# MD5 – Wikipedia

Message-digest hash algorithm

The MD5 message-digest algorithm is a cryptographically broken but hush wide used hashish function producing a 128- bit hash rate. Although MD5 was initially designed to be used as a cryptanalytic hashish function, it has been found to suffer from extensive vulnerabilities. It can still be used as a checksum to verify data integrity, but only against unintentional corruption. It remains suitable for other non-cryptographic purposes, for case for determining the partition for a particular identify in a partition database, and may be preferred due to lower computational requirements than more holocene Secure Hash Algorithms algorithm. [ 3 ] MD5 was designed by Ronald Rivest in 1991 to replace an earlier hash function MD4, [ 4 ] and was specified in 1992 as RFC 1321.

One basic prerequisite of any cryptanalytic hashish function is that it should be computationally impracticable to find two distinct messages that hash to the lapp measure. MD5 fails this requirement catastrophically ; such collisions can be found in seconds on an ordinary home computer. On 31 December 2008, the CMU Software Engineering Institute concluded that MD5 was basically “ cryptographically break and inapplicable for farther use ”. [ 5 ] The weaknesses of MD5 have been exploited in the field, most infamously by the Flame malware in 2012. As of 2019, MD5 continues to be wide used, despite its well-documented weaknesses and deprecation by security experts. [ 6 ]

## history and cryptanalysis

MD5 is one in a series of message digest algorithm designed by Professor Ronald Rivest of MIT ( Rivest, 1992 ). When analytic work indicated that MD5 ‘s harbinger MD4 was probable to be insecure, Rivest designed MD5 in 1991 as a plug surrogate. ( Hans Dobbertin did indeed later find weaknesses in MD4. ) In 1993, Den Boer and Bosselaers gave an early, although limited, the leave of finding a “ pseudo-collision “ of the MD5 compression affair ; that is, two different low-level formatting vectors that produce an identical digest. In 1996, Dobbertin announced a collision of the compression routine of MD5 ( Dobbertin, 1996 ). While this was not an assail on the full MD5 hash function, it was close enough for cryptographers to recommend switching to a replacement, such as SHA-1 ( besides compromised ) or RIPEMD-160. The size of the hashish value ( 128 bits ) is small adequate to contemplate a birthday attack. MD5CRK was a circulate stick out started in March 2004 to demonstrate that MD5 is practically insecure by finding a collision using a birthday attack. MD5CRK ended shortly after 17 August 2004, when collisions for the entire MD5 were announced by Xiaoyun Wang, Dengguo Feng, Xuejia Lai, and Hongbo Yu. [ 7 ] [ 8 ] Their analytic attack was reported to take only one hour on an IBM p690 bunch. [ 9 ] On 1 March 2005, Arjen Lenstra, Xiaoyun Wang, and Benne de Weger demonstrated construction of two X.509 certificates with different public keys and the same MD5 hashish prize, a demonstrably hardheaded collision. [ 10 ] The construction included private keys for both public key. A few days late, Vlastimil Klima described an better algorithm, able to construct MD5 collisions in a few hours on a single notebook computer. [ 11 ] On 18 March 2006, Klima published an algorithm that could find a collision within one moment on a one notebook computer, using a method acting he calls tunneling. [ 12 ] versatile MD5-related RFC errata have been published. In 2009, the United States Cyber Command used an MD5 hash value of their mission statement as a part of their official emblem. [ 13 ] On 24 December 2010, Tao Xie and Dengguo Feng announced the first gear published single-block ( 512-bit ) MD5 collision. [ 14 ] ( former collision discoveries had relied on multi-block attacks. ) For “ security reasons ”, Xie and Feng did not disclose the newly attack method. They issued a challenge to the cryptanalytic community, offering a US \$ 10,000 honor to the first finder of a different 64-byte collision before 1 January 2013. Marc Stevens responded to the challenge and published colliding single-block messages a well as the construction algorithm and sources. [ 15 ] In 2011 an informational RFC 6151 [ 16 ] was approved to update the security considerations in MD5 [ 17 ] and HMAC-MD5. [ 18 ]

## security

The security of the MD5 hash routine is sternly compromised. A collision attack exists that can find collisions within seconds on a calculator with a 2.6 GHz Pentium 4 central processing unit ( complexity of 224.1 ). [ 19 ] Further, there is besides a chosen-prefix collision attack that can produce a collision for two inputs with stipulate prefixes within seconds, using off-the-rack computing hardware ( complexity 239 ). [ 20 ] The ability to find collisions has been greatly aided by the function of off-the-rack GPUs. On an NVIDIA GeForce 8400GS graphics processor, 16–18 million hashes per second can be computed. An NVIDIA GeForce 8800 Ultra can calculate more than 200 million hashes per second. [ 21 ] These hash and collision attacks have been demonstrated in the public in respective situations, including colliding document files [ 22 ] [ 23 ] and digital certificates. [ 24 ] As of 2015, MD5 was demonstrated to be distillery quite widely used, most notably by security inquiry and antivirus companies. [ 25 ] As of 2019, one quarter of widely used content management systems were reported to still use MD5 for password hash. [ 6 ]

### overview of security issues

In 1996, a defect was found in the invention of MD5. While it was not deemed a fateful weakness at the time, cryptographers began recommending the use of other algorithm, such as SHA-1, which has since been found to be vulnerable as well. [ 26 ] In 2004 it was shown that MD5 is not collision-resistant. [ 27 ] As such, MD5 is not suitable for applications like SSL certificates or digital signatures that rely on this place for digital security. Researchers additionally discovered more unplayful flaws in MD5, and described a feasible collision attack — a method acting to create a copulate of inputs for which MD5 produces identical checksums. [ 7 ] [ 28 ] Further advances were made in breaking MD5 in 2005, 2006, and 2007. [ 29 ] In December 2008, a group of researchers used this technique to fake SSL certificate cogency. [ 24 ] [ 30 ] As of 2010, the CMU Software Engineering Institute considers MD5 “ cryptographically dampen and unsuitable for far manipulation ”, [ 31 ] and most U.S. government applications now require the SHA-2 kin of hash functions. [ 32 ] In 2012, the Flame malware exploited the weaknesses in MD5 to fake a Microsoft digital key signature. [ 33 ]

### collision vulnerabilities

In 1996, collisions were found in the compression function of MD5, and Hans Dobbertin wrote in the RSA Laboratories technical newsletter, “ The give attack does not so far threaten practical applications of MD5, but it comes quite close … in the future MD5 should nobelium longer be implemented … where a collision-resistant hash function is required. ” [ 34 ] In 2005, researchers were able to create pairs of PostScript documents [ 35 ] and X.509 certificates [ 36 ] with the lapp hash. Later that year, MD5 ‘s graphic designer Ron Rivest wrote that “ md5 and sha1 are both distinctly broken ( in terms of collision-resistance ) ”. [ 37 ] On 30 December 2008, a group of researchers announced at the 25th Chaos Communication Congress how they had used MD5 collisions to create an intermediate certificate assurance certificate that appeared to be legitimate when checked by its MD5 hash. [ 24 ] The researchers used a PS3 bunch at the EPFL in Lausanne, Switzerland [ 38 ] to change a normal SSL certificate issued by RapidSSL into a working CA certificate for that issuer, which could then be used to create other certificates that would appear to be legitimate and issued by RapidSSL. VeriSign, the issuers of RapidSSL certificates, said they stopped issuing raw certificates using MD5 as their checksum algorithm for RapidSSL once the vulnerability was announced. [ 39 ] Although Verisign declined to revoke existing certificates signed using MD5, their response was considered adequate by the authors of the exploit ( Alexander Sotirov, Marc Stevens, Jacob Appelbaum, Arjen Lenstra, David Molnar, Dag Arne Osvik, and Benne de Weger ). [ 24 ] Bruce Schneier wrote of the approach that “ we already knew that MD5 is a fracture hashish function ” and that “ no one should be using MD5 anymore ”. [ 40 ] The SSL researchers wrote, “ Our desire affect is that Certification Authorities will stop using MD5 in issuing new certificates. We besides hope that function of MD5 in other applications will be reconsidered american samoa well. ” [ 24 ] In 2012, according to Microsoft, the authors of the Flame malware used an MD5 collision to forge a Windows code-signing security. [ 33 ] MD5 uses the Merkle–Damgård construction, so if two prefixes with the same hash can be constructed, a common suffix can be added to both to make the collision more likely to be accepted as valid data by the application using it. furthermore, current collision-finding techniques allow to specify an arbitrary prefix : an attacker can create two colliding files that both begin with the like capacity. All the attacker needs to generate two colliding files is a template file with a 128-byte forget of data, aligned on a 64-byte limit, that can be changed freely by the collision-finding algorithm. An exercise MD5 collision, with the two messages differing in 6 bits, is :

d131dd02c5e6eec4 693d9a0698aff95c 2fcab5 8712467eab 4004583eb8fb7f89
55ad340609f4b302 83e4888325 71415a 085125e8f7cdc99f d91dbd degree fahrenheit280373c5b
d8823e3156348f5b ae6dacd436c919c6 dd53e2 barn487da03fd 02396306d248cda0
e99f33420f577ee8 ce54b67080 a80d1e c69821bcb6a88393 96f965 2b6ff72a70

d131dd02c5e6eec4 693d9a0698aff95c 2fcab5 0712467eab 4004583eb8fb7f89
55ad340609f4b302 83e4888325 fluorine1415a 085125e8f7cdc99f d91dbd 7280373c5b
d8823e3156348f5b ae6dacd436c919c6 dd53e2 3487da03fd 02396306d248cda0
e99f33420f577ee8 ce54b67080 280d1e c69821bcb6a88393 96f965 ab6ff72a70


Both produce the MD5 hash 79054025255fb1a26e4bc422aef54eb4. [ 41 ] The difference between the two samples is that the leading bit in each nibble has been flipped. For case, the twentieth byte ( offset 0x13 ) in the top sample, 0x87, is 10000111 in binary star. The leading bit in the byte ( besides the leading snatch in the first nybble ) is flipped to make 00000111, which is 0x07, as shown in the lower sample distribution. subsequently it was besides found to be possible to construct collisions between two files with individually chosen prefixes. This proficiency was used in the creation of the rogue CA certificate in 2008. A raw form of parallelize collision searching using MPI was proposed by Anton Kuznetsov in 2014, which allowed finding a collision in 11 hours on a computer science cluster. [ 42 ]

### Preimage vulnerability

In April 2009, an assail against MD5 was published that breaks MD5 ‘s preimage resistance. This attack is only theoretical, with a computational complexity of 2123.4 for full preimage. [ 43 ] [ 44 ]

## Applications

MD5 digests have been wide used in the software worldly concern to provide some assurance that a transferred file has arrived entire. For example, file servers often provide a pre-computed MD5 ( known as md5sum ) checksum for the files, so that a drug user can compare the checksum of the downloaded file to it. Most unix-based operate systems include MD5 total utilities in their distribution packages ; Windows users may use the included PowerShell function “ Get-FileHash ”, install a Microsoft utility, [ 45 ] [ 46 ] or use third-party applications. Android ROMs besides use this type of checksum .
As it is easy to generate MD5 collisions, it is potential for the person who created the charge to create a second charge with the same checksum, so this proficiency can not protect against some forms of malicious tampering. In some cases, the checksum can not be trusted ( for case, if it was obtained over the same impart as the download file ), in which casing MD5 can only provide error-checking functionality : it will recognize a corrupt or incomplete download, which becomes more probably when downloading larger files. historically, MD5 has been used to store a one-way hash of a password, often with key stretching. [ 47 ] [ 48 ] NIST does not include MD5 in their list of recommend hashes for password storage. [ 49 ] MD5 is besides used in the field of electronic discovery, to provide a unique identifier for each document that is exchanged during the legal discovery serve. This method can be used to replace the Bates postage numbering system that has been used for decades during the exchange of newspaper documents. As above, this custom should be discouraged due to the facilitate of collision attacks.

## algorithm

fluorine is a nonlinear function; one function is used in each round. M i denotes a 32-bit block of the message input, and K i denotes a 32-bit constant, different for each operation. < < < s denotes a left bit rotation by mho places; sulfur varies for each operation. ⊞ { \displaystyle \boxplus }32. figure 1. One MD5 operation. MD5 consists of 64 of these operations, grouped in four rounds of 16 operations.is a nonlinear function ; one affair is used in each round.denotes a 32-bit blocking of the message remark, anddenotes a 32-bit ceaseless, unlike for each operation.denotes a leave spot rotation byplaces ; varies for each operation.denotes addition modulo 2 MD5 processes a variable-length message into a fixed-length output of 128 bits. The stimulation message is broken up into chunks of 512-bit blocks ( sixteen 32-bit words ) ; the message is padded therefore 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 astir to 64 bits fewer than a multiple of 512. The remaining bits are filled up with 64 bits representing the distance of the original message, modulo 264. The main MD5 algorithm operates on a 128-bit state, divided into four 32-bit words, denoted A, B, C, and D. These are initialized to sealed specify constants. The main algorithm then uses each 512-bit message block in turn to modify the state. The serve of a message obstruct consists of four like stages, termed rounds ; each round is composed of 16 alike operations based on a non-linear affair F, modular accession, and left rotation. figure 1 illustrates one process within a round. There are four possible functions ; a different one is used in each round :

F ( B, C, D ) = ( B ∧ C ) ∨ ( ¬ B ∧ D ) G ( B, C, D ) = ( B ∧ D ) ∨ ( C ∧ ¬ D ) H ( B, C, D ) = B ⊕ C ⊕ D I ( B, C, D ) = C ⊕ ( B ∨ ¬ D ) { \displaystyle { \begin { aligned } F ( B, C, D ) & = ( B\wedge { C } ) \vee ( \neg { B } \wedge { D } ) \\G ( B, C, D ) & = ( B\wedge { D } ) \vee ( C\wedge \neg { D } ) \\H ( B, C, D ) & =B\oplus C\oplus D\\I ( B, C, D ) & =C\oplus ( B\vee \neg { D } ) \end { aligned } } }

⊕, ∧, ∨, ¬ { \displaystyle \oplus, \wedge, \vee, \neg } denote the XOR, AND, OR and NOT operations respectively .

### Pseudocode

The MD5 hash is calculated according to this algorithm. [ 50 ] All values are in little-endian .

 // : All variables are unsigned 32 bit and wrap modulo 2^32 when calculating
var int s[64], K[64]
var int i

// s specifies the per-round shift amounts
s[ 0..15] := { 7, 12, 17, 22,  7, 12, 17, 22,  7, 12, 17, 22,  7, 12, 17, 22 }
s[16..31] := { 5,  9, 14, 20,  5,  9, 14, 20,  5,  9, 14, 20,  5,  9, 14, 20 }
s[32..47] := { 4, 11, 16, 23,  4, 11, 16, 23,  4, 11, 16, 23,  4, 11, 16, 23 }
s[48..63] := { 6, 10, 15, 21,  6, 10, 15, 21,  6, 10, 15, 21,  6, 10, 15, 21 }

// Use binary integer part of the sines of integers (Radians) as constants:
for i from 0 to 63 do
K[i] := floor(232 × abs (sin(i + 1)))
end for
// (Or just use the following precomputed table):
K[ 0.. 3] := { 0xd76aa478, 0xe8c7b756, 0x242070db, 0xc1bdceee }
K[ 4.. 7] := { 0xf57c0faf, 0x4787c62a, 0xa8304613, 0xfd469501 }
K[ 8..11] := { 0x698098d8, 0x8b44f7af, 0xffff5bb1, 0x895cd7be }
K[12..15] := { 0x6b901122, 0xfd987193, 0xa679438e, 0x49b40821 }
K[16..19] := { 0xf61e2562, 0xc040b340, 0x265e5a51, 0xe9b6c7aa }
K[20..23] := { 0xd62f105d, 0x02441453, 0xd8a1e681, 0xe7d3fbc8 }
K[24..27] := { 0x21e1cde6, 0xc33707d6, 0xf4d50d87, 0x455a14ed }
K[28..31] := { 0xa9e3e905, 0xfcefa3f8, 0x676f02d9, 0x8d2a4c8a }
K[32..35] := { 0xfffa3942, 0x8771f681, 0x6d9d6122, 0xfde5380c }
K[36..39] := { 0xa4beea44, 0x4bdecfa9, 0xf6bb4b60, 0xbebfbc70 }
K[40..43] := { 0x289b7ec6, 0xeaa127fa, 0xd4ef3085, 0x04881d05 }
K[44..47] := { 0xd9d4d039, 0xe6db99e5, 0x1fa27cf8, 0xc4ac5665 }
K[48..51] := { 0xf4292244, 0x432aff97, 0xab9423a7, 0xfc93a039 }
K[52..55] := { 0x655b59c3, 0x8f0ccc92, 0xffeff47d, 0x85845dd1 }
K[56..59] := { 0x6fa87e4f, 0xfe2ce6e0, 0xa3014314, 0x4e0811a1 }
K[60..63] := { 0xf7537e82, 0xbd3af235, 0x2ad7d2bb, 0xeb86d391 }

// Initialize variables:
var int a0 := 0x67452301    // A
var int b0 := 0xefcdab89    // B
var int c0 := 0x98badcfe    // C
var int d0 := 0x10325476    // D

// Pre-processing: adding a single 1 bit
append "1" bit to message[51] // Notice : the input signal bytes are considered as bits strings, // where the beginning morsel is the most significant bite of the byte . // Pre-processing: padding with zeros
append "0" bit until message length in bits ≡ 448 (mod 512)

// Notice : the two padding steps above are implemented in a dim-witted manner // in implementations that merely work with dispatch bytes : append 0x80 // and pad with 0x00 bytes thus that the message duration in bytes ≡ 56 ( mod 64 ) .

append original length in bits mod 264 to message

// Process the message in successive 512-bit chunks:
for each 512-bit chunk of padded message do
break chunk into sixteen 32-bit words M[j], 0 ≤ j ≤ 15
// Initialize hash value for this chunk:
var int A := a0
var int B := b0
var int C := c0
var int D := d0
// Main loop:
for i from 0 to 63 do
var int F, g
if 0 ≤ i ≤ 15 then
F := (B and C) or ((not B) and D)
g := i
else if 16 ≤ i ≤ 31 then
F := (D and B) or ((not D) and C)
g := (5×i + 1) mod 16
else if 32 ≤ i ≤ 47 then
F := B xor C xor D
g := (3×i + 5) mod 16
else if 48 ≤ i ≤ 63 then
F := C xor (B or (not D))
g := (7×i) mod 16
// Be wary of the below definitions of a,b,c,d
F := F + A + K[i] + M[g]  // M[g] must be a 32-bits block
A := D
D := C
C := B
B := B + leftrotate(F, s[i])
end for
// Add this chunk's hash to result so far:
a0 := a0 + A
b0 := b0 + B
c0 := c0 + C
d0 := d0 + D
end for

var char digest[16] := a0 append b0 append c0 append d0  // (Output is in little-endian)


rather of the formulation from the original RFC 1321 shown, the trace may be used for improved efficiency ( useful if assembly language is being used – otherwise, the compiler will generally optimize the above code. Since each calculation is pendent on another in these formulations, this is frequently slower than the above method where the nand/and can be parallelised ) :

( 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 ( besides termed message digests ) are typically represented as a succession of 32 hexadecimal digits. The watch demonstrates a 43-byte ASCII remark and the comparable MD5 hash :

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


even a humble switch in the message will ( with overwhelming probability ) result in a by and large different hash, ascribable to the avalanche effect. For exercise, adding a period to the end of the prison term :

MD5("The quick brown fox jumps over the lazy dog .") =


The hash of the zero-length string is :

MD5("") =
d41d8cd98f00b204e9800998ecf8427e


The MD5 algorithm is specified for messages consisting of any count of bits ; it is not limited to multiples of eight bits ( octets, bytes ). Some MD5 implementations such as md5sum might be limited to octets, or they might not support streaming for messages of an initially undetermined length.

## Implementations

Below is a tilt of cryptography libraries that support MD5 :