# MD5

File:Ron Rivest.jpg
MD5 was designed by Ronald Rivest (one of the inventors of the RSA algorithm) in 1991.

In cryptography, MD5 (Message-Digest algorithm 5) is a widely-used cryptographic hash function with a 128-bit hash value. As an Internet standard (RFC 1321), MD5 has been employed in a wide variety of security applications, and is also commonly used to check the integrity of files.

MD5 was designed by Ronald Rivest in 1991 to replace an earlier hash function, MD4. In 1996, a flaw was found with the design of MD5; while it was not a clearly fatal weakness, cryptographers began to recommend using other algorithms, such as SHA-1 (recent claims suggest that SHA-1 has been broken, however). In 2004, more serious flaws were discovered making further use of the algorithm for security purposes questionable.

## History and cryptanalysis

MD5 is one of a series of message digest algorithms designed by Professor Ronald Rivest of MIT (Rivest, 1994). When analytic work indicated that MD5's predecessor — MD4 — was likely to be insecure, MD5 was designed in 1991 to be a secure replacement (weaknesses were indeed subsequently found in MD4 by Hans Dobbertin).

In 1993, den Boer and Bosselaers gave an early, although limited, result of finding a "pseudo-collision" of the MD5 compression function; that is, two different initialisation vectors ${\displaystyle I}$ and ${\displaystyle J}$ with 4-bit difference between them, such that:

${\displaystyle MD5compress(I,X)=MD5compress(J,X)}$

In 1996, Dobbertin announced a collision of the compression function of MD5 (Dobbertin, 1996). While this was not an attack on the full MD5 hash function, it was close enough for cryptographers to recommend switching to a replacement, such as WHIRLPOOL, SHA-1 or RIPEMD-160.

The size of the hash — 128 bits — is small enough to contemplate a brute force birthday attack. MD5CRK was a distributed project started in March 2004 with the aim of demonstrating that MD5 is practically insecure by finding a collision using a brute force attack.

However, MD5CRK ended shortly after 17 August, 2004, when collisions for the full MD5 were announced by Xiaoyun Wang, Dengguo Feng, Xuejia Lai and Hongbo Yu [1] [2]. Their analytical attack was reported to take only one hour on an IBM p690 cluster.

On 1 March 2005, Arjen Lenstra, Xiaoyun Wang, and Benne de Weger demonstrated [3] construction of two X.509 certificates with different public keys and the same MD5 hash, a demonstrably practical collision. The construction included private keys for both public keys. And a few days later, Vlastimil Klima described [4] an improved algorithm, able to construct MD5 collisions in a few hours on a single notebook computer. Given this, MD5 is definitely not practically collision-free.

Because MD5 makes only one pass over the data, if two prefixes with the same hash can be constructed, a common suffix can be added to both to make the collision more reasonable. And because the current collision-finding techniques allow the preceding hash state to be specified arbitrarily, a collision can be found for any desired prefix. All that is required to generate two colliding files is a template file, with a 128-byte block of data aligned on a 64-byte boundary, that can be changed freely by the collision-finding algorithm.

## Algorithm

File:MD5.png
Figure 1. One MD5 operation — MD5 consists of 64 of these operations, grouped in four rounds of 16 operations. F is a nonlinear function; one function is used in each round. Mi denotes a 32-bit block of the message input, and Ki denotes a 32-bit constant, different for each operation.

left shifts denotes a left bit rotation by s places; s varies for each operation. Addition denotes addition modulo 232.

MD5 processes a variable length message into a fixed-length output of 128 bits. The input message is broken up into chunks of 512-bit blocks; the message is padded so that its length is divisible by 512. The padding works as follows: first a single bit, 1, is appended to the end of the message. This is followed by as many zeros as are required to bring the length of the message up to 64 bits fewer than a multiple of 512. The remaining bits are filled up with a 64-bit integer representing the length of the original message.

The main MD5 algorithm operates on a 128-bit state, divided into four 32-bit words, denoted A, B, C and D. These are initialised to certain fixed constants. The main algorithm then operates on each 512-bit message block in turn, each block modifying the state. The processing of a message block consists of four similar stages, termed rounds; each round is composed of 16 similar operations based on a non-linear function F, modular addition, and left rotation. Figure 1 illustrates one operation within a round. There are four possible functions F, a different one is used in each round:

${\displaystyle F(X,Y,Z)=(X\wedge {Y})\vee (\neg {X}\wedge {Z})}$
${\displaystyle G(X,Y,Z)=(X\wedge {Z})\vee (Y\wedge \neg {Z})}$
${\displaystyle H(X,Y,Z)=X\oplus Y\oplus Z}$
${\displaystyle I(X,Y,Z)=Y\oplus (X\vee \neg {Z})}$

${\displaystyle \oplus ,\wedge ,\vee ,\neg }$ denote the XOR, AND, OR and NOT operations respectively.

## Pseudocode

Pseudocode for the MD5 algorithm follows.

```//Note: All variables are unsigned 32 bits and wrap modulo 2^32 when calculating

//Define r as the following
var int[64] r, k
r[ 0..15] := {7, 12, 17, 22,  7, 12, 17, 22,  7, 12, 17, 22,  7, 12, 17, 22}
r[16..31] := {5,  9, 14, 20,  5,  9, 14, 20,  5,  9, 14, 20,  5,  9, 14, 20}
r[32..47] := {4, 11, 16, 23,  4, 11, 16, 23,  4, 11, 16, 23,  4, 11, 16, 23}
r[48..63] := {6, 10, 15, 21,  6, 10, 15, 21,  6, 10, 15, 21,  6, 10, 15, 21}

//Use binary fractional part of the sines of integers as constants:
for i from 0 to 63
k[i] := floor(abs(sin(i + 1)) × 2^32)

//Initialize variables:
var int h0 := 0x67452301
var int h1 := 0xEFCDAB89
var int h3 := 0x10325476

//Pre-processing:
append "1" bit to message
append "0" bits until message length in bits ≡ 448 (mod 512)
append bit length of message as 64-bit little-endian integer to message

//Process the message in successive 512-bit chunks:
for each 512-bit chunk of message
break chunk into sixteen 32-bit little-endian words w(i), 0 ≤ i ≤ 15

//Initialize hash value for this chunk:
var int a := h0
var int b := h1
var int c := h2
var int d := h3

//Main loop:
for i from 0 to 63
if 0 ≤ i ≤ 15 then
f := (b and c) or ((not b) and d)
g := i
else if 16 ≤ i ≤ 31
f := (d and b) or ((not d) and c)
g := (5×i + 1) mod 16
else if 32 ≤ i ≤ 47
f := b xor c xor d
g := (3×i + 5) mod 16
else if 48 ≤ i ≤ 63
f := c xor (b or (not d))
g := (7×i) mod 16

temp := d
d := c
c := b
b := ((a + f + k(i) + w(g)) leftrotate r(i)) + b
a := temp

//Add this chunk's hash to result so far:
h0 := h0 + a
h1 := h1 + b
h2 := h2 + c
h3 := h3 + d

var int digest := h0 append h1 append h2 append h3 //(expressed as little-endian)
```

Note: Instead of the formulation from the original RFC 1321 shown, the following may be used for improved efficiency:

```(0  ≤ i ≤ 15): f := d xor (b and (c xor d))
(16 ≤ i ≤ 31): f := c xor (d and (b xor c))
```

## MD5 hashes

The 128-bit (16-byte) MD5 hashes (also termed message digests) are typically represented as 32-digit hexadecimal numbers. The following demonstrates a 43-byte ASCII input and the corresponding MD5 hash:

``` MD5("The quick brown fox jumps over the lazy dog") = 9e107d9d372bb6826bd81d3542a419d6
```

Even a small change in the message will (with overwhelming probability) result in a completely different hash, e.g. changing d to c:

``` MD5("The quick brown fox jumps over the lazy cog") = 1055d3e698d289f2af8663725127bd4b
```

The hash of the zero-length string is:

``` MD5("") = d41d8cd98f00b204e9800998ecf8427e
```