We put forward a new framework that makes it possible to rewrite or compress the content of any number of blocks in decentralized services exploiting the blockchain technology. As we argue, there are several reasons to prefer an editable blockchain, spanning from the necessity to remove inappropriate content and the possibility to support applications requiring re-writable storage, to "the right to be forgotten." Our approach generically leverages so-called chameleon hash functions (Krawczyk and Rabin, NDSS '00), which allow determining hash collisions efficiently, given a secret trapdoor information. We detail how to integrate a chameleon hash function in virtually any blockchain-based technology, for both cases where the power of redacting the blockchain content is in the hands of a single trusted entity and where such a capability is distributed among several distrustful parties (as is the case with Bitcoin). We also report on a proof-of-concept implementation of a redactable blockchain, building on top of Nakamoto's Bitcoin core. The prototype only requires minimal changes to the way current client software interprets the information stored in the blockchain and to the current blockchain, block, or transaction structures. Moreover, our experiments show that the overhead imposed by a redactable blockchain is small compared to the case of an immutable one.

We investigate the possibility of using proper orthogonal decomposition (POD) in reconstructing complete flow fields from gappy data. The incomplete fields are created from DNS snapshots of flow past a circular cylinder by randomly ommiting data points. We first examine the effectiveness of an existing method and subsequently introduce modifications that make the method robust and lead to the maximum possible resolution at a certain level of spatio-temporal gappiness. We simulate three levels of gappiness at approximately 20%, 50% and 80% in order to investigate the limits of applicability of the new procedure. We find that for the two lower levels of gappiness both the temporal and spatial POD modes can be recovered accurately leading to a very accurate representation of the velocity field. The resulting resolution is improved by more than five times compared to the existing method. However, for 80% gappiness only a few temporal modes are captured accurately while the corresponding spatial modes are noisy. We explain this breakdown of the method in terms of a simple perturbation analysis. This new methodology can be a building block in an effort to develop effective data assimilation techniques in fluid mechanics applications.

Abstract. Non-malleable codes are a natural relaxation of error correcting/detecting codes that have useful applications in the context of tamper resilient cryptography. Informally, a code is non-malleable if an adversary trying to tamper with an encoding of a given message can only leave it unchanged or modify it to the encoding of a completely unrelated value. This paper introduces an extension of the standard non-malleability security notion -so-called continuous non-malleability -where we allow the adversary to tamper continuously with an encoding. This is in contrast to the standard notion of non-malleable codes where the adversary only is allowed to tamper a single time with an encoding. We show how to construct continuous non-malleable codes in the common split-state model where an encoding consist of two parts and the tampering can be arbitrary but has to be independent with both parts. Our main contributions are outlined below:1. We propose a new uniqueness requirement of split-state codes which states that it is computationally hard to find two codewords X = (X0, X1) and X = (X0, X 1 ) such that both codewords are valid, but X0 is the same in both X and X . A simple attack shows that uniqueness is necessary to achieve continuous non-malleability in the split-state model. Moreover, we illustrate that none of the existing constructions satisfies our uniqueness property and hence is not secure in the continuous setting. 2. We construct a split-state code satisfying continuous non-malleability.Our scheme is based on the inner product function, collision-resistant hashing and non-interactive zero-knowledge proofs of knowledge and requires an untamperable common reference string. 3. We apply continuous non-malleable codes to protect arbitrary cryptographic primitives against tampering attacks. Previous applications of non-malleable codes in this setting required to perfectly erase the entire memory after each execution and required the adversary to be restricted in memory. We show that continuous non-malleable codes avoid these restrictions.

We propose a new framework for design under uncertainty based on stochastic computer simulations and multi-level recursive co-kriging. The proposed methodology simultaneously takes into account multi-fidelity in models, such as direct numerical simulations versus empirical formulae, as well as multi-fidelity in the probability space (e.g. sparse grids versus tensor product multi-element probabilistic collocation). We are able to construct response surfaces of complex dynamical systems by blending multiple information sources via auto-regressive stochastic modelling. A computationally efficient machine learning framework is developed based on multi-level recursive co-kriging with sparse precision matrices of Gaussian-Markov random fields. The effectiveness of the new algorithms is demonstrated in numerical examples involving a prototype problem in risk-averse design, regression of random functions, as well as uncertainty quantification in fluid mechanics involving the evolution of a Burgers equation from a random initial state, and random laminar wakes behind circular cylinders.