ETSI TS 135 206 V15.0.0 (2018-11)

Universal Mobile Telecommunications System (UMTS); LTE; 3G Security; Specification of the MILENAGE algorithm set: An example algorithm set for the 3GPP authentication and key generation functions f1, f1*, f2, f3, f4, f5 and f5*; Document 2: Algorithm specification (3GPP TS 35.206 version 15.0.0 Release 15)

ETSI TS 135 206 V15.0.0 (2018-11)

Name:ETSI TS 135 206 V15.0.0 (2018-11)   Standard name:Universal Mobile Telecommunications System (UMTS); LTE; 3G Security; Specification of the MILENAGE algorithm set: An example algorithm set for the 3GPP authentication and key generation functions f1, f1*, f2, f3, f4, f5 and f5*; Document 2: Algorithm specification (3GPP TS 35.206 version 15.0.0 Release 15)
Standard number:ETSI TS 135 206 V15.0.0 (2018-11)   language:English language
Release Date:11-Nov-2018   technical committee:3GPP SA 3 - Security
Drafting committee:   ICS number:
ETSI TS 135 206 V15.0.0 (2018-11)






TECHNICAL SPECIFICATION
Universal Mobile Telecommunications System (UMTS);
LTE;
3G Security;
Specification of the MILENAGE algorithm set: An example
algorithm set for the 3GPP authentication and key generation
functions f1, f1*, f2, f3, f4, f5 and f5*;
Document 2: Algorithm specification
(3GPP TS 35.206 version 15.0.0 Release 15)

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3GPP TS 35.206 version 15.0.0 Release 15 1 ETSI TS 135 206 V15.0.0 (2018-11)



Reference
RTS/TSGS-0335206vf00
Keywords
LTE,SECURITY,UMTS
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3GPP TS 35.206 version 15.0.0 Release 15 2 ETSI TS 135 206 V15.0.0 (2018-11)
Intellectual Property Rights
Essential patents
IPRs essential or potentially essential to normative deliverables may have been declared to ETSI. The information
pertaining to these essential IPRs, if any, is publicly available for ETSI members and non-members, and can be found
in ETSI SR 000 314: "Intellectual Property Rights (IPRs); Essential, or potentially Essential, IPRs notified to ETSI in
respect of ETSI standards", which is available from the ETSI Secretariat. Latest updates are available on the ETSI Web
server (https://ipr.etsi.org/).
Pursuant to the ETSI IPR Policy, no investigation, including IPR searches, has been carried out by ETSI. No guarantee
can be given as to the existence of other IPRs not referenced in ETSI SR 000 314 (or the updates on the ETSI Web
server) which are, or may be, or may become, essential to the present document.
Trademarks
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ETSI claims no ownership of these except for any which are indicated as being the property of ETSI, and conveys no
right to use or reproduce any trademark and/or tradename. Mention of those trademarks in the present document does
not constitute an endorsement by ETSI of products, services or organizations associated with those trademarks.
Foreword
This Technical Specification (TS) has been produced by ETSI 3rd Generation Partnership Project (3GPP).
The present document may refer to technical specifications or reports using their 3GPP identities, UMTS identities or
GSM identities. These should be interpreted as being references to the corresponding ETSI deliverables.
The cross reference between GSM, UMTS, 3GPP and ETSI identities can be found under
.
Modal verbs terminology
In the present document "shall", "shall not", "should", "should not", "may", "need not", "will", "will not", "can" and
"cannot" are to be interpreted as described in clause 3.2 of the ETSI Drafting Rules (Verbal forms for the expression of
provisions).
"must" and "must not" are NOT allowed in ETSI deliverables except when used in direct citation.
ETSI

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3GPP TS 35.206 version 15.0.0 Release 15 3 ETSI TS 135 206 V15.0.0 (2018-11)
Contents
Intellectual Property Rights . 2
Foreword . 2
Modal verbs terminology . 2
Foreword . 4
Introduction . 4
0 The name "MILENAGE" . 5
1 Outline of the document . 5
1.1 References . 5
2 INTRODUCTORY INFORMATION . . 6
2.1 Introduction . 6
2.2 Notation . 6
2.2.1 Radix . 6
2.2.2 Conventions . 6
2.2.3 Bit/Byte ordering . 6
2.2.4 List of Symbols . 6
2.3 List of Variables . 7
2.4 Algorithm Inputs and Outputs . 7
3 The algorithm framework and the specific example algorithms . 8
4 Definition of the example algorithms . 9
4.1 Algorithm Framework . 9
4.2 Specific Example Algorithms. 9
5 Implementation considerations . 10
5.1 OP computed on or off the USIM? . 10
C
5.2 Customising the choice of block cipher . 10
5.3 Further customisation . 10
5.4 Resistance to side channel attacks . 11
Annex 1: Figure of the Algorithms . 12
Annex 2: Specification of the Block Cipher Algorithm Rijndael . 13
A2.1 Introduction . 13
A2.2 The State and External Interfaces of Rijndael . 13
A2.3 Internal Structure . 14
A2.4 The Byte Substitution Transformation . 14
A2.5 The Shift Row Transformation . 15
A2.6 The Mix Column Transformation . 15
A2.7 The Round Key addition . 16
A2.8 Key schedule . 16
A2.9 The Rijndael S-box . 17
Annex 3: Simulation Program Listing - Byte Oriented . 18
Annex 4: Rijndael Listing - 32-Bit Word Oriented . 25
Annex A (informative): Change history . 31
History . 32

ETSI

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3GPP TS 35.206 version 15.0.0 Release 15 4 ETSI TS 135 206 V15.0.0 (2018-11)
Foreword
rd
This Technical Specification (TS) has been produced by the 3 Generation Partnership Project (3GPP).
The contents of the present document are subject to continuing work within the TSG and may change following formal
TSG approval. Should the TSG modify the contents of the present document, it will be re-released by the TSG with an
identifying change of release date and an increase in version number as follows:
Version x.y.z
where:
x the first digit:
1 presented to TSG for information;
2 presented to TSG for approval;
3 or greater indicates TSG approved document under change control.
y the second digit is incremented for all changes of substance, i.e. technical enhancements, corrections,
updates, etc.
z the third digit is incremented when editorial only changes have been incorporated in the document.
Introduction
This document has been prepared by the 3GPP Task Force, and contains an example set of algorithms which may be
used as the authentication and key generation functions f1, f1*, f2, f3, f4, f5 and f5*. (It is not mandatory that the
particular algorithms specified in this document are used — all seven functions are operator-specifiable rather than
being fully standardised). This document is one five, which between them form the entire specification of the example
algorithms, entitled:
- 3GPP TS 35.205: "3rd Generation Partnership Project; Technical Specification Group Services and System
Aspects; 3G Security; Specification of the MILENAGE Algorithm Set: An example algorithm set for the 3GPP
authentication and key generation functions f1, f1*, f2, f3, f4, f5 and f5*;
Document 1: General".
- 3GPP TS 35.206: "3rd Generation Partnership Project; Technical Specification Group Services and System
Aspects; 3G Security; Specification of the MILENAGE Algorithm Set: An example algorithm set for the 3GPP
authentication and key generation functions f1, f1*, f2, f3, f4, f5 and f5*;
Document 2: Algorithm Specification".
- 3GPP TS 35.207: "3rd Generation Partnership Project; Technical Specification Group Services and System
Aspects; 3G Security; Specification of the MILENAGE Algorithm Set: An example algorithm set for the 3GPP
authentication and key generation functions f1, f1*, f2, f3, f4, f5 and f5*;
Document 3: Implementors' Test Data".
- 3GPP TS 35.208: "3rd Generation Partnership Project; Technical Specification Group Services and System
Aspects; 3G Security; Specification of the MILENAGE Algorithm Set: An example algorithm set for the 3GPP
authentication and key generation functions f1, f1*, f2, f3, f4, f5 and f5*;
Document 4: Design Conformance Test Data".
- 3GPP TR 35.909: "3rd Generation Partnership Project; Technical Specification Group Services and System
Aspects; 3G Security; Specification of the MILENAGE Algorithm Set: An example algorithm set for the 3GPP
authentication and key generation functions f1, f1*, f2, f3, f4, f5 and f5*;
Document 5: Summary and results of design and evaluation".
ETSI

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3GPP TS 35.206 version 15.0.0 Release 15 5 ETSI TS 135 206 V15.0.0 (2018-11)
0 The name "MILENAGE"
The name of this algorithm set is "MILENAGE". It should be pronounced like a French word — something like "mi-
le-nahj".
1 Outline of the document
Section 2 introduces the algorithms and describes the notation used in the subsequent sections.
Section 3 explains how the algorithms are designed as a framework in such a way that various "customising
components" can be selected in order to customise the algorithm for a particular operator.
Section 4 defines the example algorithms. The algorithm framework is defined in section 4.1; in section 4.2, specific
instances of the components are selected to define the specific example algorithm set.
Section 5 explains various options and considerations for implementation of the algorithms, including considerations to
be borne in mind when modifying the customising components.
Illustrative pictures are given in Annex 1. Annex 2 gives a specification of the block cipher algorithm which is used as a
cryptographic kernel in the definition of the example algorithms. Annexes 3 and 4 contain source code in the C
programming language: Annex 3 gives a complete and straightforward implementation of the algorithm set, while
Annex 4 gives an example of an alternative high-performance implementation just of the kernel function.
1.1 References
The following documents contain provisions which, through reference in this text, constitute provisions of the present
document.
- References are either specific (identified by date of publication, edition number, version number, etc.) or
non-specific.
- For a specific reference, subsequent revisions do not apply.
- For a non-specific reference, the latest version applies. In the case of a reference to a 3GPP document (including
a GSM document), a non-specific reference implicitly refers to the latest version of that document in the same
Release as the present document.
[1] 3GPP TS 33.102 v3.5.0: "3rd Generation Partnership Project; Technical Specification Group
Services and System Aspects; 3G Security; Security Architecture".
[2] 3GPP TS 33.105 v3.4.0: "3rd Generation Partnership Project; Technical Specification Group
Services and System Aspects; 3G Security; Cryptographic Algorithm Requirements".
[3] 3GPP TS 35.206: "3rd Generation Partnership Project; Technical Specification Group Services
and System Aspects; 3G Security; Specification of the MILENAGE Algorithm Set: An example
algorithm set for the 3GPP authentication and key generation functions f1, f1*, f2, f3, f4, f5 and
f5*; Document 2: Algorithm Specification" (this document).
[4] 3GPP TS 35.207: "3rd Generation Partnership Project; Technical Specification Group Services
and System Aspects; 3G Security; Specification of the MILENAGE Algorithm Set: An example
algorithm set for the 3GPP authentication and key generation functions f1, f1*, f2, f3, f4, f5 and
f5*; Document 3: Implementors' Test Data".
[5] 3GPP TS 35.208: "3rd Generation Partnership Project; Technical Specification Group Services
and System Aspects; 3G Security; Specification of the MILENAGE Algorithm Set: An example
algorithm set for the 3GPP authentication and key generation functions f1, f1*, f2, f3, f4, f5 and
f5*; Document 4: Design Conformance Test Data".
[6] Joan Daemen and Vincent Rijmen: "AES Proposal: Rijndael", available at
http://csrc.nist.gov/encryption/aes/round2/AESAlgs/Rijndael/Rijndael.pdf or
http://www.esat.kuleuven.ac.be/~rijmen/rijndael/rijndaeldocV2.zip
[7] http://csrc.nist.gov/encryption/aes/
ETSI

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3GPP TS 35.206 version 15.0.0 Release 15 6 ETSI TS 135 206 V15.0.0 (2018-11)
[8] Thomas S. Messerges, "Securing the AES finalists against Power Analysis Attacks", in FSE 2000,
Seventh Fast Software Encryption Workshop, ed. Schneier, Springer Verlag, 2000.
[9] P. C. Kocher, "Timing Attacks on Implementations of Diffie-Hellman, RSA, DSS, and Other
Systems", in CRYPTO'96, Lecture Notes in Computer Science #1109, Springer Verlag, 1996.
[10] J. Kelsey, B. Schneier, D. Wagner, C. Hall, "Side Channel Cryptanalysis of Product Ciphers", in
ESORICS'98, Lecture Notes in Computer Science #1485, Springer Verlag, 1998.
[11] L. Goubin, J. Patarin, "DES and differential power analysis", in CHES'99, Lecture Notes in
Computer Science #1717, Springer Verlag, 1999.
[12] P. Kocher, J. Jaffe, B. Jun, "Differential Power Analysis", in CRYPTO'99, Lecture Notes in
Computer Science #1666, Springer Verlag, 1999.
[13] L. Goubin, J.-S. Coron, "On boolean and arithmetic masking against differential power analysis",
in CHES'00, Lecture Notes in Computer Science series, Springer Verlag (to appear).
2 INTRODUCTORY INFORMATION
2.1 Introduction
Within the security architecture of the 3GPP system there are seven security functions f1, f1*, f2, f3, f4, f5 and f5*.
The operation of these functions falls within the domain of one operator, and the functions are therefore to be specified
by each operator rather than being fully standardised. The algorithms specified in this document are examples that may
be used by an operator who does not wish to design his own.
The inputs and outputs of all seven algorithms are defined in section 2.4.
2.2 Notation
2.2.1 Radix
We use the prefix 0x to indicate hexadecimal numbers.
2.2.2 Conventions
We use the assignment operator '=', as used in several programming languages. When we write
=
we mean that assumes the value that had before the assignment took place. For instance,
x = x + y + 3
means
(new value of x) becomes (old value of x) + (old value of y) + 3.
2.2.3 Bit/Byte ordering
All data variables in this specification are presented with the most significant bit (or byte) on the left hand side and the
least significant bit (or byte) on the right hand side. Where a variable is broken down into a number of substrings, the
leftmost (most significant) substring is numbered 0, the next most significant is numbered 1, and so on through to the
least significant.
2.2.4 List of Symbols
= The assignment operator.
⊕ The bitwise exclusive-OR operation
|| The concatenation of the two operands.
E[x] The result of applying a block cipher encryption to the input value x using the key k.
k
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3GPP TS 35.206 version 15.0.0 Release 15 7 ETSI TS 135 206 V15.0.0 (2018-11)
rot(x,r) The result of cyclically rotating the 128-bit value x by r bit positions towards the most significant
bit. If x = x[0] || x[1] || … x[127], and y = rot(x,r),
then y = x[r] || x[r+1] || … x[127] || x[0] || x[1] || x[r-1].
th
X[i] The i bit of the variable X. (X = X[0] || X[1] || X[2] || …. ).

2.3 List of Variables
AK a 48-bit anonymity key that is the output of either of the functions f5 and f5*.
AMF a 16-bit authentication management field that is an input to the functions f1 and f1*.
c1,c2,c3,c4,c5 128-bit constants, which are XORed onto intermediate variables.
CK a 128-bit confidentiality key that is the output of the function f3.
IK a 128-bit integrity key that is the output of the function f4.
IN1 a 128-bit value constructed from SQN and AMF and used in the computation of the functions f1
and f1*.
K a 128-bit subscriber key that is an input to the functions f1, f1*, f2, f3, f4, f5 and f5*.
MAC-A a 64-bit network authentication code that is the output of the function f1.
MAC-S a 64-bit resynchronisation authentication code that is the output of the function f1*.
OP a 128-bit Operator Variant Algorithm Configuration Field that is a component of the functions f1,
f1*, f2, f3, f4, f5 and f5*.
OP a 128-bit value derived from OP and K and used within the computation of the functions.
C
OUT1,OUT2,OUT3,OUT4,OUT5
128-bit computed values from which the outputs of the functions f1, f1*, f2, f3, f4, f5 and f5* are
obtained.
r1,r2,r3,r4,r5 integers in the range 0–127 inclusive, which define amounts by which intermediate variables are
cyclically rotated.
RAND a 128-bit random challenge that is an input to the functions f1, f1*, f2, f3, f4, f5 and f5*.
RES a 64-bit signed response that is the output of the function f2.
SQN a 48-bit sequence number that is an input to either of the functions f1 and f1*. (For f1* this input
is more precisely called SQN .)
MS
TEMP a 128-bit value used within the computation of the functions.

2.4 Algorithm Inputs and Outputs
The inputs to the algorithms are given in tables 1 and 2, the outputs in tables 3–9 below.
Table 1: inputs to f1 and f1*
Parameter Size (bits) Comment
K 128 Subscriber key K[0]…K[127]
RAND 128 Random challenge RAND[0]…RAND[127]
SQN 48 Sequence number SQN[0]…SQN[47]. (For f1* this input is
more precisely called SQNMS.)
AMF 16 Authentication management field AMF[0]…AMF[15]

Table 2: inputs to f2, f3, f4, f5 and f5*
Parameter Size (bits) Comment
K 128 Subscriber key K[0]…K[127]
RAND 128 Random challenge RAND[0]…RAND[127]

Table 3: f1 output
Parameter Size (bits) Comment
MAC-A 64 Network authentication code MAC-A[0]…MAC-A[63]

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3GPP TS 35.206 version 15.0.0 Release 15 8 ETSI TS 135 206 V15.0.0 (2018-11)
Table 4: f1* output
Parameter Size (bits) Comment
MAC-S 64 Resynch authentication code MAC-S[0]…MAC-S[63]

Table 5. f2 output
Parameter Size (bits) Comment
RES 64 Response RES[0]…RES[63]

Table 6. f3 output
Parameter Size (bits) Comment
CK 128 Confidentiality key CK[0]…CK[127]

Table 7. f4 output
Parameter Size (bits) Comment
IK 128 Integrity key IK[0]…IK[127]

Table 8. f5 output
Parameter Size (bits) Comment
AK 48 Anonymity key AK[0]…AK[47]

Table 9. f5* output
Parameter Size (bits) Comment
AK 48 Resynch anonymity key AK[0]…AK[47]

Note: Both f5 and f5* outputs are called AK according to reference [2]. In practice only one of them will be calculated
in each instance of the authentication and key agreement procedure.

3 The algorithm framework and the specific example
algorithms
The example algorithm set makes use of the following components:
- A block cipher encryption function, which takes a 128-bit input and a 128-bit key and returns a 128-bit output.
.
If the input is x, the key is k and the output is y, we write y = E[x]k
- A 128-bit value OP. This is an Operator Variant Algorithm Configuration Field, which the Task Force was
asked to include as a simple means to provide separation between the functionality of the algorithms when used
by different operators. It is left to each operator to select a value for OP. The algorithm set is designed to be
secure whether or not OP is publicly known; however, operators may see some advantage in keeping their value
of OP secret. This and other aspects of the use of OP are discussed further in section 5.
In the specific example algorithm set, a particular block cipher is used. But the algorithms have been designed so that
this component can be replaced by any operator who wishes to create his own customised algorithm set. In that sense
this document defines an algorithm framework, and the example algorithm set is one that fits within the framework.
This is how the algorithm set is defined in section 4: in section 4.1 the framework is defined in terms of the block
cipher, and then in section 4.2 a block cipher is selected to give a fully specified algorithm set.
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3GPP TS 35.206 version 15.0.0 Release 15 9 ETSI TS 135 206 V15.0.0 (2018-11)
4 Definition of the example algorithms
4.1 Algorithm Framework
A 128-bit value OPC is derived from OP and K as follows:
OP = OP ⊕ E[OP] .
C K

An intermediate 128-bit value TEMP is computed as follows:
TEMP = E[RAND ⊕ OPC]K.
A 128-bit value IN1 is constructed as follows:
IN1[0] . IN1[47] = SQN[0] . SQN[47]
IN1[48] . IN1[63] = AMF[0] . AMF[15]
IN1[64] . IN1[111] = SQN[0] . SQN[47]
IN1[112] . IN1[127] = AMF[0] . AMF[15]

Five 128-bit constants c1, c2, c3, c4, c5 are defined as follows:
c1[i] = 0 for 0 ≤ i ≤ 127
c2[i] = 0 for 0 ≤ i ≤ 127, except that c2[127] = 1
c3[i] = 0 for 0 ≤ i ≤ 127, except that c3[126] = 1
c4[i] = 0 for 0 ≤ i ≤ 127, except that c4[125] = 1
c5[i] = 0 for 0 ≤ i ≤ 127, except that c5[124] = 1
Five integers r1, r2, r3, r4, r5 are defined as follows:
r1 = 64; r2 = 0; r3 = 32; r4 = 64; r5 = 96

Five 128-bit blocks OUT1, OUT2, OUT3, OUT4, OUT5 are computed as follows:
OUT1 = E[TEMP ⊕ rot(IN1 ⊕ OPC, r1) ⊕ c1]K ⊕ OPC
OUT2 = E[rot(TEMP⊕ OPC, r2) ⊕ c2]K ⊕ OPC
OUT3 = E[rot(TEMP⊕ OP , r3) ⊕ c3] ⊕ OP
C K C
OUT4 = E[rot(TEMP⊕ OP , r4) ⊕ c4] ⊕ OP
C K C
OUT5 = E[rot(TEMP⊕ OPC, r5) ⊕ c5]K ⊕ OPC

The outputs of the various functions are then defined as follows:
Output of f1 = MAC-A, where MAC-A[0] . MAC-A[63] = OUT1[0] . OUT1[63]
Output of f1* = MAC-S, where MAC-S[0] . MAC-S[63] = OUT1[64] . OUT1[127]
Output of f2 = RES, where RES[0] . RES[63] = OUT2[64] . OUT2[127]
Output of f3 = CK, where CK[0] . CK[127] = OUT3[0] . OUT3[127]
Output of f4 = IK, where IK[0] . IK[127] = OUT4[0] . OUT4[127]
Output of f5 = AK, where AK[0] . AK[47] = OUT2[0] . OUT2[47]
Output of f5* = AK, where AK[0] . AK[47] = OUT5[0] . OUT5[47]

(The repeated reference to AK is not a mistake: AK is the name of the output of either f5 or f5*, and these two functions
will not in practice be computed simultaneously.)
4.2 Specific Example Algorithms
The specific example algorithm set is defined by specifying the block cipher encryption function E[], which we do in
this section. (It is left to each operator to specify the Operator Variant Algorithm Configuration Field OP.)
The block cipher selected is Rijndael [6]. This is the algorithm proposed as the Advanced Encryption Standard [7].
More precisely, it is Rijndael with 128-bit key and 128-bit block size.
E[x] = the result of applying the Rijndael encryption algorithm
k
 to the 128-bit value x under the 128-bit key k.
Although the definitive specification of Rijndael is in [6], a complete specification of Rijndael with 128-bit key and
128-bit block size is also given in Annex 2 of this document.
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3GPP TS 35.206 version 15.0.0 Release 15 10 ETSI TS 135 206 V15.0.0 (2018-11)
The inputs to and output of Rijndael are defined as strings of bytes. The 128-bit string x = x[0] || x[1] || … x[127] is
treated as a string of bytes by taking x[0] || x[1] || … x[7] as the first byte, x[8] || x[9] || … x[15] as the second byte, and
so on. The key and output string are converted in the same way.
Note that the following patent statement has been made publicly (and included in [6]) by the authors of the Rijndael
algorithm: "Rijndael or any of its implementations is not and will not be subject to patents."
5 Implementation considerations
5.1 OP computed on or off the USIM?
C
Recall that OP is an Operator Variant Algorithm Configuration Field. It is expected that each operator will define a
value of OP which will then be used for al
...

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