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We present "Ouroboros Praos", a proof-of-stake blockchain protocol that, for the first time, provides security against fully-adaptive corruption in the semi-synchronous setting: Specifically, the adversary can corrupt any participant of a dynamically evolving population of stakeholders at any moment as long the stakeholder distribution maintains an honest majority of stake; furthermore, the protocol tolerates an adversarially-controlled message delivery delay unknown to protocol participants. To achieve these guarantees we formalize and realize in the universal composition setting a suitable form of forward secure digital signatures and a new type of verifiable random function that maintains unpredictability under malicious key generation. Our security proof develops a general combinatorial framework for the analysis of semi-synchronous blockchains that may be of independent interest. We prove our protocol secure under standard cryptographic assumptions in the random oracle model. Tokyo Institute of Technology and IOHK, bdavid@c.titech.ac.jp. IOHK, peter.gazi@iohk.io.

Recently, it has been shown that one-dimensional quantum walks can mix more quickly than classical random walks, suggesting that quantum Monte Carlo algorithms can outperform their classical counterparts. We study two quantum walks on the n-dimensional hypercube, one in discrete time and one in continuous time. In both cases we show that the quantum walk mixes in (π/4)n steps, faster than the Θ(n log n) steps required by the classical walk. In the continuous-time case, the probability distribution is exactly uniform at this time. More importantly, these walks expose several subtleties in the definition of mixing time for quantum walks. Even though the continuous-time walk has an O (n) instantaneous mixing time at which it is precisely uniform, it never approaches the uniform distribution when the stopping time is chosen randomly as in [AAKV01]. Our analysis treats interference between terms of different phase more carefully than is necessary for the walk on the cycle; previous general bounds predict an exponential, rather than linear, mixing time for the hypercube.

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The Hidden Subgroup Problem is the foundation of many quantum algorithms. An efficient solution is known for the problem over Abelian groups and this was used in Simon's algorithm and Shor's Factoring and Discrete Log algorithms. The non-Abelian case is open; an efficient solution would give rise to an efficient quantum algorithm for Graph Isomorphism. We fully analyze a natural generalization of the Abelian case solution to the non-Abelian case, and give an efficient solution to the problem for normal subgroups. We show, however, that this immediate generalization of the Abelian algorithm does not efficiently solve Graph Isomorphism.

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Abstract. We consider the symmetric encryption problem which manifests when two parties must securely transmit a message m with a short shared secret key. As we permit arbitrarily powerful adversaries, any encryption scheme must leak information about m -the mutual information between m and its ciphertext cannot be zero. Despite this, we present a family of encryption schemes which guarantee that for any message space in {0, 1} n with minimum entropy n − and for any Boolean function h : {0, 1} n → {0, 1}, no adversary can predict h(m) from the ciphertext of m with more than 1/n ω(1) advantage; this is achieved with keys of length +ω(log n). In general, keys of length +s yield a bound of 2 −Θ(s) on the advantage. These encryption schemes rely on no unproven assumptions and can be implemented efficiently.