3GPP机密性和完整性算法规范128-EEA3和128-EIA3（三）----机密性算法(EEA3）和完整性算法（EIA3）

3GPP机密性和完整性算法规范128-EEA3和128-EIA3（一）----密钥生成原理

3GPP机密性和完整性算法规范128-EEA3和128-EIA3（二）----祖冲之算法的C语言实现

3GPP机密性和完整性算法规范128-EEA3和128-EIA3（三）----机密性算法(EEA3）和完整性算法（EIA3）

3GPP机密性和完整性算法规范128-EEA3和128-EIA3（四）----测试用例

3GPP机密性和完整性算法规范128-EEA3和128-EIA3（五）----文档代码资源

英文文档，特别提示，文中有EEA3和EIA3的代码

 

1 OUTLINE OF THE NORMATIVE PART

Section 2 introduces the algorithm and describes the notation used in the subsequent sections.

Section 3 specifies the confidentiality algorithm 128 ‐ EEA3.

Section 4 specifies the integrity algorithm 128 ‐ EIA3.

2

INTRODUCTORY INFORMATION

2.1

Introduction

Within the security architecture of the LTE system there are standardized algorithms for

confidentiality and integrity. Two sets of algorithms 128‐EEA1/128‐EIA1 and 128‐EEA2/128‐EIA2

have already been specified [1‐2]. In this document the third set of these algorithms

( 128 ‐ EEA3 / 128 ‐ EIA3 ) based on ZUC [3] are proposed.

The confidentiality algorithm 128 ‐ EEA3 is a stream cipher that is used to encrypt/decrypt blocks

of data using a confidentiality key CK . The block of data may be between 1 and 65504 bits long.

The algorithm uses ZUC as a keystream generator.

The integrity algorithm 128 ‐ EIA3 computes a 32‐bit MAC (Message Authentication Code) of a

given input message using an integrity key IK . The core algorithms adopted by the MAC are a

universal hash and ZUC.

2.2

Notations

2.2.1 Radix

In this document, integers are represented as decimal numbers unless specified otherwise. We

use the prefix “0x” to indicate hexadecimal numbers and the subscript “2” to indicate a number

in binary representation.

Example 1.

Integer a can be written in different representations:

a = 1234567890     // decimal representation

   = 0x499602D2    // hexadecimal representation

   = 1001001100101100000001011010010 2 //binary representation

2.2.2 Bit/Byte ordering

All data variables in this document are presented with the most significant bit/byte on the left

and the least significant bit/byte on the right. When a variable is broken down into a number of

substrings, the leftmost substring is numbered by 0, the next most significant substring is

numbered by 1 and so on throughout to the least significant substring.

Example 2.

Let a =1001001100101100000001011010010 2 . Then the leftmost bit 1 of integer a

represents its most significant bit, and the rightmost bit 0 represents its least significant bit.   

Example 3.

Let a =10010010100101100000001011010010 2 . If a is subdivided into 4 of 8‐bit

substrings a [0], a [1], a [2] and a [3], then we have

a [0] = 10010010 2 , a [1] = 10010110 2 , a [2] = 00000010 2 , a [3] = 11010010 2 .

2.2.3 Operation notations

In this document, operation notations are defined as follows:

a ║ b   Concatenation of substrings a and b

 

⎡ x ⎤    The smallest integer no less than x

 

⊕    Exclusive‐OR

 

a << t   Left shift of integer a by t bits

Example 4.

For two substrings a = 0x1234 and b = 0x5678, then their concatenation will be   

   

c = a ║ b =0x12345678.

 

2.2.4 List of Variables

COUNT            The 32‐bit counter.

BEARER          The 5‐bit bearer identity.

DIRECTION     The 1‐bit input indicating the direction of transmission.

CK                    The 128‐bit confidentiality key.

IK                      The 128‐bit integrity key.

LENGTH           The number of bits to be encrypted/decrypted.

M                       The input message.

C                       The output message.

KEY                  The 128‐bit initial key to ZUC.

IV                      The 128‐bit initial vector to ZUC.

L                       The number of key words generated by ZUC.

z[i]                    The i‐th key bit of keystream generated by ZUC.

 

3

CONFIDENTIALITY ALGORITHM 128-EEA3

3.1

Introduction

The confidentiality algorithm 128 ‐ EEA3 is a stream cipher that is used to encrypt/decrypt blocks

of data under a confidentiality key. The block of data can be between 1 and 65504 bits in length.

3.2

Inputs and Outputs

The inputs to the algorithm are given in Table 1, the output in Table 2.

 

Table 1 The inputs to 128 ‐ EEA3

Parameter            Size(bits)                        Remark

COUNT                32                                   The counter

BEARER              5                                     The bearer identity

DIRECTION        1                                      The direction of transmission

CK                       128                                  Confidentiality key

LENGTH              32                                   The length of the input message

M                          LENGTH                        The input bit stream

 

Table 2 The output of 128 ‐ EEA3

Parameter            Size(bits)                        Remark

C                          LENGTH                        The output bit stream

 

3.3

Initialisation

In this section we define how ZUC’s parameters, the initial key KEY and the initial vector IV, are

initialized with the confidentiality key CK and initialization variables before the generation of

keystream.

Let

CK=CK[0] ║ CK[1] ║ CK[2] ║ … ║ CK[15]

be the 128‐bit confidentiality key, where CK[i] (0 ≤ i ≤ 15) are bytes. We set the 128‐bit initial key

KEY to ZUC as

KEY = KEY[0] ║ KEY[1] ║ KEY[2] ║ … ║ KEY[15],

where KEY[i] (0 ≤ i ≤ 15) are bytes. Then

KEY[i]=CK[i], i=0,1,2,…,15.

Let

COUNT=COUNT[0] ║ COUNT[1] ║ COUNT[2] ║ COUNT[3]

be the 32‐bit counter, where COUNT[i] ( 0 ≤ i ≤ 3) are bytes. We set the 128‐bit initial vector to ZUC

as

IV = IV[0] ║ IV[1] ║ IV[2] ║ … ║ IV[15],

where IV[i] ( 0 ≤ i ≤ 15) are bytes. Then

IV[0] = COUNT[0], IV[1] = COUNT[1],

IV[2] = COUNT[2], IV[3] = COUNT[3],

IV[4] = BEARER ║ DIRECTION ║ 00 2 ,

IV[5] = IV[6] = IV[7] = 00000000 2 ,

IV[8] = IV[0], IV[9] = IV[1],

IV[10] = IV[2], IV[11] = IV[3],

IV[12] = IV[4], IV[13] = IV[5],

IV[14] = IV[6], IV[15] = IV[7].

 

3.4

Keystream Generation

Let ZUC generate keystream of L words. When each of the word is expanded into a 32‐bit string,

then we get a binary string z[0], z[1], …, z[32 × L‐1], where z[0] is the most significant bit of the

first output word of ZUC and z[31] is the least significant bit. To encrypt a message of LENGTH bits,

it is required that L= ⎡ LENGTH/32 ⎤ .

3.5

Encryption/Decryption

Encryption/decryption operations are identical operations and are performed by the exclusive‐OR

of the input message M with the generated keystream z.

Let

M = M[0] ║ M[1] ║ M[2] ║ … ║ M[LENGTH‐1]

be the input bit stream of length LENGTH and

C = C[0] ║ C[1] ║ C[2] ║ … ║ C[LENGTH‐1]

be the corresponding output bit stream of length LENGTH, where M[i] and C[i] are bits,

i=0,1,2,…,LENGTH‐1. Then

C[i] = M[i] ⊕ z[i],i=0,1,2,…,LENGTH‐1

 

 

4

INTEGRITY ALGORITHM 128-EIA3

4.1

Introduction

The integrity algorithm 128 ‐ EIA3 is a message authentication code (MAC) function that is used to

compute the MAC of an input message using an integrity key IK. The message can be between 1

and 65504 bits in length.

4.2

Inputs and Outputs

The inputs to the algorithm are given in Table 3, and the output is in Table 4.

 

Table 3 The inputs to 128 ‐ EIA3

Parameter                                   Size (bits)                          Remark

COUNT                                       32                                      The counter

BEARER                                     5                                        The bearer identity

DIRECTION                                1                                        The direction of transmission

IK                                                128                                    The integrity key

LENGTH                                     32                                      The bits of the input message

M                                                LENGTH                            The input message

 

Table 4 The output of 128 ‐ EIA3

Parameter                                   Size(bits)                           Remark

MAC                                            32                                     The MAC

 

4.3

Initialisation

In this section we define how ZUC’s parameters, the initial key KEY and the initial vector IV, are

initialized with the integrity key IK and initialization variables before the generation of keystream.

Let

IK = IK[0] ║ IK[1] ║ IK[2] ║ … ║ IK[15]

be the 128‐bit integrity key, where IK[i]( 0 ≤ i ≤ 15) are bytes. We set the 128‐bit initial key KEY to

ZUC as

KEY = KEY[0] ║ KEY[1] ║ KEY[2] ║ … ║ KEY[15]

where KEY[i](0 ≤ i ≤ 15) are bytes. Then

KEY[i] = IK[i], i=0,1,2,…,15.

Let the 32‐bit counter COUNT be   

COUNT=COUNT[0] ║ COUNT[1] ║ COUNT[2] ║ COUNT[3]

where COUNT[i] are bytes, i=0,1,2,3. We set the 128‐bit initial vector IV to ZUC as

IV = IV[0] ║ IV[1] ║ IV[2] ║ … ║ IV[15],

where IV[i]( 0 ≤ i ≤ 15) are bytes. Then

IV[0] = COUNT[0], IV[1] = COUNT[1],

IV[2] = COUNT[2], IV[3] = COUNT[3],

IV[4] = BEARER ║ 000 2 , IV[5] =00000000 2 ,

IV[6] = 00000000 2 , IV[7] = 00000000 2 ,

IV[8] = IV[0] ⊕ (DIRECTION << 7), IV[9] = IV[1],

IV[10] = IV[2], IV[11] = IV[3],

IV[12] = IV[4], IV[13] = IV[5],

IV[14] = IV[6] ⊕ (DIRECTION << 7), IV[15] = IV[7].

4.4

Generating the keystream

Let ZUC generate a keystream of L= ⎡ LENGTH/32 ⎤ +2 words. Denote the generated bit string by z[0],

z[1], …, z[32 × L‐1], where z[0] is the most significant bit of the first output word of ZUC and z[31]

is the least significant bit.   

For each i=0,1,2,…,32 × (L‐1), let

z i = z[i] ║ z[i+1] ║ … ║ z[i+31].

Then each z i is a 32‐bit word.

4.5

Compute the MAC

Let T be a 32‐bit word. Set T = 0.

For each i=0,1,2,…,LENGTH‐1, if M[i] = 1, then

T=T z i ⊕ .

Set

T=T ⊕ z LENGTH .

Finally we take T z

⊕

32 × (L‐1) as the output MAC, i.e.

MAC= T ⊕ z 32 × (L‐1)

 

 

 

 

 

A C implementation of 128-EEA3

typedef unsigned char u8;

typedef unsigned int u32;

 

/* The ZUC algorithm, see ref. [3]*/

void ZUC(u8* k, u8* iv, u32* ks, int len)

{

/* The initialization of ZUC, see page 17 of ref. [3]*/

Initialization(k, iv);

/* The procedure of generating keystream of ZUC, see page 18 of ref. [3]*/

GenerateKeystream(ks, len);

}

 

void EEA3(u8* CK,u32 COUNT,u32 BEARER,u32 DIRECTION,u32 LENGTH,u32* M,u32* C)

{

u32 *z, L, i;

u8 IV[16];

L = (LENGTH+31)/32;

z = (u32 *) malloc(L*sizeof(u32));

 

IV[0] = (COUNT>>24) & 0xFF;

IV[1] = (COUNT>>16) & 0xFF;

IV[2] = (COUNT>>8) & 0xFF;

IV[3] = COUNT & 0xFF;

IV[4] = ((BEARER << 3) | ((DIRECTION&1)<<2)) & 0xFC;

IV[5] = 0;

IV[6] = 0;

IV[7] = 0;

IV[8] = IV[0];

IV[9] = IV[1];

IV[10] = IV[2];

IV[11] = IV[3];

IV[12] = IV[4];

IV[13] = IV[5];

IV[14] = IV[6];

IV[15] = IV[7];

ZUC(CK,IV,z,L);

for (i=0; i

{

C[i] = M[i] ^ z[i];

}

free(z);

}

 

 

 

ANNEX 2

A C implementation of 128-EIA3

typedef unsigned char u8;

typedef unsigned int u32;

 

void ZUC(u8* k, u8* iv, u32* keystream, int length); /*see Annex 1*/

u32 GET_WORD(u32 * DATA, u32 i)

{

u32 WORD, ti;

ti = i % 32;

if (ti == 0) {

WORD = DATA[i/32];

}

else {

WORD = (DATA[i/32]<>(32-ti));

}

return WORD;

}

 

u8 GET_BIT(u32 * DATA, u32 i)

{

return (DATA[i/32] & (1<<(31-(i%32)))) ? 1 : 0;

}

 

void EIA3(u8* IK,u32 COUNT,u32 DIRECTION,u32 BEARER,u32 LENGTH,u32* M,u32* MAC)

{

u32 *z, N, L, T, i;

u8 IV[16];

IV[0] = (COUNT>>24) & 0xFF;

IV[1] = (COUNT>>16) & 0xFF;

IV[2] = (COUNT>>8) & 0xFF;

IV[3] = COUNT & 0xFF;

IV[4] = (BEARER << 3) & 0xF8;

IV[5] = IV[6] = IV[7] = 0;

IV[8] = ((COUNT>>24) & 0xFF) ^ ((DIRECTION&1)<<7);

IV[9] = (COUNT>>16) & 0xFF;

IV[10] = (COUNT>>8) & 0xFF;

IV[11] = COUNT & 0xFF;

IV[12] = IV[4];

IV[13] = IV[5];

IV[14] = IV[6] ^ ((DIRECTION&1)<<7);

IV[15] = IV[7];

N = LENGTH + 64;

L = (N + 31) / 32;

z = (u32 *) malloc(L*sizeof(u32));

ZUC(IK, IV, z, L);

T = 0;

for (i=0; i

if (GET_BIT(M,i)) {

T ^= GET_WORD(z,i);

}

}

T ^= GET_WORD(z,LENGTH);

*MAC = T ^ z[L-1];

free(z);

}