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26-505: The Merkle–Damgård construction was described in Ralph Merkle 's Ph.D. thesis in 1979. Ralph Merkle and Ivan Damgård independently proved that the structure is sound: that is, if an appropriate padding scheme is used and the compression function is collision-resistant , then the hash function will also be collision-resistant. The Merkle–Damgård hash function first applies an MD-compliant padding function to create an input whose size

52-761: A Distinguished Professor at Georgia Tech , where he led the Georgia Tech Information Security Center . In 2006 he returned to the San Francisco Bay Area, where he has been a senior research fellow at IMM, a faculty member at Singularity University , and a board member of the Alcor Life Extension Foundation . He was awarded the IEEE Richard W. Hamming Medal in 2010. He is active in the field of molecular manipulation and self-replicating machines and has published books on

78-448: A bigger internal state (the last result) into a smaller output hash size or to guarantee a better mixing and avalanche effect on the bits in the hash sum. The finalisation function is often built by using the compression function. (Note that in some documents a different terminology is used: the act of length padding is called "finalisation".) The popularity of this construction is due to the fact, proven by Merkle and Damgård , that if

104-461: A collision-resistant compression function. The hash function PARSHA-256 was designed using the parallel algorithm and the compression function of SHA-256. As mentioned in the introduction, the padding scheme used in the Merkle–Damgård construction must be chosen carefully to ensure the security of the scheme. Mihir Bellare gives sufficient conditions for a padding scheme to possess to ensure that

130-453: A padding that encodes the length of the original message. This is called length padding or Merkle–Damgård strengthening . In the diagram, the one-way compression function is denoted by f , and transforms two fixed length inputs to an output of the same size as one of the inputs. The algorithm starts with an initial value, the initialization vector (IV). The IV is a fixed value (algorithm- or implementation-specific). For each message block,

156-516: A scheme for communication over an insecure channel , as part of a class project at UC Berkeley. The scheme is now recognized to be an early example of public key cryptography . He co-invented the Merkle–Hellman knapsack cryptosystem , invented cryptographic hashing (now called the Merkle–Damgård construction based on a pair of articles published 10 years later that established the security of

182-436: A wide-pipe hash function can be made approximately twice as fast if the wide-pipe state can be divided in half in the following manner: one half is input to the succeeding compression function while the other half is combined with the output of that compression function. The main idea of the hash construction is to forward half of the previous chaining value forward to XOR it to the output of the compression function. In so doing

208-452: Is 8 bytes (64 bits). We get two blocks (the padding octets shown with the lightblue background color): This implies that other messages having the same content but ending with additional zeros at the end will result in the same hash value. In the above example, another almost-identical message (0x48617368496e7075 74 00 ) will generate the same hash value as the original message "HashInput" above. In other words, any message having extra zeros at

234-441: Is a multiple of a fixed number (e.g. 512 or 1024) — this is because compression functions cannot handle inputs of arbitrary size. The hash function then breaks the result into blocks of fixed size, and processes them one at a time with the compression function, each time combining a block of the input with the output of the previous round. In order to make the construction secure, Merkle and Damgård proposed that messages be padded with

260-430: Is very similar to the Merkle–Damgård construction but has a larger internal state size, meaning that the bit-length that is internally used is larger than the output bit-length. If a hash of n bits is desired, then the compression function f takes 2 n bits of chaining value and m bits of the message and compresses this to an output of 2 n bits. Therefore, in a final step, a second compression function compresses

286-519: The IEEE Richard W. Hamming Medal in 2010 and has published works on molecular manipulation and self-replicating machines . Ralph Merkle is a grandnephew of baseball star Fred Merkle and is married to video game designer Carol Shaw . He serves on the board of directors of the cryonics organization Alcor Life Extension Foundation and appears in the science fiction novel The Diamond Age . While an undergraduate, Merkle devised Merkle's Puzzles ,

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312-496: The Merkle–Hellman knapsack cryptosystem, and inventing cryptographic hashing ( Merkle–Damgård construction ) and Merkle trees . He has worked as a manager at Elxsi , research scientist at Xerox PARC (Palo Alto Research Center), and a nanotechnology theorist at Zyvex . Merkle has held positions as a Distinguished Professor at Georgia Tech , senior research fellow at IMM, faculty member at Singularity University , and board member at Alcor Life Extension Foundation . He received

338-606: The science fiction novel The Diamond Age , involving nanotechnology. Mihir Bellare Mihir Bellare is a cryptographer and professor at the University of California San Diego . He holds a Bachelor of Science degree from the California Institute of Technology and a Ph.D. from the Massachusetts Institute of Technology . He has published several seminal papers in the field of cryptography (notably in

364-449: The MD construction is secure: it suffices that the scheme be "MD-compliant" (the original length-padding scheme used by Merkle is an example of MD-compliant padding). The conditions are: Here, | X | denotes the length of X . With these conditions in place, a collision in the MD hash function exists exactly when there is a collision in the underlying compression function. Therefore,

390-459: The Merkle–Damgård construction is provably secure when the underlying compression function is secure. To be able to feed the message to the compression function, the last block must be padded with constant data (generally with zeroes) to a full block. For example, suppose the message to be hashed is "HashInput" (9 octet string, 0x48617368496e707574 in ASCII ) and the block size of the compression function

416-421: The area of provable security), many of which were co-written with Phillip Rogaway . Bellare has published a number of papers in the field of Format-Preserving Encryption . His students include Michel Abdalla, Chanathip Namprempre, Tadayoshi Kohno and Anton Mityagin. Bellare is one of the authors of skein . In 2003 Bellare was a recipient of RSA Conference 's Sixth Annual Award for outstanding contributions in

442-483: The compression (or compacting) function f takes the result so far, combines it with the message block, and produces an intermediate result. The last block is padded with zeros as needed and bits representing the length of the entire message are appended. (See below for a detailed length-padding example.) To harden the hash further, the last result is then sometimes fed through a finalisation function . The finalisation function can have several purposes such as compressing

468-426: The construction takes in longer message blocks every iteration than the original wide pipe. Using the same function f as before, it takes n -bit chaining values and n + m bits of the message. However, the price to pay is the extra memory used in the construction for feed-forward. The MD construction is inherently sequential. There is a parallel algorithm which constructs a collision-resistant hash function from

494-434: The end makes it indistinguishable from the one without them. To prevent this situation, the first bit of the first padding octet is changed to "1" (0x80), yielding: However, most common implementations use a fixed bit-size (generally 64 or 128 bits in modern algorithms) at a fixed position at the end of the last block for inserting the message length value (see SHA-1 pseudocode ). Further improvement can be made by inserting

520-578: The field of mathematics for his research in cryptography. In 2013 he became a Fellow of the Association for Computing Machinery . In 2019 he was awarded Levchin Prize for Real-World Cryptography for his outstanding contributions to the design and analysis of real-world cryptosystems, including the development of random oracle model, modes of operation, HMAC , and models for key exchange. Bellare's papers cover topics including: On September 14, 2022, Bellare

546-456: The last internal hash value ( 2 n bits) to the final hash value ( n bits). This can be done as simply as discarding half of the last 2 n -bit output. SHA-512/224 and SHA-512/256 take this form since they are derived from a variant of SHA-512. SHA-384 and SHA-224 are similarly derived from SHA-512 and SHA-256, respectively, but the width of their pipe is much less than 2 n . It has been demonstrated by Mridul Nandi and Souradyuti Paul that

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572-406: The length value in the last block if there is enough space. Doing so avoids having an extra block for the message length. If we assume the length value is encoded on 5 bytes (40 bits), the message becomes: Storing the message length out-of-band in metadata, or otherwise embedded at the start of the message, is an effective mitigation of the length extension attack , as long as invalidation of either

598-451: The message length and checksum are both considered failure of integrity checking. Ralph Merkle Ralph C. Merkle (born February 2, 1952) is an American computer scientist and mathematician. He is one of the inventors of public-key cryptography , the inventor of cryptographic hashing , and more recently a researcher and speaker on cryonics . Merkle is a renowned cryptographer, known for devising Merkle's Puzzles , co-inventing

624-439: The one-way compression function f is collision resistant , then so is the hash function constructed using it. Unfortunately, this construction also has several undesirable properties: Due to several structural weaknesses of Merkle–Damgård construction, especially the length extension problem and multicollision attacks, Stefan Lucks proposed the use of the wide-pipe hash instead of Merkle–Damgård construction. The wide-pipe hash

650-523: The scheme), and invented Merkle trees . The Merkle–Damgård construction is at the heart of many hashing algorithms. At Xerox PARC Merkle designed the Khufu and Khafre block ciphers and the Snefru hash function. Merkle was the manager of compiler development at Elxsi from 1980. In 1988, he became a research scientist at Xerox PARC . In 1999 he became a nanotechnology theorist for Zyvex . In 2003 he became

676-439: The subject. Ralph Merkle is a grandnephew of baseball star Fred Merkle ; son of Theodore Charles Merkle, director of Project Pluto ; and brother of Judith Merkle Riley , a historical writer. Merkle is married to Carol Shaw , the video game designer best known for the 1982 Atari 2600 game River Raid . Merkle is on the board of directors of the cryonics organization Alcor Life Extension Foundation . Merkle appears in

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