485 research outputs found
Using Simon's Algorithm to Attack Symmetric-Key Cryptographic Primitives
We present new connections between quantum information and the field of
classical cryptography. In particular, we provide examples where Simon's
algorithm can be used to show insecurity of commonly used cryptographic
symmetric-key primitives. Specifically, these examples consist of a quantum
distinguisher for the 3-round Feistel network and a forgery attack on CBC-MAC
which forges a tag for a chosen-prefix message querying only other messages (of
the same length). We assume that an adversary has quantum-oracle access to the
respective classical primitives. Similar results have been achieved recently in
independent work by Kaplan et al. Our findings shed new light on the
post-quantum security of cryptographic schemes and underline that classical
security proofs of cryptographic constructions need to be revisited in light of
quantum attackers.Comment: 14 pages, 2 figures. v3: final polished version, more formal
definitions adde
Cloud Data Auditing Using Proofs of Retrievability
Cloud servers offer data outsourcing facility to their clients. A client
outsources her data without having any copy at her end. Therefore, she needs a
guarantee that her data are not modified by the server which may be malicious.
Data auditing is performed on the outsourced data to resolve this issue.
Moreover, the client may want all her data to be stored untampered. In this
chapter, we describe proofs of retrievability (POR) that convince the client
about the integrity of all her data.Comment: A version has been published as a book chapter in Guide to Security
Assurance for Cloud Computing (Springer International Publishing Switzerland
2015
Bloom Filters in Adversarial Environments
Many efficient data structures use randomness, allowing them to improve upon
deterministic ones. Usually, their efficiency and correctness are analyzed
using probabilistic tools under the assumption that the inputs and queries are
independent of the internal randomness of the data structure. In this work, we
consider data structures in a more robust model, which we call the adversarial
model. Roughly speaking, this model allows an adversary to choose inputs and
queries adaptively according to previous responses. Specifically, we consider a
data structure known as "Bloom filter" and prove a tight connection between
Bloom filters in this model and cryptography.
A Bloom filter represents a set of elements approximately, by using fewer
bits than a precise representation. The price for succinctness is allowing some
errors: for any it should always answer `Yes', and for any it should answer `Yes' only with small probability.
In the adversarial model, we consider both efficient adversaries (that run in
polynomial time) and computationally unbounded adversaries that are only
bounded in the number of queries they can make. For computationally bounded
adversaries, we show that non-trivial (memory-wise) Bloom filters exist if and
only if one-way functions exist. For unbounded adversaries we show that there
exists a Bloom filter for sets of size and error , that is
secure against queries and uses only
bits of memory. In comparison, is the best
possible under a non-adaptive adversary
Order-Revealing Encryption and the Hardness of Private Learning
An order-revealing encryption scheme gives a public procedure by which two
ciphertexts can be compared to reveal the ordering of their underlying
plaintexts. We show how to use order-revealing encryption to separate
computationally efficient PAC learning from efficient -differentially private PAC learning. That is, we construct a concept
class that is efficiently PAC learnable, but for which every efficient learner
fails to be differentially private. This answers a question of Kasiviswanathan
et al. (FOCS '08, SIAM J. Comput. '11).
To prove our result, we give a generic transformation from an order-revealing
encryption scheme into one with strongly correct comparison, which enables the
consistent comparison of ciphertexts that are not obtained as the valid
encryption of any message. We believe this construction may be of independent
interest.Comment: 28 page
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Are PCPs Inherent in Efficient Arguments?
Starting with Kilian (STOC ‘92), several works have shown how to use probabilistically checkable proofs (PCPs) and cryptographic primitives such as collision-resistant hashing to construct very efficient argument systems (a.k.a. computationally sound proofs), for example with polylogarithmic communication complexity. Ishai et al. (CCC ‘07) raised the question of whether PCPs are inherent in efficient arguments, and to what extent. We give evidence that they are, by showing how to convert any argument system whose soundness is reducible to the security of some cryptographic primitive into a PCP system whose efficiency is related to that of the argument system and the reduction (under certain complexity assumptions).Engineering and Applied Science
HardIDX: Practical and Secure Index with SGX
Software-based approaches for search over encrypted data are still either
challenged by lack of proper, low-leakage encryption or slow performance.
Existing hardware-based approaches do not scale well due to hardware
limitations and software designs that are not specifically tailored to the
hardware architecture, and are rarely well analyzed for their security (e.g.,
the impact of side channels). Additionally, existing hardware-based solutions
often have a large code footprint in the trusted environment susceptible to
software compromises. In this paper we present HardIDX: a hardware-based
approach, leveraging Intel's SGX, for search over encrypted data. It implements
only the security critical core, i.e., the search functionality, in the trusted
environment and resorts to untrusted software for the remainder. HardIDX is
deployable as a highly performant encrypted database index: it is logarithmic
in the size of the index and searches are performed within a few milliseconds
rather than seconds. We formally model and prove the security of our scheme
showing that its leakage is equivalent to the best known searchable encryption
schemes. Our implementation has a very small code and memory footprint yet
still scales to virtually unlimited search index sizes, i.e., size is limited
only by the general - non-secure - hardware resources
On Improving Communication Complexity in Cryptography
Cryptography grew to be much more than "the study of secret writing". Modern cryptography is concerned with establishing properties such as privacy, integrity and authenticity in protocols for secure communication and computation. This comes at a price: Cryptographic tools usually introduce an overhead, both in terms of communication complexity (that is, number and size of messages transmitted) and computational efficiency (that is, time and memory required). As in many settings communication between the parties involved is the bottleneck, this thesis is concerned with improving communication complexity in cryptographic protocols.
One direction towards this goal is scalable cryptography: In many cryptographic schemes currently deployed, the security degrades linearly with the number of instances (e.g. encrypted messages) in the system. As this number can be huge in contexts like cloud computing, the parameters of the scheme have to be chosen considerably larger - and in particular depending on the expected number of instances in the system - to maintain security guarantees. We advance the state-of-the-art regarding scalable cryptography by constructing schemes where the security guarantees are independent of the number of instances. This allows to choose smaller parameters, even when the expected number of instances is immense.
- We construct the first scalable encryption scheme with security against active adversaries which has both compact public keys and ciphertexts. In particular, we significantly reduce the size of the public key to only about 3% of the key-size of the previously most efficient scalable encryption scheme. (Gay,Hofheinz, and Kohl, CRYPTO, 2017)
- We present a scalable structure-preserving signature scheme which improves both in terms of public-key and signature size compared to the previously best construction to about 40% and 56% of the sizes, respectively. (Gay, Hofheinz, Kohl, and Pan, EUROCRYPT, 2018)
Another important area of cryptography is secure multi-party computation, where the goal is to jointly evaluate some function while keeping each party’s input private. In traditional approaches towards secure multi-party computation either the communication complexity scales linearly in the size of the function, or the computational efficiency is poor. To overcome this issue, Boyle, Gilboa, and Ishai (CRYPTO, 2016) introduced the notion of homomorphic secret sharing. Here, inputs are shared between parties such that each party does not learn anything about the input, and such that the parties can locally evaluate functions on the shares. Homomorphic secret sharing implies secure computation where the communication complexity only depends on the size of the inputs, which is typically much smaller than the size of the function. A different approach towards efficient secure computation is to split the protocol into an input-independent preprocessing phase, where long correlated strings are generated, and a very efficient online phase. One example for a useful correlation are authenticated Beaver triples, which allow to perform efficient multiplications in the online phase such that privacy of the inputs is preserved and parties deviating the protocol can be detected. The currently most efficient protocols implementing the preprocessing phase require communication linear in the number of triples to be generated. This results typically in high communication costs, as the online phase requires at least one authenticated Beaver triple per multiplication.
We advance the state-of-the art regarding efficient protocols for secure computation with low communication complexity as follows.
- We construct the first homomorphic secret sharing scheme for computing arbitrary functions in NC 1 (that is, functions that are computably by circuits with logarithmic depth) which supports message spaces of arbitrary size, has only negligible correctness error, and does not require expensive multiplication on ciphertexts. (Boyle, Kohl, and Scholl, EUROCRYPT, 2019)
- We introduce the notion of a pseudorandom correlation generator for general correlations. Pseudorandom correlation generators allow to locally extend short correlated seeds into long pseudorandom correlated strings. We show that pseudorandom correlation generators can replace the preprocessing phase in many protocols, leading to a preprocessing phase with sublinear communication complexity. We show connections to homomorphic secret sharing schemes and give the first instantiation of pseudorandom correlation generators for authenticated Beaver triples at reasonable computational efficiency. (Boyle, Couteau, Gilboa, Ishai, Kohl, and Scholl, CRYPTO, 2019
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