LEA Block Cipher

Introduction

LEA is a 128-bit block cipher with support for 128, 192 and 256-bit keys published in 2014. It was designed by Deukjo Hong, Jung-Keun Lee, Dong-Chan Kim, Daesung Kwon, Kwon Ho Ryu, and Dong-Geon Lee. The only operations used for encryption and the key schedule are 32-bit Addition, eXclusive OR and Rotation (ARX structure): the designers state “the usage of 32-bit and 64-bit processors will grow rapidly compared to 8-bit and 16-bit ones”. Today I’ll just focus on an implementation using 128-bit keys referred to as LEA-128. This just about fits onto the 32-bit x86 architecture. The 256-bit version requires additional registers and is probably better suited for 64-bit mode.

Key Schedule

During generation of subkeys, a number of predefined constants are used.

\textbf{Constants. }
\text{The key schedule uses several constants for generating round keys, which are defined as}

\delta[0] = 0xc3efe9db, \quad \delta[1] = 0x44626b02,
\delta[2] = 0x79e27c8a, \quad \delta[3] = 0x78df30ec,
\delta[4] = 0x715ea49e, \quad \delta[5] = 0xc785da0a,
\delta[6] = 0xe04ef22a, \quad \delta[7] = 0xe5c40957.

\text{They are obtained from hexadecimal expression of } \sqrt{766965},
\text{ where 76, 69 and 65 are ASCII codes of 'L', 'E' and 'A'.}

You can obtain the values using a tool like speedcrunch.

There are 3 different key schedule functions but I only focus on the 128-bit variant for now.

\textbf{Key Schedule with a 128-Bit Key. }
\text{Let } K = (K[0], K[1], K[2], K[3]) \text{ be a 128-bit key. We set } T[i] = K[i]\: for \: 0\leq 4.   \text{ Round key} RK_i = (RK_i[0], RK_i[1],\dots , RK_i[5])\: for\: 0\leq i < 24 \text{ are produced through the following relations:}

T[0]\leftarrow ROL_1(T[0]\oplus ROL_i(\delta[i\:mod\: 4])),\\  T[1]\leftarrow ROL_3(T[1]\oplus ROL_{i+1}(\delta[i\:mod\: 4])),\\  T[2]\leftarrow ROL_6(T[2]\oplus ROL_{i+2}(\delta[i\:mod\: 4])),\\  T[3]\leftarrow ROL_{11}(T[3]\oplus ROL_{i+3}(\delta[i\:mod\: 4])),\\  RK_i\leftarrow (T[0], T[1], T[2], T[3], T[1]).

Compact code

The following function combines encryption and key scheduling. It will encrypt 128-bits of data using a 128-bit master key mk. I’d suggest using this with counter (CTR) mode.

#define R(v,n)(((v)>>(n))|((v)<<(32-(n))))
typedef unsigned int W;

void lea128(void*mk,void*p) {
    W r,t,*x=p,*k=mk;
    W c[4]=
      {0xc3efe9db,0x88c4d604,
       0xe789f229,0xc6f98763};

    for(r=0;r<24;r++){
      t=c[r%4];
      c[r%4]=R(t,28);
      *k=R(*k+t,31);
      k[1]=R(k[1]+R(t,31),29);
      k[2]=R(k[2]+R(t,30),26);
      k[3]=R(k[3]+R(t,29),21);      
      t=*x;
      *x=R((*x^*k)+(x[1]^k[1]),23);
      x[1]=R((x[1]^k[2])+(x[2]^k[1]),5);
      x[2]=R((x[2]^k[3])+(x[3]^k[1]),3);
      x[3]=t;
    }
}

x86 assembly

You might notice the constants are different from C source. For whatever reason, the last 3 are rotated a number of bits left before entering the encryption loop. Obviously a compiler will be smart enough to see this and automatically optimize, but for assembly code, we must rotate them manually. They’re stored on the stack using PUSHAD. EDI, ESI, EBP and ESP are used for TD array. ESP has to be initialized after the PUSHAD for obvious reasons. We don’t want to cause an exception.

; -----------------------------------------------
; LEA-128/128 Block Cipher in x86 assembly (Encryption only)
;
; size: 136 bytes
;
; global calls use cdecl convention
;
; -----------------------------------------------

    %ifndef BIN
      global lea128
      global _lea128
    %endif

    bits 32

struc pushad_t
  _edi resd 1
  _esi resd 1
  _ebp resd 1
  _esp resd 1
  _ebx resd 1
  _edx resd 1
  _ecx resd 1
  _eax resd 1
  .size:
endstruc

; plain text
%define w0 dword[esi+4*0]
%define w1 dword[esi+4*1]
%define w2 dword[esi+4*2]
%define w3 dword[esi+4*3]
%define w4 ecx

; key
%define w5 ebx
%define w6 edx
%define w7 edi
%define w8 ebp

%define LEA128_RNDS 24

lea128:
_lea128:
    pushad
    ; initialize 4 constants
    mov    edi, 0xc3efe9db   ; c0
    mov    esi, 0x88c4d604   ; c1
    mov    ebp, 0xe789f229   ; c2
    pushad
    mov    dword[esp+_esp], 0xc6f98763   ; c3
    mov    esi, [esp+64+4]   ; esi = key
    ; load key
    lodsd
    xchg   eax, w5
    lodsd
    xchg   eax, w6
    lodsd
    xchg   eax, w7
    lodsd
    xchg   eax, w8
    mov    esi, [esp+64+8]   ; esi = data
    xor    eax, eax          ; i = 0
lea_l0:
    push   eax
    ; t = c[r%4]; 
    and    al, 3
    mov    w4, [esp+eax*4+4]
    ; c[r%4] = R(t, 28);
    ror    dword[esp+eax*4+4], 28
    ; **************************************
    ; create sub key
    ; **************************************
    ; k[0] = R(k[0] + t, 31);
    add    w5, w4
    rol    w5, 1
    ; k[1] = R(k[1] + R(t, 31), 29);
    rol    w4, 1
    add    w6, w4
    ror    w6, 29
    ; k[2] = R(k[2] + R(t, 30), 26);
    rol    w4, 1
    add    w7, w4
    ror    w7, 26
    ; k[3] = R(k[3] + R(t, 29), 21); 
    rol    w4, 1
    add    w8, w4
    ror    w8, 21
    ; **************************************
    ; encrypt block
    ; **************************************
    ; t = x[0];
    push   w0
    ; x[0] = R((x[0] ^ k[0]) + (x[1] ^ k[1]), 23);
    mov    w4, w1
    xor    w4, w6
    xor    w0, w5
    add    w0, w4
    ror    w0, 23
    ; x[1] = R((x[1] ^ k[2]) + (x[2] ^ k[1]), 5);
    mov    w4, w2
    xor    w4, w6
    xor    w1, w7
    add    w1, w4
    ror    w1, 5
    ; x[2] = R((x[2] ^ k[3]) + (x[3] ^ k[1]), 3);
    mov    w4, w3
    xor    w4, w6
    xor    w2, w8
    add    w2, w4
    ror    w2, 3
    ; x[3] = t;
    pop    w3
    pop    eax
    ; i++;
    inc    eax
    ; i<LEA128_RNDS
    cmp    al, LEA128_RNDS
    jnz    lea_l0

    popad
    popad
    ret

ARM64 assembly

// LEA-128/128 in ARM64 assembly
// 224 bytes

    .arch armv8-a

    // include the MOVL macro
    .include "../../include.inc"

    .text
    .global lea128

lea128:
    mov    x11, x0
    mov    x12, x1

    // allocate 16 bytes
    sub    sp, sp, 4*4

    // load immediate values
    movl   w0, 0xc3efe9db
    movl   w1, 0x88c4d604
    movl   w2, 0xe789f229
    movl   w3, 0xc6f98763

    // store on stack
    str    w0, [sp    ]
    str    w1, [sp,  4]
    str    w2, [sp,  8]
    str    w3, [sp, 12]

    // for(r=0;r<24;r++) {
    mov    w8, wzr

    // load 128-bit key
    ldp    w4, w5, [x11]
    ldp    w6, w7, [x11, 8]

    // load 128-bit plaintext
    ldp    w0, w1, [x12]
    ldp    w2, w3, [x12, 8]
L0:
    // t=c[r%4];
    and    w9, w8, 3 
    ldr    w10, [sp, x9, lsl 2]
	
    // c[r%4]=R(t,28);
    mov    w11, w10, ror 28
    str    w11, [sp, x9, lsl 2]

    // k[0]=R(k[0]+t,31);
    add    w4, w4, w10
    ror    w4, w4, 31

    // k[1]=R(k[1]+R(t,31),29);
    ror    w11, w10, 31
    add    w5, w5, w11
    ror    w5, w5, 29

    // k[2]=R(k[2]+R(t,30),26);
    ror    w11, w10, 30
    add    w6, w6, w11
    ror    w6, w6, 26

    // k[3]=R(k[3]+R(t,29),21);
    ror    w11, w10, 29
    add    w7, w7, w11
    ror    w7, w7, 21

    // t=x[0];
    mov    w10, w0

    // w[0]=R((w[0]^k[0])+(w[1]^k[1]),23);
    eor    w0, w0, w4
    eor    w9, w1, w5
    add    w0, w0, w9
    ror    w0, w0, 23

    // w[1]=R((w[1]^k[2])+(w[2]^k[1]),5);
    eor    w1, w1, w6
    eor    w9, w2, w5
    add    w1, w1, w9
    ror    w1, w1, 5

    // w[2]=R((w[2]^k[3])+(w[3]^k[1]),3);
    eor    w2, w2, w7
    eor    w3, w3, w5
    add    w2, w2, w3
    ror    w2, w2, 3

    // w[3]=t;
    mov    w3, w10

    // r++
    add    w8, w8, 1
    // r < 24
    cmp    w8, 24
    bne    L0

    // save 128-bit ciphertext
    stp    w0, w1, [x12]
    stp    w2, w3, [x12, 8]

    add    sp, sp, 4*4
    ret

Sources here.

Thanks to 0x4d_ for submitting \LaTeX formulas.

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This entry was posted in assembly, cryptography, encryption, programming and tagged , , , . Bookmark the permalink.

1 Response to LEA Block Cipher

  1. Pingback: Shellcode: Encryption Algorithms in ARM Assembly | modexp

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