wood/draft-wood-cfrg-aead-limits
(https://github.com/chris-wood/draft-wood-cfrg-aead-limits).
Status of This Memo
This Internet-Draft is submitted in full conformance with the
provisions of BCP 78 and BCP 79.
Internet-Drafts are working documents of the Internet Engineering
Task Force (IETF). Note that other groups may also distribute
working documents as Internet-Drafts. The list of current Internet-
Drafts is at https://datatracker.ietf.org/drafts/current/.
Internet-Drafts are draft documents valid for a maximum of six months
and may be updated, replaced, or obsoleted by other documents at any
time. It is inappropriate to use Internet-Drafts as reference
material or to cite them other than as "work in progress."
This Internet-Draft will expire on 15 February 2021.
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Copyright Notice
Copyright (c) 2020 IETF Trust and the persons identified as the
document authors. All rights reserved.
This document is subject to BCP 78 and the IETF Trust's Legal
Provisions Relating to IETF Documents (https://trustee.ietf.org/
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Please review these documents carefully, as they describe your rights
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Table of Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . 3
2. Requirements Notation . . . . . . . . . . . . . . . . . . . . 4
3. Notation . . . . . . . . . . . . . . . . . . . . . . . . . . 4
4. Calculating Limits . . . . . . . . . . . . . . . . . . . . . 6
5. Single-User AEAD Limits . . . . . . . . . . . . . . . . . . . 6
5.1. AEAD_AES_128_GCM and AEAD_AES_256_GCM . . . . . . . . . . 7
5.1.1. Confidentiality Limit . . . . . . . . . . . . . . . . 7
5.1.2. Integrity Limit . . . . . . . . . . . . . . . . . . . 7
5.2. AEAD_CHACHA20_POLY1305 . . . . . . . . . . . . . . . . . 7
5.3. AEAD_AES_128_CCM . . . . . . . . . . . . . . . . . . . . 8
5.3.1. Confidentiality Limit . . . . . . . . . . . . . . . . 8
5.3.2. Integrity Limit . . . . . . . . . . . . . . . . . . . 8
5.4. AEAD_AES_128_CCM_8 . . . . . . . . . . . . . . . . . . . 9
6. Multi-User AEAD Limits . . . . . . . . . . . . . . . . . . . 9
6.1. AEAD_AES_128_GCM and AEAD_AES_256_GCM . . . . . . . . . . 9
6.1.1. Confidentiality Limit . . . . . . . . . . . . . . . . 9
6.1.2. Integrity Limit . . . . . . . . . . . . . . . . . . . 9
6.2. AEAD_CHACHA20_POLY1305, AEAD_AES_128_CCM, and
AEAD_AES_128_CCM_8 . . . . . . . . . . . . . . . . . . . 10
6.2.1. AEAD_CHACHA20_POLY1305 . . . . . . . . . . . . . . . 10
6.2.2. AEAD_AES_128_CCM and AEAD_AES_128_CCM_8 . . . . . . . 10
7. Security Considerations . . . . . . . . . . . . . . . . . . . 11
8. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 11
9. References . . . . . . . . . . . . . . . . . . . . . . . . . 11
9.1. Normative References . . . . . . . . . . . . . . . . . . 11
9.2. Informative References . . . . . . . . . . . . . . . . . 12
Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . 13
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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].
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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.
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+========+====================================================+
| Symbol | Description |
+========+====================================================+
| n | Number of bits per block |
+--------+----------------------------------------------------+
| k | Size of the AEAD key (in bits) |
+--------+----------------------------------------------------+
| t | Size of the authentication tag (in bits) |
+--------+----------------------------------------------------+
| l | Length of each message (in blocks) |
+--------+----------------------------------------------------+
| s | Total plaintext length in all messages (in blocks) |
+--------+----------------------------------------------------+
| q | Number of user encryption attempts |
+--------+----------------------------------------------------+
| v | Number of attacker forgery attempts |
+--------+----------------------------------------------------+
| p | Adversary attack probability |
+--------+----------------------------------------------------+
| o | Offline adversary work (in number of encryption |
| | and decryption queries; multi-user setting only) |
+--------+----------------------------------------------------+
| u | Number of users or keys (multi-user setting only) |
+--------+----------------------------------------------------+
Table 1
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.
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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.
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5.1. AEAD_AES_128_GCM and AEAD_AES_256_GCM
The CL and IL values for AES-GCM are derived in [AEBounds] and
summarized below. For this AEAD, n = 128 and t = 128 [GCM]. In this
example, the length s is the sum of AAD and plaintext, as described
in [GCMProofs].
5.1.1. Confidentiality Limit
CA <= ((s + q + 1)^2) / 2^129
This implies the following usage limit:
q + s <= p^(1/2) * 2^(129/2) - 1
Which, for a message-based protocol with "s <= q * l", if we assume
that every packet is size "l", produces the limit:
q <= (p^(1/2) * 2^(129/2) - 1) / (l + 1)
5.1.2. Integrity Limit
IA <= 2 * (v * (l + 1)) / 2^128
This implies the following limit:
v <= (p * 2^127) / (l + 1)
5.2. AEAD_CHACHA20_POLY1305
The only known analysis for AEAD_CHACHA20_POLY1305
[ChaCha20Poly1305Bounds] combines the confidentiality and integrity
limits into a single expression, covered below:
CA <= v * ((8 * l) / 2^106)
IA <= v * ((8 * l) / 2^106)
This advantage is a tight reduction based on the underlying Poly1305
PRF [Poly1305]. It implies the following limit:
v <= (p * 2^103) / l
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5.3. AEAD_AES_128_CCM
The CL and IL values for AEAD_AES_128_CCM are derived from
[CCM-ANALYSIS] and specified in the QUIC-TLS mapping specification
[I-D.ietf-quic-tls]. This analysis uses the total number of
underlying block cipher operations to derive its bound. For CCM,
this number is the sum of: the length of the associated data in
blocks, the length of the ciphertext in blocks, the length of the
plaintext in blocks, plus 1.
In the following limits, this is simplified to a value of twice the
length of the packet in blocks, i.e., 2l represents the effective
length, in number of block cipher operations, of a message with l
blocks. This simplification is based on the observation that common
applications of this AEAD carry only a small amount of associated
data compared to ciphertext. For example, QUIC has 1 to 3 blocks of
AAD.
For this AEAD, n = 128 and t = 128.
5.3.1. Confidentiality Limit
CA <= (2l * q)^2 / 2^n
<= (2l * q)^2 / 2^128
This implies the following limit:
q <= sqrt((p * 2^126) / l^2)
5.3.2. Integrity Limit
IA <= v / 2^t + (2l * (v + q))^2 / 2^n
<= v / 2^128 + (2l * (v + q))^2 / 2^128
This implies the following limit:
v + (2l * (v + q))^2 <= p * 2^128
In a setting where "v" or "q" is sufficiently large, "v" is
negligible compared to "(2l * (v + q))^2", so this this can be
simplified to:
v + q <= p^(1/2) * 2^63 / l
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5.4. AEAD_AES_128_CCM_8
The analysis in [CCM-ANALYSIS] also applies to this AEAD, but the
reduced tag length of 64 bits changes the integrity limit calculation
considerably.
IA <= v / 2^t + (2l * (v + q))^2 / 2^n
<= v / 2^64 + (2l * (v + q))^2 / 2^128
This results in reducing the limit on "v" by a factor of 2^64.
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.
6.1. AEAD_AES_128_GCM and AEAD_AES_256_GCM
Concrete multi-user bounds for AEAD_AES_128_GCM and AEAD_AES_256_GCM
exist due to [GCM-MU]. AES-GCM without nonce randomization is also
discussed in [GCM-MU], though this section does not include those
results as they do not apply to protocols such as TLS 1.3 [RFC8446].
6.1.1. Confidentiality Limit
CA <= ((v + q) * l)^2 / (u * 2^128)
This implies the following limit:
v + q <= sqrt(p * u * 2^128) / l
6.1.2. Integrity Limit
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CA <= (1 / 2^1024) + ((2 * (v + q)) / 2^256)
+ ((2 * o * (v + q)) / 2^(k + 128))
+ (128 * ((v + q) + ((v + q) * l)) / 2^k)
When k = 128, the last term in this inequality dominates. Thus, we
can simplify this to:
CA <= (128 * ((v + q) + ((v + q) * l)) / 2^128)
This implies the following limit:
v + q <= (p * 2^128) / (128 * (l + 1))
When k = 256, the second and fourth terms in the CA inequality
dominate. Thus, we can simplify this to:
CA <= ((2 * (v + q)) / 2^256)
+ (128 * ((v + q) + ((v + q) * l)) / 2^256)
This implies the following limit:
v + q <= (p * 2^255) / ((64 * l) + 65)
6.2. AEAD_CHACHA20_POLY1305, AEAD_AES_128_CCM, and AEAD_AES_128_CCM_8
There are currently no concrete multi-user bounds for
AEAD_CHACHA20_POLY1305, AEAD_AES_128_CCM, or AEAD_AES_128_CCM_8.
Thus, to account for the additional factor "u", i.e., the number of
users, each "p" term in the confidentiality and integrity limits is
replaced with "p / u".
6.2.1. AEAD_CHACHA20_POLY1305
The combined confidentiality and integrity limit for
AEAD_CHACHA20_POLY1305 is as follows.
v <= ((p / u) * 2^106) / 8l
<= (p * 2^103) / (l * u)
6.2.2. AEAD_AES_128_CCM and AEAD_AES_128_CCM_8
The integrity limit for AEAD_AES_128_CCM is as follows.
v + q <= (p / u)^(1/2) * 2^63 / l
Likewise, the integrity limit for AEAD_AES_128_CCM_8 is as follows.
v * 2^64 + (2l * (v + q))^2 <= (p / u) * 2^128
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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.
9. References
9.1. Normative References
[AEBounds] Luykx, A. and K. Paterson, "Limits on Authenticated
Encryption Use in TLS", 8 March 2016,
.
[CCM-ANALYSIS]
Jonsson, J., "On the Security of CTR + CBC-MAC",
DOI 10.1007/3-540-36492-7_7, Selected Areas in
Cryptography pp. 76-93, 2003,
.
[ChaCha20Poly1305Bounds]
Procter, G., "A Security Analysis of the Composition of
ChaCha20 and Poly1305", 11 August 2014,
.
[GCM] Dworkin, M., "Recommendation for Block Cipher Modes of
Operation: Galois/Counter Mode (GCM) and GMAC",
NIST Special Publication 800-38D, November 2007.
[GCMProofs]
Iwata, T., Ohashi, K., and K. Minematsu, "Breaking and
Repairing GCM Security Proofs", 1 August 2012,
.
[MUSecurity]
Bellare, M., Boldyreva, A., and S. Micali, "Public-Key
Encryption in a Multi-user Setting: Security Proofs and
Improvements", May 2000,
.
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[Poly1305] Bernstein, D., "The Poly1305-AES Message-Authentication
Code", DOI 10.1007/11502760_3, Fast Software
Encryption pp. 32-49, 2005,
.
[RFC2119] Bradner, S., "Key words for use in RFCs to Indicate
Requirement Levels", BCP 14, RFC 2119,
DOI 10.17487/RFC2119, March 1997,
.
[RFC5116] McGrew, D., "An Interface and Algorithms for Authenticated
Encryption", RFC 5116, DOI 10.17487/RFC5116, January 2008,
.
[RFC6655] McGrew, D. and D. Bailey, "AES-CCM Cipher Suites for
Transport Layer Security (TLS)", RFC 6655,
DOI 10.17487/RFC6655, July 2012,
.
[RFC8174] Leiba, B., "Ambiguity of Uppercase vs Lowercase in RFC
2119 Key Words", BCP 14, RFC 8174, DOI 10.17487/RFC8174,
May 2017, .
[RFC8439] Nir, Y. and A. Langley, "ChaCha20 and Poly1305 for IETF
Protocols", RFC 8439, DOI 10.17487/RFC8439, June 2018,
.
9.2. Informative References
[GCM-MU] Hoang, V., Tessaro, S., and A. Thiruvengadam, "The Multi-
user Security of GCM, Revisited",
DOI 10.1145/3243734.3243816, Proceedings of the 2018 ACM
SIGSAC Conference on Computer and Communications Security,
January 2018, .
[I-D.ietf-quic-tls]
Thomson, M. and S. Turner, "Using TLS to Secure QUIC",
Work in Progress, Internet-Draft, draft-ietf-quic-tls-29,
9 June 2020, .
[NonceDisrespecting]
Bock, H., Zauner, A., Devlin, S., Somorovsky, J., and P.
Jovanovic, "Nonce-Disrespecting Adversaries -- Practical
Forgery Attacks on GCM in TLS", 17 May 2016,
.
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[RFC8446] Rescorla, E., "The Transport Layer Security (TLS) Protocol
Version 1.3", RFC 8446, DOI 10.17487/RFC8446, August 2018,
.
[TLS] Rescorla, E., "The Transport Layer Security (TLS) Protocol
Version 1.3", RFC 8446, DOI 10.17487/RFC8446, August 2018,
.
Authors' Addresses
Felix Günther
ETH Zurich
Email: mail@felixguenther.info
Martin Thomson
Mozilla
Email: mt@lowentropy.net
Christopher A. Wood
Cloudflare
Email: caw@heapingbits.net
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