ISO/IEC 9797-3:2011

INTERNATIONAL ISO/IEC
STANDARD 9797-3
First edition
2011-11-15
Information technology — Security
techniques — Message Authentication
Codes (MACs) —
Part 3:
Mechanisms using a universal hash-
function
Technologies de l'information — Techniques de sécurité — Codes
d'authentification de message (MAC) —
Partie 3: Mécanismes utilisant une fonction de hachage universelle

Reference number
©
ISO/IEC 2011
©  ISO/IEC 2011
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ii © ISO/IEC 2011 – All rights reserved

Contents Page
Foreword . iv
Introduction . v
1  Scope . 1
2  Normative references . 1
3  Terms and definitions . 1
4  Symbols and abbreviated terms . 2
5  General model . 4
6  Mechanisms . 5
6.1  Introduction . 5
6.2  UMAC . 5
6.2.1  Description of UMAC . 5
6.2.2  Requirements . 5
6.2.3  Notation and auxiliary functions . 5
6.2.4  Key preprocessing . 9
6.2.5  Message preprocessing. 9
6.2.6  Message hashing . 9
6.2.7  Layered hash-functions . 10
6.2.8  Finalization . 12
6.3  Badger . 12
6.3.1  Description of Badger . 12
6.3.2  Requirements . 12
6.3.3  Notation and auxiliary functions . 13
6.3.4  Key preprocessing . 13
6.3.5  Message preprocessing. 14
6.3.6  Message hashing . 14
6.3.7  Finalization . 16
6.4  Poly1305-AES . 16
6.4.1  Description of Poly1305-AES . 16
6.4.2  Requirements . 16
6.4.3  Key preprocessing . 16
6.4.4  Message preprocessing. 16
6.4.5  Message hashing . 17
6.4.6  Finalization . 17
6.5  GMAC . 18
6.5.1  Description of GMAC . 18
6.5.2  Requirements . 18
6.5.3  Notation and auxiliary functions . 18
6.5.4  Key preprocessing . 19
6.5.5  Message preprocessing. 19
6.5.6  Message hashing . 19
6.5.7  Finalization . 19
Annex A (normative) Object Identifiers . 20
Annex B (informative) Test Vectors . 22
Annex C (informative) Security Information . 24
Bibliography . 25

© ISO/IEC 2011 – All rights reserved iii

Foreword
ISO (the International Organization for Standardization) and IEC (the International Electrotechnical
Commission) form the specialized system for worldwide standardization. National bodies that are members of
ISO or IEC participate in the development of International Standards through technical committees
established by the respective organization to deal with particular fields of technical activity. ISO and IEC
technical committees collaborate in fields of mutual interest. Other international organizations, governmental
and non-governmental, in liaison with ISO and IEC, also take part in the work. In the field of information
technology, ISO and IEC have established a joint technical committee, ISO/IEC JTC 1.
International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2.
The main task of the joint technical committee is to prepare International Standards. Draft International
Standards adopted by the joint technical committee are circulated to national bodies for voting. Publication as
an International Standard requires approval by at least 75 % of the national bodies casting a vote.
Attention is drawn to the possibility that some of the elements of this document may be the subject of patent
rights. ISO and IEC shall not be held responsible for identifying any or all such patent rights.
ISO/IEC 9797-3 was prepared by Joint Technical Committee ISO/IEC JTC 1, Information technology,
Subcommittee SC 27, IT Security techniques.
ISO/IEC 9797 consists of the following parts, under the general title Information technology — Security
techniques — Message Authentication Codes (MACs):
 Part 1: Mechanisms using a block cipher
 Part 2: Mechanisms using a dedicated hash-function
 Part 3: Mechanisms using a universal hash-function
iv © ISO/IEC 2011 – All rights reserved

Introduction
In an IT environment, it is often required that one can verify that electronic data has not been altered in an
unauthorized manner and that one can provide assurance that a message has been originated by an entity in
possession of the secret key. A MAC (Message Authentication Code) algorithm is a commonly used data
integrity mechanism that can satisfy these requirements.
This part of ISO/IEC 9797 specifies four MAC algorithms using universal hash-functions: UMAC, Badger,
Poly1305-AES and GMAC.
These mechanisms can be used as data integrity mechanisms to verify that data has not been altered in an
unauthorized manner. They can also be used as message authentication mechanisms to provide assurance
that a message has been originated by an entity in possession of the secret key. The strength of the data
integrity mechanism and message authentication mechanism is dependent on the length (in bits) and secrecy
of the key, on the length (in bits) of a hash-code produced by the hash-function, on the strength of the hash-
function, on the length (in bits) of the MAC, and on the specific mechanism.
[7]
NOTE A general framework for the provision of integrity services is specified in ISO/IEC 10181-6 .
© ISO/IEC 2011 – All rights reserved v

INTERNATIONAL STANDARD ISO/IEC 9797-3:2011(E)

Information technology — Security techniques — Message
Authentication Codes (MACs) —
Part 3:
Mechanisms using a universal hash-function
1 Scope
This part of ISO/IEC 9797 specifies the following MAC algorithms that use a secret key and a universal
hash-function with an n-bit result to calculate an m-bit MAC based on the block ciphers specified in
ISO/IEC 18033-3 and the stream ciphers specified in ISO/IEC 18033-4:
a) UMAC;
b) Badger;
c) Poly1305-AES;
d) GMAC.
2 Normative references
The following referenced documents are indispensable for the application of this document. For dated
references, only the edition cited applies. For undated references, the latest edition of the referenced
document (including any amendments) applies.
ISO/IEC 9797-1, Information technology — Security techniques — Message Authentication Codes (MACs) —
Part 1: Mechanisms using a block cipher
ISO/IEC 18031, Information technology — Security techniques — Random bit generation
ISO/IEC 18033-3, Information technology — Security techniques — Encryption algorithms — Part 3: Block
ciphers
ISO/IEC 18033-4, Information technology — Security techniques — Encryption algorithms — Part 4: Stream
ciphers
3 Terms and definitions
For the purposes of this document, the terms and definitions given in ISO/IEC 9797-1 and the following apply.
3.1
empty string
string of symbols of length zero
© ISO/IEC 2011 – All rights reserved 1

3.2
key
sequence of symbols that controls the operation of a cryptographic transformation
3.3
nonce
number used once
3.4
prime number
positive integer greater than 1 which has no integer divisors other than 1 and itself
3.5
tag
result of a MAC algorithm, adjoined to a possibly encrypted message to provide integrity protection
3.6
universal hash-function
function mapping strings of bits to fixed-length strings of bits, indexed by a parameter called the key, satisfying
the property that for all distinct inputs, the probability over all keys that the outputs collide is small
[4]
NOTE Universal hash-functions were introduced by Carter and Wegman , and their application in MAC algorithms
[10]
was first described by Wegman and Carter .
4 Symbols and abbreviated terms
The following notation is used in this part of ISO/IEC 9797:
th
bit(S,n) Returns the integer 1 if the n bit of the string S is 1, otherwise returns the integer 0 (indices
begin at 1).
bitlength(S) Length of a string S in bits.
bitstr2uint(S) The non-negative integer whose binary representation is the string S. More formally, if S is t
t-1 t-2 1
bits long then bitstr2uint(S) = 2 * bit(S,1) + 2 * bit(S,2) + . + 2 * bit(S,t-1) + bit(S,t).
NOTE Bit strings are treated big-endian, i.e. the first bit is the most significant.
blocklen Block length of the underlying block cipher in octets.
ceil Rounding-up operation, i.e. if x is a floating-point number, then ceil(x) is the smallest integer n
with n  x.
Enc(K, X) Encryption of a plaintext block X under a key K using a block cipher Enc.
floor Rounding-down operation, i.e. if x is a floating-point number, then floor(x) is the largest integer
n with n  x.
H Hash value.
K Master key.
...