Abstract. We consider basic notions of security for cryptographic hash functions: collision resistance, preimage resistance, and second-preimage resistance. We give seven different definitions that correspond to these three underlying ideas, and then we work out all of the implications and separations among these seven definitions within the concrete-security, provable-security framework. Because our results are concrete, we can show two types of implications, conventional and provisional , where the strength of the latter depends on the amount of compression achieved by the hash function. We also distinguish two types of separations, conditional and unconditional . When constructing counterexamples for our separations, we are careful to preserve specified hash-function domains and ranges; this rules out some pathological counterexamples and makes the separations more meaningful in practice. Four of our definitions are standard while three appear to be new; some of our relations and separations have appeared, others have not. Here we give a modern treatment that acts to catalog, in one place and with carefully-considered nomenclature, the most basic security notions for cryptographic hash functions.

We consider the setting of HTTP traffic over encrypted tunnels, as used to conceal the identity of websites visited by a user. It is well known that traffic analysis (TA) attacks can accurately identify the website a user visits despite the use of encryption, and previous work has looked at specific attack/countermeasure pairings. We provide the first comprehensive analysis of general-purpose TA countermeasures. We show that nine known countermeasures are vulnerable to simple attacks that exploit coarse features of traffic (e.g., total time and bandwidth). The considered countermeasures include ones like those standardized by TLS, SSH, and IPsec, and even more complex ones like the traffic morphing scheme of Wright et al. As just one of our results, we show that despite the use of traffic morphing, one can use only total upstream and downstream bandwidth to identifywith 98% accuracy-which of two websites was visited. One implication of what we find is that, in the context of website identification, it is unlikely that bandwidth-efficient, generalpurpose TA countermeasures can ever provide the type of security targeted in prior work.

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Abstract. We give a provable-security treatment for the key-wrap problem, providing definitions, constructions, and proofs. We suggest that key-wrap's goal is security in the sense of deterministic authenticated-encryption (DAE), a notion that we put forward. We also provide an alternative notion, a pseudorandom injection (PRI), which we prove to be equivalent. We provide a DAE construction, SIV, analyze its concrete security, develop a blockcipher-based instantiation of it, and suggest that the method makes a desirable alternative to the schemes of the X9.102 draft standard. The construction incorporates a method to turn a PRF that operates on a string into an equally efficient PRF that operates on a vector of strings, a problem of independent interest. Finally, we consider IVbased authenticated-encryption (AE) schemes that are maximally forgiving of repeated IVs, a goal we formalize as misuse-resistant AE. We show that a DAE scheme with a vector-valued header, such as SIV, directly realizes this goal.

Abstract. Encryption that is only semantically secure should not be used on messages that depend on the underlying secret key; all bets are off when, for example, one encrypts using a shared key K the value K.Here we introduce a new notion of security, KDM security, appropriate for key-dependent messages. The notion makes sense in both the publickey and shared-key settings. For the latter we show that KDM security is easily achievable within the random-oracle model. By developing and achieving stronger notions of encryption-scheme security it is hoped that protocols which are proven secure under "formal" models of security can, in time, be safely realized by generically instantiating their primitives.