Abstract We point out that the seemingly strong pseudorandom oracle preserving (PRO-Pr) propertyof hash function domain-extension 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 collision-resistant (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 multi-property preserving, namelythat one should have a single transform that is simultaneously at least collision-resistance preserving, pseudorandom function preserving and PRO-Pr. We present an efficient new transformthat is proven to be multi-property preserving in this sense.

The Fiat-Shamir paradigm for transforming identification schemes into signature schemes has been popular since its introduction because it yields efficient signature schemes, and has been receiving renewed interest of late as the main tool in deriving forward-secure signature schemes. In this paper, minimal (meaning necessary and sufficient) conditions on the identification scheme to ensure security of the signature scheme in the random oracle model are determined, both in the usual and in the forward-secure cases. Specifically, it is shown that the signature scheme is secure (resp. forward-secure) against chosen-message attacks in the random oracle model if and only if the underlying identification scheme is secure (resp. forward-secure) against impersonation under passive (i.e., eavesdropping only) attacks, and has its commitments drawn at random from a large space. An extension is proven incorporating a random seed into the Fiat-Shamir transform so that the commitment space assumption may be removed. Keywords: Signature schemes, identification schemes, Fiat-Shamir transform, forward security,

We strengthen the foundations of deterministic public-key encryption via definitional equivalences and standard-model constructs based on general assumptions. Specifically we consider seven notions of privacy for deterministic encryption, including six forms of semantic security and an indistinguishability notion, and show them all equivalent. We then present a deterministic scheme for the secure encryption of uniformly and independently distributed messages based solely on the existence of trapdoor one-way permutations. We show a generalization of the construction that allows secure deterministic encryption of independent high-entropy messages. Finally we show relations between deterministic and standard (randomized) encryption.

Abstract We initiate a study of on-line ciphers. These are ciphers that can take input plaintexts oflarge and varying lengths and will output the ith block of the ciphertext after having processedonly the first i blocks of the plaintext. Such ciphers permit length-preserving encryption of adata stream with only a single pass through the data. We provide security definitions for this primitive and study its basic properties. We then provide attacks on some possible candidates,including CBC with fixed IV. We then provide two constructions, HCBC1 and HCBC2, basedon a given block cipher E and a family of computationally AXU functions. HCBC1 is provensecure against chosen-plaintext attacks assuming that E is a PRP secure against chosen-plaintextattacks, while HCBC2 is proven secure against chosen-ciphertext attacks assuming that E is aPRP secure against chosen-ciphertext attacks.

We present a new mechanized prover for showing correspondence assertions for cryptographic protocols in the computational model. Correspondence assertions are useful in particular for establishing authentication. Our technique produces proofs by sequences of games, as standard in cryptography. These proofs are valid for a number of sessions polynomial in the security parameter, in the presence of an active adversary. Our technique can handle a wide variety of cryptographic primitives, including shared- and public-key encryption, signatures, message authentication codes, and hash functions. It has been implemented in the tool CryptoVerif and successfully tested on examples from the literature.

Recent collision-finding attacks against hash functions such as MD5 and SHA-1 motivate the use of provably collision-resistant (CR) functions in their place. Finding a collision in a provably CR function implies the ability to solve some hard problem (e.g., factoring). Unfortunately, existing provably CR functions make poor replacements for hash functions as they fail to deliver behaviors demanded by practical use. In particular, they are easily distinguished from a random oracle. We initiate an investigation into building hash functions from provably CR functions. As a method for achieving this, we present the Mix-Compress-Mix (MCM) construction; it envelopes any provably CR function H (with suitable regularity properties) between two injective “mixing” stages. The MCM construction simultaneously enjoys (1) provable collision-resistance in the standard model, and (2) indifferentiability from a monolithic random oracle when the mixing stages themselves are indifferentiable from a random oracle that observes injectivity. We instantiate our new design approach by specifying a blockcipher-based construction that

In the dedicated-key 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 SHA-1, 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 dedicated-key setting (as compared to the more traditional approach), highlighting several unique features of the former. Should one choose to build hash functions in the dedicated-key setting, we suggest utilizing multi-property-preserving (MPP) domain extension transforms. We analyze seven existing dedicated-key transforms with regard to the MPP goal and propose two simple

We initiate the cryptographic study of order-preserving symmetric encryption (OPE), a primitive suggested in the database community by Agrawal et al. (SIGMOD ’04) for allowing efficient range queries on encrypted data. Interestingly, we first show that a straightforward relaxation of standard security notions for encryption such as indistinguishability against chosen-plaintext attack (IND-CPA) is unachievable by a practical OPE scheme. Instead, we propose a security notion in the spirit of pseudorandom functions (PRFs) and related primitives asking that an OPE scheme look “as-random-as-possible ” subject to the order-preserving constraint. We then design an efficient OPE scheme and prove its security under our notion based on pseudorandomness of an underlying blockcipher. Our construction is based on a natural relation we uncover between a random order-preserving function and the hypergeometric probability distribution. In particular, it makes black-box use of an efficient sampling algorithm for the latter. 1

Abstract. Format-preserving encryption (FPE) encrypts a plaintext of some specified format into a ciphertext of identical format—for example, encrypting a valid credit-card number into a valid creditcard number. The problem has been known for some time, but it has lacked a fully general and rigorous treatment. We provide one, starting off by formally defining FPE and security goals for it. We investigate the natural approach for achieving FPE on complex domains, the “rank-then-encipher ” approach, and explore what it can and cannot do. We describe two flavors of unbalanced Feistel networks that can be used for achieving FPE, and we prove new security results for each. We revisit the cycle-walking approach for enciphering on a non-sparse subset of an encipherable domain, showing that the timing information that may be divulged by cycle walking is not a damaging thing to leak. 1

Abstract. CertiCrypt [1] is a framework that assists the construction of machine-checked cryptographic proofs that can be automatically verified by third parties. To date, CertiCrypt has been used to prove formally the exact security of widely studied cryptographic systems, such as the OAEP padding scheme and the Full Domain Hash digital signature scheme. The purpose of this article is to provide a gentle introduction to CertiCrypt. For concreteness, we focus on a simple but illustrative example, namely the semantic security of the Hashed ElGamal encryption scheme in both, the standard and the random oracle model. 1