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Properties of AEAD algorithms
CryptoPro
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General
Network Working Group
authenticated encryption, mode of operation, AEAD, properties
Authenticated Encryption with Associated Data (AEAD) algorithms provide confidentiality and integrity of data. The extensive use of AEAD algorithms in various highlevel applications has caused the need for AEAD algorithms with additional properties and motivated research in the area. This document gives definitions for the most common of those properties intending to improve consistency in the field.
Introduction
An Authenticated Encryption with Associated Data (AEAD) algorithm is an extension of authenticated encryption, which provides confidentiality for the plaintext to be encrypted and integrity for the plaintext and some Associated Data (sometimes called Header). AEAD algorithms are used in numerous applications and have become an important field in cryptographic research.
Background
AEAD algorithms are formally defined in . The main benefit of AEAD algorithms is that they provide data confidentiality and integrity and have a simple unified interface.
The importance of the AEAD algorithms is mainly explained by their exploitation simplicity: they have a unified interface, easytounderstand security guarantees, and are much easier to implement properly than MAC and encryption schemes separately. Therefore, their embedding into highlevel schemes and protocols is highly transparent since, for example, there is no need for additional key derivation procedures. Apart from that, when using the AEAD algorithm, it is possible to reduce the key and state sizes and improve the data processing speed. For instance, such algorithms are mandatory for TLS 1.3 , IPsec ESP , and QUIC . Hence, the research and standardization efforts in the field are extremely active. Most AEAD algorithms usually come with security guarantees, formal proofs, usage guidelines, and reference implementations.
Even though providing core properties of AEAD algorithms is enough for many applications, some environments require other unusual cryptographic properties, which commonly require additional analysis and research. With the growing number of such properties and research papers, misunderstanding and confusion inevitably appear. Some properties might be understood in different ways; for some, only nontrivial formal security notions are provided, while others require modification or extension of the standard AEAD interface to support additional functionality. Therefore, the risk of misuse of AEAD algorithms increases, which can lead to security issues.
Scope
In the following document, we provide a short overview of the most common properties of AEAD algorithms by giving highlevel definitions of these properties in . The document aims to improve clarity and establish a common language in the field.
Conventions Used in This Document
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 when, and only when, they appear in all capitals, as shown here.
AEAD algorithms
This section gives a general definition of an AEAD algorithm following .
Definition. An AEAD algorithm is defined by two operations, which are authenticated encryption and authenticated decryption:

A deterministic operation of authenticated encryption has four inputs, each a binary string: a secret key K of a fixed bit length, a nonce N, associated data A, and a plaintext P. The plaintext contains the data to be encrypted and authenticated, and the associated data contains the data to be authenticated only. Each nonce value must be unique in every distinct invocation of the operation for any particular value of the key. The authenticated encryption operation outputs a ciphertext C.

A deterministic operation of authenticated decryption has four inputs, each a binary string: a secret key K of a fixed bit length, a nonce N, associated data A, and a ciphertext C. The operation verifies the integrity of the ciphertext and associated data and decrypts the ciphertext. It returns a special symbol FAIL if the inputs are not authentic; otherwise, the operation returns a plaintext P.
For more details on AEAD definition, please refer to .
Throughout this document, by default, we will consider noncebased AEAD algorithms, which have an interface from the definition above, and give no other restrictions on their structure. However, some properties defined in the document apply only to particular classes of such algorithms, like block cipherbased AEAD algorithms (such algorithms use block cipher as a building block). If that is the case, we explicitly point that out in the corresponding section. Some other properties, on the contrary, are defined for algorithms with extended or completely different interfaces. We address that issue in .
We will call an AEAD algorithm secure if it provides such properties as Confidentiality and Data integrity, defined in , against any active noncerespecting adversary. Even though we aim to give highlevel definitions, we sometimes use the advantage notion. Specifically, we will use the Authenticated Encryption advantage notion. We adopt the corresponding definition from .
Definition. Authenticated Encryption advantage is the probability of an active adversary succeeding in breaking the authenticatedencryption properties of the AEAD algorithm. In this document, the definition of authenticated encryption advantage roughly is the probability that an attacker successfully distinguishes the ciphertext outputs of the AEAD scheme from the outputs of a random function or is able to forge a ciphertext that will be accepted as valid.
AEAD properties
Classification of AEAD properties
In this document we use a highlevel classification of additional properties. The classification aims to give an intuition on how one can benefit from the property. The additional properties fall into one of these three categories:

Security properties. We say that the property is a security property if it considers new threats or adversarial capabilities, in addition to those of the usual noncerespecting adversary, which aims to break confidentiality or data integrity.

Implementation properties. We say that the property is an implementation property if it allows for more efficient implementations of the AEAD algorithm in special cases or environments.

Additional functionality properties. We say that the property is an additional functionality property if it provides new features in addition to the regular authenticated encryption with associated data.
We notice that the distinction between the security and additional functionality properties might be vague. The convention in this document is that additional functionality requires some extension of the standard AEAD interface. In fact, each additional functionality property defines a new class of algorithms, which is not a subclass of regular AEAD. Hence, the basic threats and adversarial capabilities must be redefined for each of these classes. As a result, additional functionality properties consider the basic threats and adversarial capabilities for their class of algorithms and, in contrast to security properties, not the extended ones.
Base properties
Confidentiality
Definition. An AEAD algorithm guarantees that the plaintext is available only to those authorized to obtain it, i.e., those possessing the secret key. That property is required for the AEAD algorithm to be called secure.
Synonyms. Privacy.
Further reading. ,
Data integrity
Definition. An AEAD algorithm guarantees that the plaintext and the associated data have not been changed or forged by those not authorized to, i.e., those not possessing the secret key. That property is required for the AEAD algorithm to be called secure.
Synonyms. Message authentication.
Further reading. ,
Security properties
Blockwise security
Definition. An AEAD algorithm provides security even if an adversary can adaptively choose the next block of the plaintext depending on already computed ciphertext blocks during an encryption operation.
Note. The case when an adversary can adaptively choose the next block of the ciphertext depending on already computed blocks of the plaintext, which appear in the device memory before the integrity verification during the decryption, can also be considered. This case is strongly related to RUP security, defined in .
Further reading. ,
Key Dependent Messages (KDM) security
Definition. An AEAD algorithm provides security even when keydependent plaintexts are encrypted.
Notes. KDM security is achievable only if nonces are chosen randomly and associated data is keyindependent.
Further reading.
Key commitment
Definition. An AEAD algorithm guarantees that it is difficult to find a tuple of the nonce, associated data, and ciphertext such that it can be decrypted correctly with more than one key.
Synonyms. Keyrobustness, key collision resistance.
Further reading. , ,
Leakage resistance
Definition. An AEAD algorithm provides security even if some additional information about computations of an encryption (and possibly decryption) operation is obtained via sidechannel leakages.
Further reading. ,
Multiuser security
Definition. An AEAD algorithm Authenticated Encryption advantage increases sublinearly in the number of users.
Further reading.
Nonce misuse
Definition. An AEAD algorithm provides security (resilience or resistance) even if an adversary can repeat nonces in its encryption queries. Nonce misuse resilience and resistance are defined as follows:

Nonce misuse resilience. Security is provided only for messages encrypted with unique nonces.

Nonce misuse resistance. Security is provided for all messages.
Further reading. ,
Noncehiding
Definition. An AEAD algorithm decryption operation doesn't require the nonce to perform decryption and provides privacy for the nonce value used for encryption.
Note. In noncehiding AEAD algorithms, the ciphertext contains information equivalent to an encrypted nonce. Hence, retrieving information about nonce from the ciphertext has to be difficult.
Further reading.
Reforgeability resilience
Definition. An AEAD algorithm guarantees that once a successful forgery for the algorithm has been found, it is still hard to find any subsequent forgery.
Further reading. ,
Release of unverified plaintext (RUP) security
Definition. An AEAD algorithm provides security even if the plaintext is released for every ciphertext, including those with failed integrity verification.
Further reading.
Implementation properties
Inversefree
Definition. A block cipherbased AEAD algorithm can be securely implemented without evaluating the block cipher inverse.
Lightweight
Definition. An AEAD algorithm can be efficiently and securely implemented on resourceconstrained devices. In particular, it meets the criteria required in the NIST Lightweight Cryptography competition .
Further reading.
Online
Definition. An AEAD algorithm encryption (decryption) operation can be implemented with a constant memory and a single onedirection pass over the plaintext (ciphertext), writing out the result during that pass.
Further reading.
Parallelizable
Definition. An AEAD algorithm can fully exploit the parallel computation infrastructure.
Synonyms. Pipelineable.
Further reading.
Single pass
Definition. An AEAD algorithm encryption (decryption) operation can be implemented with a single pass over the plaintext (ciphertext).
Static Associated Data
Definition. An AEAD algorithm allows precomputation for static (or repeating) associated data so that static AD doesn't significantly contribute to the computational cost of encryption.
ZKfriendly
Definition. An AEAD algorithm operates on binary and prime fields with a low number of nonlinear operations (often called multiplicative complexity). Thus, it allows efficient implementation using a domainspecific language (DSL) for writing zkSNARKs circuits.
Synonyms. ZKfocused, Arithmetizationoriented, Low Multiplicative Complexity
Further reading.
Additional functionality properties
Incremental
Definition. An AEAD algorithm allows encrypting and authenticating a message (associated data and a plaintext pair), which only partly differs from some previous message, faster than processing it from scratch.
Further reading. , ,
Remotelykeyed
Definition. An AEAD algorithm can be implemented with most of the operations in encryption/decryption performed by an insecure (i.e., it leaks all intermediate values) device, which has no access to the key, while another secure device performs operations involving the key.
Further reading. ,
Robust
Definition. An AEAD algorithm allows the user to choose an arbitrary value l >= 0 for every plaintext and then encrypts it into a ciphertext, which is l bits longer.
Further reading.
Security Considerations
This document defines the properties of AEAD algorithms. However, the document does not describe any concrete mechanisms providing these properties, neither it describes how to achieve them. In fact, one can claim that an AEAD algorithm provides any of the defined properties only if its analysis in the relevant models was carried out.
IANA Considerations
This document has no IANA actions.
References
Normative References
Informative References
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