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26
The Security of the Cipher Block Chaining Message Authentication Code
, 2000
"... Let F be some block cipher (eg., DES) with block length l. The Cipher Block Chaining Message Authentication Code (CBC MAC) specifies that an mblock message x: Xl...xm be authenticated among parties who share a secret key a for the block cipher by tagging x with a prefix of ym, where Y0: 01 and Y ..."
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Cited by 197 (37 self)
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Let F be some block cipher (eg., DES) with block length l. The Cipher Block Chaining Message Authentication Code (CBC MAC) specifies that an mblock message x: Xl...xm be authenticated among parties who share a secret key a for the block cipher by tagging x with a prefix of ym, where Y0: 01 and Yi: Fa(miYi1) for i: 1,2,...,m. This method is a pervasively used international and U.S. standard. We provide its first formal justification, showing the following general lemma: cipher block chaining a pseudorandom function yields a pseudorandom function. Underlying our results is a technical lemma of independent interest, bounding the success probability of a computationally unbounded adversary in distinguishing between a random m/bit to/bit function and the CBC MAC of a random/bit to/bit function.
MerkleDamg˚ard Revisited: How to Construct a Hash Function
 Advances in Cryptology, Crypto 2005
"... The most common way of constructing a hash function (e.g., SHA1) is to iterate a compression function on the input message. The compression function is usually designed from scratch or made out of a blockcipher. In this paper, we introduce a new security notion for hashfunctions, stronger than col ..."
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Cited by 79 (8 self)
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The most common way of constructing a hash function (e.g., SHA1) is to iterate a compression function on the input message. The compression function is usually designed from scratch or made out of a blockcipher. In this paper, we introduce a new security notion for hashfunctions, stronger than collisionresistance. Under this notion, the arbitrary length hash function H must behave as a random oracle when the fixedlength building block is viewed as a random oracle or an ideal blockcipher. The key property is that if a particular construction meets this definition, then any cryptosystem proven secure assuming H is a random oracle remains secure if one plugs in this construction (still assuming that the underlying fixedlength primitive is ideal). In this paper, we show that the current design principle behind hash functions such as SHA1 and MD5 — the (strengthened) MerkleDamg˚ard transformation — does not satisfy this security notion. We provide several constructions that provably satisfy this notion; those new constructions introduce minimal changes to the plain MerkleDamg˚ard construction and are easily implementable in practice.
MultiPropertyPreserving Hash Domain Extension and the EMD Transform
 Advances in Cryptology – ASIACRYPT 2006
, 2006
"... Abstract We point out that the seemingly strong pseudorandom oracle preserving (PROPr) propertyof hash function domainextension transforms defined and implemented by Coron et. al. [12] can actually weaken our guarantees on the hash function, in particular producing a hash functionthat fails to be ..."
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Cited by 59 (7 self)
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Abstract We point out that the seemingly strong pseudorandom oracle preserving (PROPr) propertyof hash function domainextension transforms defined and implemented by Coron et. al. [12] can actually weaken our guarantees on the hash function, in particular producing a hash functionthat fails to be even collisionresistant (CR) even though the compression function to which the transform is applied is CR. Not only is this true in general, but we show that all the transformspresented in [12] have this weakness. We suggest that the appropriate goal of a domain extension transform for the next generation of hash functions is to be multiproperty preserving, namelythat one should have a single transform that is simultaneously at least collisionresistance preserving, pseudorandom function preserving and PROPr. We present an efficient new transformthat is proven to be multiproperty preserving in this sense.
Hash Functions in the DedicatedKey Setting: Design Choices and MPP Transforms
 In ICALP ’07, volume 4596 of LNCS
, 2007
"... In the dedicatedkey setting, one starts with a compression function f: {0, 1} k ×{0, 1} n+d → {0, 1} n and builds a family of hash functions H f: K × M → {0, 1} n indexed by a key space K. This is different from the more traditional design approach used to build hash functions such as MD5 or SHA1, ..."
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Cited by 13 (1 self)
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In the dedicatedkey setting, one starts with a compression function f: {0, 1} k ×{0, 1} n+d → {0, 1} n and builds a family of hash functions H f: K × M → {0, 1} n indexed by a key space K. This is different from the more traditional design approach used to build hash functions such as MD5 or SHA1, in which compression functions and hash functions do not have dedicated key inputs. We explore the benefits and drawbacks of building hash functions in the dedicatedkey setting (as compared to the more traditional approach), highlighting several unique features of the former. Should one choose to build hash functions in the dedicatedkey setting, we suggest utilizing multipropertypreserving (MPP) domain extension transforms. We analyze seven existing dedicatedkey transforms with regard to the MPP goal and propose two simple
Concealment and its applications to authenticated encryption
 In EUROCRYPT 2003
, 2003
"... Abstract. We introduce a new cryptographic primitive we call concealment, which is related, but quite different from the notion of commitment. A concealment is a publicly known randomized transformation, which, on input m, outputs a hider h and a binder b. Together, h and b allow one to recover m, b ..."
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Cited by 10 (2 self)
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Abstract. We introduce a new cryptographic primitive we call concealment, which is related, but quite different from the notion of commitment. A concealment is a publicly known randomized transformation, which, on input m, outputs a hider h and a binder b. Together, h and b allow one to recover m, but separately, (1) the hider h reveals “no information” about m, while (2) the binder b can be “meaningfully opened ” by at most one hider h. While setting b = m, h = ∅ is a trivial concealment, the challenge is to make b  ≪ m, which we call a “nontrivial ” concealment. We show that nontrivial concealments are equivalent to the existence of collisionresistant hash functions. Moreover, our construction of concealments is extremely simple, optimal, and yet very general, giving rise to a multitude of efficient implementations. We show that concealments have natural and important applications in the area of authenticated encryption. Specifically, let AE be an authenticated encryption scheme (either public or symmetrickey) designed
Domain extension of public random functions: Beyond the birthday barrier
 In Advances in Cryptology – CRYPTO ’07 (2007), Lecture Notes in Computer Science
, 2007
"... Combined with the iterated constructions of Coron et al., our result leads to the first iterated construction of a hash function f0; 1g\Lambda ! f0; 1gn from a component function f0; 1gn! f0; 1gn that withstands all recently proposed generic attacks against iterated hash functions, like Joux's ..."
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Cited by 8 (1 self)
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Combined with the iterated constructions of Coron et al., our result leads to the first iterated construction of a hash function f0; 1g\Lambda ! f0; 1gn from a component function f0; 1gn! f0; 1gn that withstands all recently proposed generic attacks against iterated hash functions, like Joux's multicollision attack, Kelsey and Schneier's secondpreimage attack, and Kelsey and Kohno's herding attacks. 1 Introduction 1.1 Secret vs. Public Random Functions Primitives that provide some form of randomness are of central importance in cryptography, both as a primitive assumed to be given (e.g. a secret key), and as a primitive constructed from a weaker one to &quot;behave like &quot; a certain ideal random primitive (e.g. a random function), according to some security notion.
Elastic Block Ciphers
, 2004
"... We introduce a new concept of elastic block ciphers, symmetrickey encryption algorithms that for a variable size input do not expand the plaintext, (i.e., do not require plaintext padding), while maintaining the diffusion property of traditional block ciphers and adjusting their computational loa ..."
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Cited by 7 (7 self)
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We introduce a new concept of elastic block ciphers, symmetrickey encryption algorithms that for a variable size input do not expand the plaintext, (i.e., do not require plaintext padding), while maintaining the diffusion property of traditional block ciphers and adjusting their computational load proportionally to the size increase. Elastic block ciphers are ideal for applications where lengthpreserving encryption is most beneficial, such as protecting variablelength database entries or network packets.
A new mode of operation for block ciphers and lengthpreserving MACs
 of Lecture Notes in Computer Science
, 2008
"... Abstract. We propose a new mode of operation, enciphered CBC, for domain extension of lengthpreserving functions (like block ciphers), which is a variation on the popular CBC mode of operation. Our new mode is twice slower than CBC, but has many (propertypreserving) properties not enjoyed by CBC a ..."
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Cited by 5 (2 self)
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Abstract. We propose a new mode of operation, enciphered CBC, for domain extension of lengthpreserving functions (like block ciphers), which is a variation on the popular CBC mode of operation. Our new mode is twice slower than CBC, but has many (propertypreserving) properties not enjoyed by CBC and other known modes. Most notably, it yields the first constantrate Variable Input Length (VIL) MAC from any length preserving Fixed Input Length (FIL) MAC. This answers the question of Dodis and Puniya from Eurocrypt 2007. Further, our mode is a secure domain extender for PRFs (with basically the same security as encrypted CBC). This provides a hedge against the security of the block cipher: if the block cipher is pseudorandom, one gets a VILPRF, while if it is “only ” unpredictable, one “at least ” gets a VILMAC. Additionally, our mode yields a VIL random oracle (and, hence, a collisionresistant hash function) when instantiated with lengthpreserving random functions, or even random permutations (which can be queried from both sides). This means that one does not have to rekey the block cipher during the computation, which was critically used in most previous constructions (analyzed in the ideal cipher model). 1
Getting the Best Out of Existing Hash Functions or What if We Are Stuck with
 SHA?. Applied Cryptography and Network Security – ACNS ’08. LNCS
, 2008
"... Cascade chaining is a very efficient and popular mode of operation for building various kinds of cryptographic hash functions. In particular, it is the basis of the most heavily utilized SHA function family. Recently, many researchers pointed out various practical and theoretical deficiencies of thi ..."
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Cited by 4 (1 self)
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Cascade chaining is a very efficient and popular mode of operation for building various kinds of cryptographic hash functions. In particular, it is the basis of the most heavily utilized SHA function family. Recently, many researchers pointed out various practical and theoretical deficiencies of this mode, which resulted in a renewed interest in building specialized modes of operations and new hash functions with better security. Unfortunately, it appears unlikely that a new hash function (say, based on a new mode of operation) would be widely adopted before being standardized, which is not expected to happen in the foreseeable future. Instead, it seems likely that practitioners would continue to use the cascade chaining, and the SHA family in particular, and try to work around the deficiencies mentioned above. In this paper we provide a thorough treatment of how to soundly design a secure hash function H ′ from a given cascadebased hash function H for various cryptographic applications, such as collisionresistance, onewayness, pseudorandomness, etc. We require each proposed construction of H ′ to satisfy the following “axioms”. 1. The construction should consist of one or two “blackbox ” calls to H. 2. In particular, one is not allowed to know/use anything about the internals of H, such as modifying the initialization vector or affecting the value of the chaining variable. 3. The construction should support variablelength inputs. 4. Compared to a single evaluation of H(M), the evaluation of H ′ (M) should make at most a fixed (small constant) number of extra calls to the underlying compression function of H. In other words, the efficiency of H ′ is negligibly close to that of H. We discuss several popular modes of operation satisfying the above axioms. For each such mode and for each given desired security requirement, we discuss the weakest requirement on the compression function of H which would make this mode secure. We also give the implications of these results for using existing hash functions SHAx, where x ∈ {1,224,256,384,512}.
Multipropertypreserving Domain Extension Using Polynomialbased Modes of Operation
 Advances in cryptology – EUROcrYPT’10, LNCS
"... Abstract. In this paper, we propose a new doublepiped mode of operation for multipropertypreserving domain extension of MACs (message authentication codes), PRFs (pseudorandom functions) and PROs (pseudorandom oracles). Our mode of operation performs twice as fast as the original doublepiped mode ..."
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Cited by 3 (0 self)
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Abstract. In this paper, we propose a new doublepiped mode of operation for multipropertypreserving domain extension of MACs (message authentication codes), PRFs (pseudorandom functions) and PROs (pseudorandom oracles). Our mode of operation performs twice as fast as the original doublepiped mode of operation of Lucks [15] while providing comparable security. Our construction, which uses a class of polynomialbased compression functions proposed by Stam [22, 23], makes a single call to a 3nbit to nbit primitive at each iteration and uses a finalization function f2 at the last iteration, producing an nbit hash function H[f1, f2] satisfying the following properties. 1. H[f1, f2] is unforgeable up to O(2 n /n) query complexity as long as f1 and f2 are unforgeable. 2. H[f1, f2] is pseudorandom up to O(2 n /n) query complexity as long as f1 is unforgeable and f2 is pseudorandom. 3. H[f1, f2] is indifferentiable from a random oracle up to O(2 2n/3) query complexity as long as f1 and f2 are public random functions. To our knowledge, our result constitutes the first time O(2 n /n) unforgeability has been achieved using only an unforgeable primitive of nbit output length. (Yasuda showed unforgeability of O(2 5n/6) for Lucks ’ construction assuming an unforgeable primitive, but the analysis is suboptimal; in the appendix, we show how Yasuda’s bound can be improved to O(2 n).) In related work, we strengthen Stam’s collision resistance analysis of polynomialbased compression functions (showing that unforgeability of the primitive suffices) and discuss how to implement our mode by replacing f1 with a 2nbit key blockcipher in DaviesMeyer mode or by replacing f1 with the cascade of two 2nbit to nbit compression functions. 1