MD2 (hash function)

The MD2 Message-Digest Algorithm is a cryptographic hash function developed by Ronald Rivest in 1989.^[2] The algorithm is optimized for 8-bit computers. MD2 is specified in IETF RFC 1319.^[3] The "MD" in MD2 stands for "Message Digest".

MD2

General
Designers	Ronald Rivest
First published	August 1989[1]
Series	MD2, MD4, MD5, MD6
Detail
Digest sizes	128 bits
Rounds	18

Even though MD2 is not yet fully compromised, the IETF retired MD2 to "historic" status in 2011, citing "signs of weakness". It is deprecated in favor of SHA-256 and other strong hashing algorithms.^[4]

Nevertheless, as of 2014^[update], it remained in use in public key infrastructures as part of certificates generated with MD2 and RSA.^{[citation needed]}

Description

The 128-bit hash value of any message is formed by padding it to a multiple of the block length (128 bits or 16 bytes) and adding a 16-byte checksum to it. For the actual calculation, a 48-byte auxiliary block and a 256-byte S-table are used. The constants were generated by shuffling the integers 0 through 255 using a variant of Durstenfeld's algorithm with a pseudorandom number generator based on decimal digits of π (pi)^[3][5] (see nothing up my sleeve number). The algorithm runs through a loop where it permutes each byte in the auxiliary block 18 times for every 16 input bytes processed. Once all of the blocks of the (lengthened) message have been processed, the first partial block of the auxiliary block becomes the hash value of the message.

The S-table values in hex are:

{ 0x29, 0x2E, 0x43, 0xC9, 0xA2, 0xD8, 0x7C, 0x01, 0x3D, 0x36, 0x54, 0xA1, 0xEC, 0xF0, 0x06, 0x13, 
  0x62, 0xA7, 0x05, 0xF3, 0xC0, 0xC7, 0x73, 0x8C, 0x98, 0x93, 0x2B, 0xD9, 0xBC, 0x4C, 0x82, 0xCA, 
  0x1E, 0x9B, 0x57, 0x3C, 0xFD, 0xD4, 0xE0, 0x16, 0x67, 0x42, 0x6F, 0x18, 0x8A, 0x17, 0xE5, 0x12, 
  0xBE, 0x4E, 0xC4, 0xD6, 0xDA, 0x9E, 0xDE, 0x49, 0xA0, 0xFB, 0xF5, 0x8E, 0xBB, 0x2F, 0xEE, 0x7A, 
  0xA9, 0x68, 0x79, 0x91, 0x15, 0xB2, 0x07, 0x3F, 0x94, 0xC2, 0x10, 0x89, 0x0B, 0x22, 0x5F, 0x21,
  0x80, 0x7F, 0x5D, 0x9A, 0x5A, 0x90, 0x32, 0x27, 0x35, 0x3E, 0xCC, 0xE7, 0xBF, 0xF7, 0x97, 0x03, 
  0xFF, 0x19, 0x30, 0xB3, 0x48, 0xA5, 0xB5, 0xD1, 0xD7, 0x5E, 0x92, 0x2A, 0xAC, 0x56, 0xAA, 0xC6, 
  0x4F, 0xB8, 0x38, 0xD2, 0x96, 0xA4, 0x7D, 0xB6, 0x76, 0xFC, 0x6B, 0xE2, 0x9C, 0x74, 0x04, 0xF1, 
  0x45, 0x9D, 0x70, 0x59, 0x64, 0x71, 0x87, 0x20, 0x86, 0x5B, 0xCF, 0x65, 0xE6, 0x2D, 0xA8, 0x02, 
  0x1B, 0x60, 0x25, 0xAD, 0xAE, 0xB0, 0xB9, 0xF6, 0x1C, 0x46, 0x61, 0x69, 0x34, 0x40, 0x7E, 0x0F, 
  0x55, 0x47, 0xA3, 0x23, 0xDD, 0x51, 0xAF, 0x3A, 0xC3, 0x5C, 0xF9, 0xCE, 0xBA, 0xC5, 0xEA, 0x26, 
  0x2C, 0x53, 0x0D, 0x6E, 0x85, 0x28, 0x84, 0x09, 0xD3, 0xDF, 0xCD, 0xF4, 0x41, 0x81, 0x4D, 0x52, 
  0x6A, 0xDC, 0x37, 0xC8, 0x6C, 0xC1, 0xAB, 0xFA, 0x24, 0xE1, 0x7B, 0x08, 0x0C, 0xBD, 0xB1, 0x4A, 
  0x78, 0x88, 0x95, 0x8B, 0xE3, 0x63, 0xE8, 0x6D, 0xE9, 0xCB, 0xD5, 0xFE, 0x3B, 0x00, 0x1D, 0x39, 
  0xF2, 0xEF, 0xB7, 0x0E, 0x66, 0x58, 0xD0, 0xE4, 0xA6, 0x77, 0x72, 0xF8, 0xEB, 0x75, 0x4B, 0x0A, 
  0x31, 0x44, 0x50, 0xB4, 0x8F, 0xED, 0x1F, 0x1A, 0xDB, 0x99, 0x8D, 0x33, 0x9F, 0x11, 0x83, 0x14 }

MD2 hashes

The 128-bit (16-byte) MD2 hashes (also termed message digests) are typically represented as 32-digit hexadecimal numbers. The following demonstrates a 43-byte ASCII input and the corresponding MD2 hash:

 MD2("The quick brown fox jumps over the lazy dog") = 
 03d85a0d629d2c442e987525319fc471

As the result of the avalanche effect in MD2, even a small change in the input message will (with overwhelming probability) result in a completely different hash. For example, changing the letter d to c in the message results in:

 MD2("The quick brown fox jumps over the lazy cog") = 
 6b890c9292668cdbbfda00a4ebf31f05

The hash of the zero-length string is:

 MD2("") = 
 8350e5a3e24c153df2275c9f80692773

Security

Rogier and Chauvaud presented in 1995^[6] collisions of MD2's compression function, although they were unable to extend the attack to the full MD2. The described collisions was published in 1997.^[7]

In 2004, MD2 was shown to be vulnerable to a preimage attack with time complexity equivalent to 2¹⁰⁴ applications of the compression function.^[8] The author concludes, "MD2 can no longer be considered a secure one-way hash function".

In 2008, MD2 has further improvements on a preimage attack with time complexity of 2⁷³ compression function evaluations and memory requirements of 2⁷³ message blocks.^[9]

In 2009, MD2 was shown to be vulnerable to a collision attack with time complexity of 2^63.3 compression function evaluations and memory requirements of 2⁵² hash values. This is slightly better than the birthday attack which is expected to take 2^65.5 compression function evaluations.^[10]

In 2009, security updates were issued disabling MD2 in OpenSSL, GnuTLS, and Network Security Services.^[11]

See also

• Hash function security summary
• Comparison of cryptographic hash functions
• MD4
• MD5
• MD6
• SHA-1

References

1. Linn, John (August 1989). "RSA-MD2 Message Digest Algorithm". Privacy Enhancement for Internet Electronic Mail: Part III — Algorithms, Modes, and Identifiers. Rivest, Ron. IETF. sec. 4.2. doi:10.17487/RFC1115. RFC 1115. Retrieved 26 April 2021.
2. RSA Laboratories. "What are MD2, MD4, and MD5?". Public-Key Cryptography Standards (PKCS): PKCS #7: Cryptographic Message Syntax Standard. RSA Laboratories. Archived from the original on 16 January 2017.
3. Kaliski, Burt (April 1992). The MD2 Message-Digest Algorithm. IETF. p. 3. doi:10.17487/RFC1319. RFC 1319. Retrieved 22 November 2014.
4. RFC 6149, MD2 to Historic Status
5. "How is the MD2 hash function S-table constructed from Pi?". Cryptography Stack Exchange. Stack Exchange. 2 August 2014. Retrieved 23 May 2021.
6. Rogier, N.; Chauvaud, Pascal (18–19 May 1995). The Compression Function of MD2 is not Collision Free. Selected Areas in Cryptography (SAC) 1995, Ottawa, Canada (workshop record).
7. Rogier, N.; Chauvaud, Pascal (1997). "MD2 is not Secure without the Checksum Byte". Designs, Codes and Cryptography. 12 (3): 245–251. doi:10.1023/A:1008220711840. S2CID 21613457.
8. Muller, Frédéric (2004). The MD2 Hash Function is Not One-Way (PDF). ASIACRYPT 2004. pp. 214–229. doi:10.1007/978-3-540-30539-2_16. Retrieved 26 April 2021 – via International Association for Cryptologic Research.
9. Thomsen, Søren S. (2008). "An Improved Preimage Attack on MD2" (PDF). {{cite journal}}: Cite journal requires |journal= (help)
10. Knudsen, Lars R.; Mathiassen, John Erik; Muller, Frédéric; Thomsen, Søren S. (2009). "Cryptanalysis of MD2". Journal of Cryptology. 23: 72–90. doi:10.1007/s00145-009-9054-1. S2CID 2443076.
11. CVE-2009-2409

Further reading

• Knudsen, Lars R.; Mathiassen, John Erik (21–23 February 2005). Preimage and Collision Attacks on MD2 (PDF). Fast Software Encryption (FSE) 2005. Retrieved 26 April 2021.

External links