ISO/IEC 18033-4:2011/Amd 1:2020

INTERNATIONAL ISO/IEC
STANDARD 18033-4
Second edition
2011-12-15
AMENDMENT 1
2020-08
Information technology —
Security techniques — Encryption
algorithms —
Part 4:
Stream ciphers
AMENDMENT 1: ZUC
Technologies de l'information — Techniques de sécurité —
Algorithmes de chiffrement —
Partie 4: Chiffrements en flot
AMENDEMENT 1: ZUC
Reference number
ISO/IEC 18033-4:2011/Amd.1:2020(E)
©
ISO/IEC 2020
ISO/IEC 18033-4:2011/Amd.1:2020(E)

© ISO/IEC 2020
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ii © ISO/IEC 2020 – All rights reserved

ISO/IEC 18033-4:2011/Amd.1:2020(E)

Foreword
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© ISO/IEC 2020 – All rights reserved iii

ISO/IEC 18033-4:2011/Amd.1:2020(E)
Information technology — Security techniques —
Encryption algorithms —
Part 4:
Stream ciphers
AMENDMENT 1: ZUC
Introduction
Change the last paragraph as follows:
This document includes six dedicated keystream generators:
— MUGI keystream generator;
— SNOW 2.0 keystream generator;
— Rabbit keystream generator;
v2
— Decim keystream generator;
— KCipher-2 (K2) keystream generator; and
— ZUC keystream generator.
4.1
Add the following symbols:
L Linear transform with index 1 used for ZUC.
L Linear transform with index 2 used for ZUC.
SS Subfunction used for ZUC.
SUB1 Lookup table with index 1 used for ZUC.
SUB2 Lookup table with index 2 used for ZUC.

8.6
Add new subclause 8.6 as follows:
8.6  ZUC keystream generator
8.6.1  Introduction to ZUC
ZUC is a keystream generator which uses as input a 128-bit secret key K and a 128-bit initialization
vector IV. These are used to initialize state variables S (i ≥ 0). The bit/byte order is big-endian, i.e., if
i
the key and initialization vector are given as a sequence of bits/bytes, the first/leftmost bit/byte is the
© ISO/IEC 2020 – All rights reserved 1

ISO/IEC 18033-4:2011/Amd.1:2020(E)

most significant bit/byte of the corresponding data. It outputs a 32-bit keystream Z at every iteration
i
of the function Strm.
The state variable S consists of two components. The first consists of sixteen 31-bit variables:
i
(i) (i) (i) (i)
A = (A , A , …., A ),
15 14 0
and maintains the state of a linear feedback shift register. The second consists of two 32-bit variables:
(i) (i) (i)
R = (R , R ),
2 1
that maintains the state of a finite state machine. ZUC is summarised in Figure 15, which shows a
snapshot if its operation, at time i, omitting the time-dependent variable (i) from the notation.
Figure 15 — Schematic drawing of ZUC
The Init function, defined in detail in 8.6.2, takes as input the 128-bit key K and the 128-bit initialization
(0) (0)
vector IV, and produces the initial value of the state variable S = (A , R ).
(i) (i)
The Next function, defined in detail in 8.6.3, takes as input the state variable S = (A , R ) and produces
i
(i+1) (i+1)
as output the next value of the state variable S = (A , R ). The Next function runs in two modes,
i+1
depending on whether the iteration performed is part of the initialization mode or of the normal mode
of generating output.
(i) (i)
The Strm function, defined in detail in 8.6.4, takes as input the state variable S = (A , R ) and produces
i
as output the 32-bit keystream Z .
i
NOTE See document [20] for theoretical background on the design rationale for ZUC.
2 © ISO/IEC 2020 – All rights reserved

ISO/IEC 18033-4:2011/Amd.1:2020(E)

A 240-bit constant D = d || d || … || d used in ZUC:
0 1 15
d = 100010011010111, d = 010011010111100, d = 110001001101011, d = 001001101011110,
0 1 2 3
d = 101011110001001, d = 011010111100010, d = 111000100110101, d = 000100110101111,
4 5 6 7
d = 100110101111000, d = 010111100010011, d = 110101111000100, d = 001101011110001,
8 9 10 11
d = 101111000100110, d = 011110001001101, d = 111100010011010, d = 100011110101100,
12 13 14 15
where for i = 0, 1, …, 15, d is a 15-bit variable in binary notation.
i
The description uses notations defined in Clause 4 of this part of ISO/IEC 18033. For a string A which
has at least 16 bits, the notation A represents the leftmost 16 bits of A and the notation A represents
H L
the rightmost 16 bits of A. For example, if A = 1000100110111110111110101111001 is a 31-bit string,
then A =1000100110111110 and A = 0111110101111001.
H L
8.6.2  Initialization function Init
The Initialization function Init is as follows.
Input: 128-bit key K, 128-bit initialization vector IV.
(0) (0)
Output: Initial value of state variable S = (A , R ).
a) Initialize the state variable S with the key K, the 128-bit initialization vector IV and the constant D.
-33
— Set (k , k , …, k ) = K; (iv , iv , …, iv ) = IV, where k and iv are bytes for i = 0, 1, …, 15.
0 1 15 0 1 15 i i
(-33)
— Set A = k || d || iv for i = 0, 1, …, 15.
i i i i
(-33) (-33) (32)
— Set R = R = 0
1 2 .
32 32
b) Set S = Next (S , INIT), where Next denotes 32 iterations of the Next function.
-1 -33
c) Set S = Next(S , null).
0 -1
d) Output S .
8.6.3  Next-state function Next
The Next function has two modes, and is defined as follows.
(i) (i)
Input: State variable S = (A , R ), mode ∈ {INIT, null}.
i
(i+1) (i+1)
Output: Next value of the state variable S = (A , R ).
i+1
Local variables: 32-bit strings W, W , W , X , X , X and 31-bit string V.
1 2 0 1 2
(i) (i) (i) (i) (i) (i)
a) Set X = A || A ; X = A || A ; X = A || A .
0 15 H 14 L 1 11 L 9 H 2 7 L 5 H
(i) (i) (i) (i) (i+1) (i+1)
b) Set W = (X ⊕ R ) + R ; W = R + X ; W = R ⊕ X ; R = SS(L (W || W )); R
0 1 32 2 1 1 32 1 2 2 2 1 1 1L 2H 2
=SS(L (W || W )).
2 2L 1H
15 (i) 17 (i) 21 (i) 20 (i) 8 (i) 31
c) Set V = 2 A + 2 A + 2 A + 2 A + (1+2 )A mod (2 -1).
15 13 10 4 0
(i+1) 31 (i+1) (i+1)
d) If mode = INIT, set A = V + (31~W) mod (2 -1). Otherwise, set A = V. If A = 0, set
15 15 15
(i+1) 31
A = 2 -1.
(i+1) (i)
e) Set A = A for j = 0, 1, …, 14.
j j+1
(i+1) (i+1)
f) Set S = (A , R ).
i+1
g) Output S .
i+1
© ISO/IEC 2020 – All rights reserved 3

ISO/IEC 18033-4:2011/Amd.1:2020(E)

i 31 31 i j
NOTE For two 31-bit stings a and b, if b = 2 , then ab mod (2 -1) = a <<< i mod (2 - 1); if b = 2 +2 , then ab
31 31
mod (2 -1) = (a <<< i) + (a <<< j) mod (2 - 1). Reference C code for ZUC is given in document [21].
31 31
8.6.4  Keystream function Strm
The keystream function Strm is as follows:
Input: State variable S .
i
Output: 32-bit keystream Z .
i
Local variables: 32-bit strings X , X .
0 3
(i) (i) (i) (i)
a) Set X = A || A ; X = A || A .
0 15 H 14 L 3 2 L 0 H
(i) (i)
b) Set Z = ((X ⊕ R ) + R ) ⊕ X .
i 0 1 32 2 3
c) Output Z .
i
8.6.5  Function SS
The function SS is as follows:
Input: 32-bit string X.
Output: 32-bit string Y.
— Define X = x || x || x || x , where x is a byte for i = 0, 1, 2, 3.
3 2 1 0 i
— Set Y = SUB1[x ] || SUB2[x ] || SUB1[x ] || SUB2[x ].
3 2 1 0
— Output Y.
The functions SUB1 and SUB2 are defined by the following substitution tables:
SUB1 [256] = {
0x3e,0x72,0x5b,0x47,0xca,0xe0,0x00,0x33,0x04,0xd1,0x54,0x98,0x09,0xb9,0x6d,0xcb,
0x7b,0x1b,0xf9,0x32,0xaf,0x9d,0x6a,0xa5,0xb8,0x2d,0xfc,0x1d,0x08,0x53,0x03,0x90,
0x4d,0x4e,0x84,0x99,0xe4,0xce,0xd9,0x91,0xdd,0xb6,0x85,0x48,0x8b,0x29,0x6e,0xac,
0xcd,0xc1,0xf8,0x1e,0x73,0x43,0x69,0xc6,0xb5,0xbd,0xfd,0x39,0x63,0x20,0xd4,0x38,
0x76,0x7d,0xb2,0xa7,0xcf,0xed,0x57,0xc5,0xf3,0x2c,0xbb,0x14,0x21,0x06,0x55,0x9b,
0xe3,0xef,0x5e,0x31,0x4f,0x7f,0x5a,0xa4,0x0d,0x82,0x51,0x49,0x5f,0xba,0x58,0x1c,
0x4a,0x16,0xd5,0x17,0xa8,0x92,0x24,0x1f,0x8c,0xff,0xd8,0xae,0x2e,0x01,0xd3,0xad,
0x3b,0x4b,0xda,0x46,0xeb,0xc9,0xde,0x9a,0x8f,0x87,0xd7,0x3a,0x80,0x6f,0x2f,0xc8,
0xb1,0xb4,0x37,0xf7,0x0a,0x22,0x13,0x28,0x7c,0xcc,0x3c,0x89,0xc7,0xc3,0x96,0x56,
0x07,0xbf,0x7e,0xf0,0x0b,0x2b,0x97,0x52,0x35,0x41,0x79,0x61,0xa6,0x4c,0x10,0xfe,
0xbc,0x26,0x95,0x88,0x8a,0xb0,0xa3,0xfb,0xc0,0x18,0x94,0xf2,0xe1,0xe5,0xe9,0x5d,
0xd0,0xdc,0x11,0x66,0x64,0x5c,0xec,0x59,0x42,0x75,0x12,0xf5,0x74,0x9c,0xaa,0x23,
0x0e,0x86,0xab,0xbe,0x2a,0x02,0xe7,0x67,0xe6,0x44,0xa2,0x6c,0xc2,0x93,0x9f,0xf1,
0xf6,0xfa,0x36,0xd2,0x50,0x68,0x9e,0x62,0x71,0x15,0x3d,0xd6,0x40,0xc4,0xe2,0x0f,
0x8e,0x83,0x77,0x6b,0x25,0x05,0x3f,0x0c,0x30,0xea,0x70,0xb7,0xa1,0xe8,0xa9,0x65,
0x8d,0x27,0x1a,0xdb,0x81,0xb3,0xa0,0xf4,0x45,0x7a,0x19,0xdf,0xee,0x78,0x34,0x60};

SUB2 [256] = {
0x55,0xc2,0x63,0x71,0x3b,0xc8,0x47,0x86,0x9f,0x3c,0xda,0x5b,0x29,0xaa,0xfd,0x77,
0x8c,0xc5,0x94,0x0c,0xa6,0x1a,0x13,0x00,0xe3,0xa8,0x16,0x72,0x40,0xf9,0xf8,0x42,
0x44,0x26,0x68,0x96,0x81,0xd9,0x45,0x3e,0x10,0x76,0xc6,0xa7,0x8b,0x39,0x43,0xe1,
0x3a,0xb5,0x56,0x2a,0xc0,0x6d,0xb3,0x05,0x22,0x66,0xbf,0xdc,0x0b,0xfa,0x62,0x48,
0xdd,0x20,0x11,0x06,0x36,0xc9,0xc1,0xcf,0xf6,0x27,0x52,0xbb,0x69,0xf5,0xd4,0x87,
0x7f,0x84,0x4c,0xd2,0x9c,0x57,0xa4,0xbc,0x4f,0x9a,0xdf,0xfe,0xd6,0x8d,0x7a,0xeb,
0x2b,0x53,0xd8,0x5c,0xa1,0x14,0x17,0xfb,0x23,0xd5,0x7d,0x30,0x67,0x73,0x08,0x09,
0xee,0xb7,0x70,0x3f,0x61,0xb2,0x19,0x8e,0x4e,0xe5,0x4b,0x93,0x8f,0x5d,0xdb,0xa9,
0xad,0xf1,0xae,0x2e,0xcb,0x0d,0xfc,0xf4,0x2d,0x46,0x6e,0x1d,0x97,0xe8,0xd1,0xe9,
0x4d,0x37,0xa5,0x75,0x5e,0x83,0x9e,0xab,0x82,0x9d,0xb9,0x1c,0xe0,0xcd,0x49,0x89,
0x01,0xb6,0xbd,0x58,0x24,0xa2,0x5f,0x38,0x78,0x99,0x15,0x90,0x50,0xb8,0x95,0xe4,
0xd0,0x91,0xc7,0xce,0xed,0x0f,0xb4,0x6f,0xa0,0xcc,0xf0,0x02,0x4a,0x79,0xc3,0xde,
0xa3,0xef,0xea,0x51,0xe6,0x6b,0x18,0xec,0x1b,0x2c,0x80,0xf7,0x74,0xe7,0xff,0x21,
0x5a,0x6a,0x54,0x1e,0x41,0x31,0x92,0x35,0xc4,0x33,0x07,0x0a,0xba,0x7e,0x0e,0x34,
4 © ISO/IEC 2020 – All rights reserved

ISO/IEC 18033-4:2011/Amd.1:2020(E)

0x88,0xb1,0x98,0x7c,0xf3,0x3d,0x60,0x6c,0x7b,0xca,0xd3,0x1f,0x32,0x65,0x04,0x28,
0x64,0xbe,0x85,0x9b,0x2f,0x59,0x8a,0xd7,0xb0,0x25,0xac,0xaf,0x12,0x03,0xe2,0xf2}.

8.6.6  Linear transforms L and L
1 2
Both L and L are linear transforms of 32-bit strings, defined as follows:
1 2
L (X) = X ⊕ (X <<< 2) ⊕ (X <<< 10) ⊕ (X <<< 18) ⊕ (X <<< 24),
1 32 32 32 32
L (X) = X ⊕ (X <<< 8) ⊕ (X <<< 14) ⊕ (X <<< 22) ⊕ (X <<< 30).
2 32 32 32 32
Annex A
Replace the object identifiers in Annex A as follows:
EncryptionAlgorithms-4 {
iso(1) standard(0) encryption-algorithms(18033) part(4)
asn1-module(0) algorithm-object-identifiers(0) }
DEFINITIONS EXPLICIT TAGS ::= BEGIN

-- EXPORTS All; --
-- IMPORTS None; --
OID ::= OBJECT IDENTIFIER -- Alias

-- Synonyms --
is18033-4 OID ::= { iso(1) standard(0) is18033(18033) part4(4) }

id-kg OID ::= { is18033-4 keystream-generator(1) }
id-scmode OID ::= { is18033-4 stream-cipher-mode(2) }

-- Assignments --
id-kg-mugi OID ::= { id-kg mugi(1) }
id-kg-snow OID ::= { id-kg snow(2) }
id-kg-rabbit OID ::= { id-kg rabbit(3) }
id-kg-decim2 OID ::= { id-kg decim2(4) }
id-kg-k2 OID ::= { id-kg k2(5) }
id-kg-zuc OID ::= { id-kg zuc(6) }

id-scmode-additive OID ::= { id-scmode additive(1) }
id-scmode-multis01 OID ::= { id-scmode multis01(2) }

-- Algorithms and parameters --

StreamCipher ::= AlgorithmIdentifier {{ StreamCipherAlgorithms }}

StreamCipherAlgorithms ALGORITHM ::= {
additiveStreamCipher |
multiS01StreamCipher,
... -- Expect additional algorithms --
}
additiveStreamCipher ALGORITHM ::= {
OID id-scmode-additive PARMS AdditiveStreamCipherParameters
}
AdditiveStreamCipherParameters ::= KeyGenerator

multiS01StreamCipher ALGORITHM ::= {
OID id-scmode-multis01 PARMS MultiS01StreamCipherParameters
}
MultiS01StreamCipherParameters ::= SEQUENCE {
keyGenerator KeyGenerator,
© ISO/IEC 2020 – All rights reserved 5

ISO/IEC 18033-4:2011/Amd.1:2020(E)

securityParameter INTEGER DEFAULT 64,
irreduciblePolynoial BIT STRING,
redandancy BIT STRING,
publicParameterR BIT STRING
-- length determined by securityParameter
-- for full interoperability multis01 parameters should
-- include the padding method but they do not have object
-- identifiers. for the time being they will have to be
-- negotiated in an application-dependent way
}
KeyGenerator ALGORITHM ::= {
mugiKeyGenerator |
snowKeyGenerator |
rabbitKeyGenerator |
decim2KeyGenerator |
k2KeyGenerator |
zucKeyGenerator,
... -- Exp
...