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MD2 (cryptography)

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MD2
General
Designers Ronald Rivest
First published 1989
Series MD, MD2, MD3, MD4, MD5
Detail
Digest sizes 128 bits
Rounds 18

Message Digest Algorithm 2 (MD2) is a cryptographic hash function developed by Ronald Rivest in 1989. The algorithm is optimized for 8-bit computers. MD2 is specified in RFC 1319. Although other algorithms have been proposed since, such as MD4, MD5 and SHA, even as of 2004 MD2 remains in use in public key infrastructures as part of certificates generated with MD2 and RSA.

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[edit] Description

The 128-bit hash value of any message is formed by padding it to a multiple of the block length on the computer (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 generated indirectly from the digits of the fractional part of pi are used. 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's 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

[edit] 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

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

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

The hash of the zero-length string is:

 MD2("") = 8350e5a3e24c153df2275c9f80692773

[edit] Security

Rogier and Chauvaud (1997) described collisions of MD2's compression function, although they were unable to extend the attack to the full MD2.

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

[edit] References

  • John Linn, RFC 1115 - Privacy Enhancement for Internet Electronic Mail: Part III -- Algorithms, Modes, and Identifiers, Section 4.2, August 1989, Source by Ron L. Rivest October, 1988.
  • Burt Kaliski, RFC 1319 - MD2 Message Digest Algorithm, April 1992.
  • N. Rogier, Pascal Chauvaud, The compression function of MD2 is not collision free, Selected Areas in Cryptography - SAC'95 Ottawa, Canada, May 18-19, 1995 (workshop record).
  • N. Rogier, Pascal Chauvaud, MD2 is not Secure without the Checksum Byte, Designs, Codes and Cryptography, 12(3), pp245–251, 1997.
  • Frédéric Muller, The MD2 Hash Function is Not One-Way, ASIACRYPT 2004, pp214–229.
  • Lars R. Knudsen and John Erik Mathiassen, Preimage and Collision Attacks on MD2. FSE 2005.

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