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| In [[cryptography]], '''MDC-2 (Modification Detection Code 2, sometimes called Meyer-Schilling)''' is a [[cryptographic hash function]]. MDC-2 is a [[One-way compression function|hash function based on a block cipher]] with a proof of security in the ideal-cipher model.<ref>{{cite conference
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| | first = John
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| | last = Steinberger
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| | title = The Collision Intractability of MDC-2 in the Ideal-Cipher Model
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| | booktitle = Advances in Cryptology - EUROCRYPT 2007
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| | pages = 34–51
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| | publisher = Springer-Verlag
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| | date = June 23, 2007
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| | url = http://eprint.iacr.org/2006/294
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| | doi = 10.1007/978-3-540-72540-4_3
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| | accessdate = January 31, 2008}}</ref> The length of the output hash depends on the underlying block cipher used.
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| == Algorithm ==
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| For a given message <math>M</math> to hash and a given block cipher encryption function <math>E</math>, the MDC-2 algorithm proceed as followed. Let <math>n</math> be the block length, <math>A_1, B_1</math> two different constants of size <math>n</math>. If <math>M = M_1||..|M_m</math> where each <math>M_i</math> has size <math>n</math>, then the hash <math>V_m||W_m</math> of the message is given by:
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| *for <math>i = 1</math> to <math>m</math>:
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| **<math>V_i = M_i \oplus E(M_i,A_i)</math>
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| **<math>W_i = M_i \oplus E(M_i,B_i)</math>
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| **<math>V_i^L || V_i^R = V_i</math>
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| **<math>W_i^L || W_i^R = W_i</math>
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| **<math>A_{i+1} = V_i^R||W_i^L</math>
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| **<math>B_{i+1} = W_i^R||V_i^L</math>
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| *return <math>A_{m+1}||B_{m+1}</math>
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| ==MDC-2DES hashes==
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| When MDC-2 uses the [[Data Encryption Standard|DES]] block cipher, the 128-bit (16-byte) MDC-2 hashes are typically represented as 32-digit [[hexadecimal]] numbers. The following demonstrates a 43-byte [[ASCII]] input and the corresponding MDC-2 hash:
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| MDC2("The quick brown fox jumps over the lazy dog")
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| = 000ed54e093d61679aefbeae05bfe33a
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| Even a small change in the message will (with probability) result in a completely different hash, e.g. changing <tt>d</tt> to <tt>c</tt>:
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| MDC2("The quick brown fox jumps over the lazy cog")
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| = 775f59f8e51aec29c57ac6ab850d58e8
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| The hash of the zero-length string is:
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| MDC2("")
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| = 52525252525252522525252525252525
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| ==Patent issues==
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| MDC-2 was covered by {{US patent|4908861}}, issued on March 13, 1990 but filed by [[IBM]] on August 28, 1987.<br />
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| For this reason, support for MDC-2 has been disabled in [[OpenSSL]] on most [[Linux]] distributions and is not implemented by many other cryptographic libraries.
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| But the maximum lifespan of 20 years from filing date means that the {{US patent|4908861}} could not have lasted beyond August 28, 2007 ; in fact it has expired in 2002,<ref>{{Cite document
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| | title = USPTO - Patent Maintenance Fees
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| | publisher = United States Patent Office
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| | date = March 13, 2002
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| | url = https://ramps.uspto.gov/eram/getMaintFeesInfo.do?patentNum=4908861&applicationNum=07090633
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| | accessdate = 2008-01-31
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| | postscript = <!--None--> }} (Click on "Bibliographic data".)</ref> because IBM has not paid the renewal fee. The same goes for the Canadian patent. There is no patent for Europe.<br />This means that MDC2 can be freely used.
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| == See also ==
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| * [[One-way compression function]]
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| ==Notes==
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| <references/>
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| {{Cryptography navbox | hash}}
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| [[Category:Cryptographic hash functions]]
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| {{crypto-stub}}
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