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## SHA Hash Functions History & Current State

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**SHA Hash FunctionsHistory& Current State**Helsinki Institute for Information Technology, November 03, 2009. Sergey Panasenko, independent information security consultant, Moscow, Russia. serg@panasenko.ru www.panasenko.ru**SHA Hash Functions**• Hash functions cryptanalysis review. • SHA (SHA-0) & SHA-1. • SHA-2. • SHA-3 project.**Section 1. Hash functions cryptanalysis review**• typical hash function structure; • goals of hash functions cryptanalysis; • cryptanalysis methods.**Typical hash function structure**Merkle-Damgård construction:**Primary goals of hash functions cryptanalysis**Collision: m1 and m2 with the same hash: h = hash(m1)=hash(m2) Multicollision: several messages with the same hash. Theoretical time consumption: 2n/2operations for n-bit hash function.**Primary goals of hash functions cryptanalysis**First preimage: such m that for given h: hash(m)=h Second preimage: such m2 that for given m1: hash(m2)=hash(m1) Theoretical time consumption: 2noperations for n-bit hash function.**Primary goals of hash functions cryptanalysis**Secret key definition – for keyed hash functions or hash functions in keyed mode. Theoretical time consumption: 2koperations for k-bit key.**Secondary goals of hash functions cryptanalysis**Near-collision: m1 and m2 with hash values differ in several bits: hash(m1)≈hash(m2) Pseudo-collision: m1 and m2 with the same hash but with different initial values: hash(m1, IV1)=hash(m2,IV2) Theoretical time consumption: 2n/2operations for n-bit hash function.**Secondary goals of hash functions cryptanalysis**Pseudo-preimage: such m that for given h: hash(IV, m)=h where IV is non-standard initial value. Theoretical time consumption: 2noperations for n-bit hash function.**Attacks on hash functions**• Step-by-step searching over the target space. • They define theoretical time consumption of any goal. • Can be used for finding collisions, preimages or secret keys. • Highly parallelizable. • Can be accelerated greatly by specific hardware. • Can be used in context of other attacks. • They define suitable hash or key sizes. Brute-force attacks**Attacks on hash functions**• A kind of brute-force attacks on a reduced target space (e.g. words of any dictionary). • Typical application: finding a password for given hash value. • Offline work – precounting a table for searching the required password. Dictionary attacks**Attacks on hash functions**The simplest case of tables: one hash for every password. Dictionary attacks**Attacks on hash functions**Hash chains – reducing the memory (Martin Hellman, 1980): p1h1p2h2… pNhN Dictionary attacks**Attacks on hash functions**Hash chains – collision example: Dictionary attacks**Attacks on hash functions**Strengthening hash chains: • Several tables with different R-functions. • Variable length chains. Dictionary attacks**Attacks on hash functions**Several R-functions R1…RN-1 for every column of strings: • cyclic strings are impossible; • collisions lead to strings coincidence when occur in the same column only – that can be detected. Dictionary attacks. Rainbow tables**Attacks on hash functions**Invented by Philip Oechslin in 2003. Can be further strengthened by combining with variable-length chains. Are in active use for cracking real systems: • http://project-rainbowcrack.com; • http://lasecwww.epfl.ch; • http://www.freerainbowtables.com. Dictionary attacks. Rainbow tables**Attacks on hash functions**Countermeasures: • Salt – randomizing hashing; • Increasing time to hash – e. g. multiple hashing. Example: Niels Provos & David Mazières (1999) – bcrypt hash function. Uses salt & cost variables. Cost defines the number of internal block cipher key extension rounds: 2cost+1+1 Dictionary attacks. Rainbow tables**Attacks on hash functions**“Square root attack”: O() tries required to find the same element from an array with N elements. Application to hash functions (Gideon Yuval, 1979): • An adversary prepares r variants of fraud document f and r variants of original document m. • He searches among these variants such mx and fy that hash(mx)=hash(fy). • User signs mx, but his signature is correct when verifying it for fy. Birthday paradox**Attacks on hash functions**Another variant of hash chains: mihash(mi)hash(hash(mi)) … All hash values are compared with previous values and values of other chains. Disadvantage: huge memory requirements. Jean-Jacques Quisquater, Jean-Paul Delescaille, 1987: store distinguished pointsonly. Their coincidence signals about found collision. Low memory requirements. Collision search**Attacks on hash functions**Michael Wiener and Paul Van Oorschot, 1994: parallel collision search with specific values: Collisions search**Attacks on hash functions**Birthday paradox & collisions search • Mihir Bellare and Tadayoshi Kohno, 2004: “amount of regularity” of hash functions – asoutput value distribution is regular. The less regular, the easy to find collision. • Bart Preneel, 2003: hash value size analysis. 160 bits are enough for at least 20 years.**Attacks on hash functions**Florent Chabaud & Antoine Joux, 1998: SHI1 algorithm: Differential cryptanalysis**Attacks on hash functions**Differential cryptanalysis**Attacks on hash functions**Result: propagation of the difference is cancelled by the corrected bits. After 6 iterations the difference is 0. This is 6-round local collision: two messages differ in 6 bits (after expansion) but lead to the same hash value. Next step: construct messages which can expand with required difference. Attackers use disturbance vector – the table shows which bits of messages must be different to achieve the collision. Differential cryptanalysis**Attacks on hash functions**Differential cryptanalysis F. Chabaud & A. Joux: SHI1 – SHI2 – SHI3 – SHA Step-by-step including non-linear operation into the iterations. From deterministic to probabilistic constructions: the same principles of attack can be applied to real SHA algorithm.**Attacks on hash functions**Boomerang attack Invented by David Wagner for block ciphers in 1999. Applied to hash functions (SHA & SHA-1) by Antoine Joux and Thomas Peyrin, 2007. Boomerang attack uses one or more auxiliary differences besides the main difference. This significantly improves the probability of finding collisions.**Attacks on hash functions**Boomerang attack**Attacks on hash functions**Algebraic cryptanalysis Uses algebraic properties of an algorithm. Successfully applied to block ciphers (e. g. works of Nicolas Courtois against AES). Can be used in context of other attacks. Example: Makoto Sugita, Mitsuru Kawazoe, Hideki Imai (2006) attacked reduced-round SHA-1 by algebraic and differential cryptanalysis in complex.**Attacks on hash functions**Message modification Xiaoyun Wang, Hongbo Yu, 2005: step-by-step modifying the message to meet the criteria for differential cryptanalysis. Message modification technique allows to speed up the collision search by fulfilling the required criteria for internal variables.**Attacks on hash functions**Meet in the middle attack Can be applied when a function can be represent as two subfunctions: and if the second subfunction can be invertible.**Attacks on hash functions**Meet in the middle attack Finding preimage for a hash value H: • Count hash1() for variants of the first half of messages (and store them in a table): Tx=hash1(M1x,IV). 2. Count inverted hash2() for variants of the second half of messages: Ty = hash2-1(M2y,H). 3. Searching for equivalent Tx and Ty.**Attacks on hash functions**Correcting blocks Allows to find preimages or collisions. Example for collisions: 1. Select arbitrary messages M and M*. 2. Find such corrected blocks X and X* that: hash(M ||X) = hash(M* ||X*).**Attacks on hash functions**Fixed points A fixed point occurs when it is possible to find such message block Mi that: hash(M) = hash(M||Mi), i. e. intermediate hash value remains the same after processing Mi block. Can be used for finding collisions.**Attacks on hash functions**Block-level manipulations • inserting, • removing, • permutation, • substitution of message blocks without affecting the hash value.**Attacks on hash functions**Two-block collisions Eli Biham et al., 2004:**Attacks on hash functions**Multi-block collisions**Attacks on hash functions**Specific attacks on block cipher based hash functions Allows to find collisions based on some weaknesses of an underlying block cipher: • weak keys, • equivalent keys, • groups of keys, • related-keys attacks.**Attacks on hash functions**This group of attacks are invented by Paul Kocher, 1996. Passive side-channel attacks (an adversary only readsside-channel information): • Electromagnetic attacks. • Power attacks (simple & differential). • Timing attacks. • Error-message attacks. Side-channel attacks**Attacks on hash functions**Active side-channel attacks (an adversary influences on hash function realization): • Optical, radiation or heating attacks. • Spike & glitch attacks. • Fault attacks (simple and differential). • Hardware modification. Side-channel attacks**Attacks on hash functions**Countermeasures: • Constant time consumption of operations. • Inserting random delays, noises, random variables etc, redundant computations. • Error messages without extra information. • Doubling calculations with comparing their results. • Shielding. • Detecting of external actions. Side-channel attacks**Attacks on hash functions**Other cryptanalytic methods • Using neutral bits (Eli Biham & Rafi Chen, 2004) – such bits of a message which do not influence on final or intermediate results during some rounds. • Attacks that can use specifics of hash functions realizations in network protocols, signature schemes etc. • Length-extension attack – inserting some data to the end of a message to find a collision.**Section 2. SHA & SHA-1**• SHA structure; • SHA-1 structure; • SHA cryptanalysis; • SHA-1 cryptanalysis.**SHA**Secure Hash Algorithm. Invented by U.S. National Security Agency in 1992. U.S. hashing standard in 1993-1995 (FIPS 180). Must be used by U.S. Ministries and Agencies for hashing non-classified information. Recommended for commercial organizations. Renamed to SHA-0 after SHA-1 invention. Overview**SHA**160-bit hash value. Input data size – from 0 to (264-1) bits. Merkle-Damgaard construction with 512-bit data blocks. Last block is always padded by: • “1” bit; • zero bits when required; • 64-bit input data length in bits. High-level structure**SHA**• 512-bit block is represented as 32-bit words W0…W15. • The following 32-bit words W16…W79 are calculated: Wn=Wn-3Wn-8Wn-14Wn-16. Message block expansion**SHA**80 iterations: Compression function**SHA**fi functions: f(x, y, z) = (x & y) | (~x & z), i = 0…19; f(x, y, z) = xyz, i = 20…39, 60…79; f(x, y, z) = (x& y) | (x& z) | (y& z), i = 40…59. Compression function**SHA**Intermediate hash values: 32-bit registers A…E. Chaining by addition modulo 232: A = A + a; B = B + b, etc. No finalization is performed: output hash value is concatenation of A…E after processing all message blocks. Chaining and finalization**SHA-1**U.S. hashing standard since 1995 (FIPS 180-1, FIPS 180-2). Will be withdrawn (for some applications) in 2010. All procedures are the same as in SHA algorithm, except the message block expansion. Overview & high-level structure