105 research outputs found
Limits to Non-Malleability
There have been many successes in constructing explicit non-malleable codes for various classes of tampering functions in recent years, and strong existential results are also known. In this work we ask the following question:
When can we rule out the existence of a non-malleable code for a tampering class ??
First, we start with some classes where positive results are well-known, and show that when these classes are extended in a natural way, non-malleable codes are no longer possible. Specifically, we show that no non-malleable codes exist for any of the following tampering classes:
- Functions that change d/2 symbols, where d is the distance of the code;
- Functions where each input symbol affects only a single output symbol;
- Functions where each of the n output bits is a function of n-log n input bits.
Furthermore, we rule out constructions of non-malleable codes for certain classes ? via reductions to the assumption that a distributional problem is hard for ?, that make black-box use of the tampering functions in the proof. In particular, this yields concrete obstacles for the construction of efficient codes for NC, even assuming average-case variants of P ? NC
Non-Malleable Codes for Small-Depth Circuits
We construct efficient, unconditional non-malleable codes that are secure
against tampering functions computed by small-depth circuits. For
constant-depth circuits of polynomial size (i.e. tampering
functions), our codes have codeword length for a -bit
message. This is an exponential improvement of the previous best construction
due to Chattopadhyay and Li (STOC 2017), which had codeword length
. Our construction remains efficient for circuit depths as
large as (indeed, our codeword length remains
, and extending our result beyond this would require
separating from .
We obtain our codes via a new efficient non-malleable reduction from
small-depth tampering to split-state tampering. A novel aspect of our work is
the incorporation of techniques from unconditional derandomization into the
framework of non-malleable reductions. In particular, a key ingredient in our
analysis is a recent pseudorandom switching lemma of Trevisan and Xue (CCC
2013), a derandomization of the influential switching lemma from circuit
complexity; the randomness-efficiency of this switching lemma translates into
the rate-efficiency of our codes via our non-malleable reduction.Comment: 26 pages, 4 figure
A LASSO-based approach to sample sites for phylogenetic tree search
Motivation
In recent years, full-genome sequences have become increasingly available and as a result many modern phylogenetic analyses are based on very long sequences, often with over 100 000 sites. Phylogenetic reconstructions of large-scale alignments are challenging for likelihood-based phylogenetic inference programs and usually require using a powerful computer cluster. Current tools for alignment trimming prior to phylogenetic analysis do not promise a significant reduction in the alignment size and are claimed to have a negative effect on the accuracy of the obtained tree.
Results
Here, we propose an artificial-intelligence-based approach, which provides means to select the optimal subset of sites and a formula by which one can compute the log-likelihood of the entire data based on this subset. Our approach is based on training a regularized Lasso-regression model that optimizes the log-likelihood prediction accuracy while putting a constraint on the number of sites used for the approximation. We show that computing the likelihood based on 5% of the sites already provides accurate approximation of the tree likelihood based on the entire data. Furthermore, we show that using this Lasso-based approximation during a tree search decreased running-time substantially while retaining the same tree-search performance
Non-Malleable Codes for Bounded Depth, Bounded Fan-in Circuits
We show how to construct efficient, unconditionally secure non-malleable codes for bounded output locality. In particular, our scheme is resilient against functions such that any output bit is dependent on at most bits, where is the total number of bits in a codeword and a constant. Notably, this tampering class includes
Non-Malleable Codes from Average-Case Hardness: AC0, Decision Trees, and Streaming Space-Bounded Tampering
We show a general framework for constructing non-malleable codes against tampering families with average-case hardness bounds. Our framework adapts ideas from the Naor-Yung double encryption paradigm such that to protect against tampering in a class F, it suffices to have average-case hard distributions for the class, and underlying primitives (encryption and non-interactive, simulatable proof systems) satisfying certain properties with respect to the class.
We instantiate our scheme in a variety of contexts, yielding efficient, non-malleable codes (NMC) against the following tampering classes:
1. Computational NMC against AC0 tampering, in the CRS model,
assuming a PKE scheme with decryption in AC0 and NIZK.
2. Computational NMC against bounded-depth decision trees (of depth , where is
the number of input variables and constant ), in the CRS model and under the same computational assumptions as above.
3. Information theoretic NMC (with no CRS) against a streaming,
space-bounded adversary, namely an adversary modeled as a read-once branching program with bounded width.
Ours are the first constructions that achieve each of the above in an efficient way, under the standard notion of non-malleability
Adaptive and Concurrent Secure Computation from New Notions of Non-Malleability
We present a unified framework for obtaining general secure computation that achieves adaptive- Universally Composable (UC)-security. Our framework captures essentially all previous results on adaptive concurrent secure computation, both in relaxed models (e.g., quasi-polynomial time simulation), as well as trusted setup models (e.g., the CRS model, the imperfect CRS model). This provides conceptual simplicity and insight into what is required for adaptive and concurrent security, as well as yielding improvements to set-up assumptions and/or computational assumptions. Moreover, using our framework we provide first constructions of concurrent secure computation protocols that are adaptively secure in the timing model, and in the non-uniform simulation model.
Conceptually, our framework can be viewed as an adaptive analogue to the recent work of Lin, Pass and Venkitasubramaniam [STOC `09], who considered only non-adaptive adversaries. Their main insight was that stand-alone non-malleability was sufficient for UC-security. A main conceptual contribution of this work is, quite surprisingly, that it is indeed the case even when considering adaptive security.
A key element in our construction is a commitment scheme that satisfies a new notion of non-malleability. The notion of concurrent equivocal non-malleable commitments, intuitively, guarantees that even when a man-in-the-middle adversary observes concurrent equivocal commitments and decommitments, the binding property of the commitments continues to hold for commitments made by the adversary. This notion is stronger than standard notions of concurrent non-malleable commitments which either consider only specific commits (e.g., statistically-binding) or specific scenarios (e.g., the commitment phase and the decommitment phase are executed in a non-overlapping manner). Previously, commitments that satisfy our definition, have been constructed in setup models, but either require existence of stronger encryption schemes such as CCA-secure encryption or require independent ``trapdoors\u27\u27 provided by the setup for every pair of parties to ensure non-malleability. We here provide a construction that eliminates these requirements and require only a single trapdoor
A Black-Box Construction of Non-Malleable Encryption from Semantically Secure Encryption
We show how to transform any semantically secure encryption scheme into a
non-malleable one, with a black-box construction that achieves a quasi-linear
blow-up in the size of the ciphertext.
This improves upon the previous non-black-box construction of Pass,
Shelat and Vaikuntanathan (Crypto \u2706). Our construction also
extends readily to guarantee non-malleability under a bounded-CCA2
attack, thereby simultaneously improving on both results in the work
of Cramer et al. (Asiacrypt \u2707).
Our construction departs from the oft-used paradigm of re-encrypting the same
message with different keys and then proving consistency of encryption.
Instead, we encrypt an encoding of the message; the encoding is based on an
error-correcting code with certain properties of reconstruction and secrecy
from partial views, satisfied, e.g., by a Reed-Solomon code
Improved, Black-Box, Non-Malleable Encryption from Semantic Security
We give a new black-box transformation from any semantically secure encryption scheme into a non-malleable one which has a better rate than the best previous work of Coretti et al. (TCC 2016-A). We achieve a better rate by departing from the āmatrix encodingā methodology used by previous constructions, and working directly with a single codeword. We also use a Shamir secret-share packing technique to improve the rate of the underlying error-correcting code
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