139,591 research outputs found
A Formula That Generates Hash Collisions
We present an explicit formula that produces hash collisions for the
Merkle-Damg{\aa}rd construction. The formula works for arbitrary choice of
message block and irrespective of the standardized constants used in hash
functions, although some padding schemes may cause the formula to fail. This
formula bears no obvious practical implications because at least one of any
pair of colliding messages will have length double exponential in the security
parameter. However, due to ambiguity in existing definitions of collision
resistance, this formula arguably breaks the collision resistance of some hash
functions.Comment: 10 page
Collision-Resistance from Multi-Collision-Resistance
Collision-resistant hash functions (CRH) are a fundamental and ubiquitous cryptographic primitive. Several recent works have studied a relaxation of CRH called t-way multi-collision-resistant hash functions (t-MCRH). These are families of functions for which it is computationally hard to find a t-way collision, even though such collisions are abundant (and even (t-1)-way collisions may be easy to find). The case of t=2 corresponds to standard CRH, but it is natural to study t-MCRH for larger values of t.
Multi-collision-resistance seems to be a qualitatively weaker property than standard collision-resistance. Nevertheless, in this work we show a non-blackbox transformation of any moderately shrinking t-MCRH, for t in {2,4}, into an (infinitely often secure) CRH. This transformation is non-constructive - we can prove the existence of a CRH but cannot explicitly point out a construction.
Our result partially extends to larger values of t. In particular, we show that for suitable values of t>t\u27, we can transform a t-MCRH into a t\u27-MCRH, at the cost of reducing the shrinkage of the resulting hash function family and settling for infinitely often security. This result utilizes the list-decodability properties of Reed-Solomon codes
Formal Computational Unlinkability Proofs of RFID Protocols
We set up a framework for the formal proofs of RFID protocols in the
computational model. We rely on the so-called computationally complete symbolic
attacker model. Our contributions are: i) To design (and prove sound) axioms
reflecting the properties of hash functions (Collision-Resistance, PRF); ii) To
formalize computational unlinkability in the model; iii) To illustrate the
method, providing the first formal proofs of unlinkability of RFID protocols,
in the computational model
Proofs of Quantumness from Trapdoor Permutations
Assume that Alice can do only classical probabilistic polynomial-time computing while Bob can do quantum polynomial-time computing. Alice and Bob communicate over only classical channels, and finally Bob gets a state with some bit strings and . Is it possible that Alice can know but Bob cannot? Such a task, called {\it remote state preparations}, is indeed possible under some complexity assumptions, and is bases of many quantum cryptographic primitives such as proofs of quantumness, (classical-client) blind quantum computing, (classical) verifications of quantum computing, and quantum money. A typical technique to realize remote state preparations is to use 2-to-1 trapdoor collision resistant hash functions: Alice sends a 2-to-1 trapdoor collision resistant hash function to Bob, and Bob evaluates it coherently, i.e., Bob generates . Bob measures the second register to get the measurement result , and sends to Alice. Bob\u27s post-measurement state is , where . With the trapdoor, Alice can learn from , but due to the collision resistance, Bob cannot. This Alice\u27s advantage can be leveraged to realize the quantum cryptographic primitives listed above. It seems that the collision resistance is essential here. In this paper, surprisingly, we show that the collision resistance is not necessary for a restricted case: we show that (non-verifiable) remote state preparations of secure against {\it classical} probabilistic polynomial-time Bob can be constructed from classically-secure (full-domain) trapdoor permutations. Trapdoor permutations are not likely to imply the collision resistance, because black-box reductions from collision-resistant hash functions to trapdoor permutations are known to be impossible. As an application of our result, we construct proofs of quantumness from classically-secure (full-domain) trapdoor permutations
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