1,290 research outputs found
Generic oracles, uniform machines, and codes
AbstractThe basic properties of generic oracles are reviewed, and proofs given that they separate P and NP and are weakly incompressible. A new notion of generic oracle, called t-generic, is defined. It is shown that t-generic oracles do not exist, and consequently a nondeterministic oracle machine which for any oracle X accepts the tautologies relativized to X when running with oracle X does not run in polynomial time at any oracle. A weak form of t-generic oracle, called r-generic, is shown to exist, and it is shown that if there exists an r-generic oracle X at which the r-query relativized tautologies are not in co NPX then NP ≠ co NP. The notion of a code for the Boolean functions is defined, and it is shown that generic oracles do not have short codes in any code. Universal circuits of size O(n log4 n) are shown to exist, and it is shown that increasing the number of ⋏, ⋎ gates from g to 2g + 1 allows the computation of new Boolean functions
Verifiable Quantum Advantage without Structure
We show the following hold, unconditionally unless otherwise stated, relative
to a random oracle with probability 1:
- There are NP search problems solvable by BQP machines but not BPP machines.
- There exist functions that are one-way, and even collision resistant,
against classical adversaries but are easily inverted quantumly. Similar
separations hold for digital signatures and CPA-secure public key encryption
(the latter requiring the assumption of a classically CPA-secure encryption
scheme). Interestingly, the separation does not necessarily extend to the case
of other cryptographic objects such as PRGs.
- There are unconditional publicly verifiable proofs of quantumness with the
minimal rounds of interaction: for uniform adversaries, the proofs are
non-interactive, whereas for non-uniform adversaries the proofs are two message
public coin.
- Our results do not appear to contradict the Aaronson-Ambanis conjecture.
Assuming this conjecture, there exist publicly verifiable certifiable
randomness, again with the minimal rounds of interaction.
By replacing the random oracle with a concrete cryptographic hash function
such as SHA2, we obtain plausible Minicrypt instantiations of the above
results. Previous analogous results all required substantial structure, either
in terms of highly structured oracles and/or algebraic assumptions in
Cryptomania and beyond.Comment: 46 page
A Tamper and Leakage Resilient von Neumann Architecture
We present a universal framework for tamper and leakage resilient computation on a von
Neumann Random Access Architecture (RAM in short). The RAM has one CPU that accesses
a storage, which we call the disk. The disk is subject to leakage and tampering. So is the bus
connecting the CPU to the disk. We assume that the CPU is leakage and tamper-free. For
a fixed value of the security parameter, the CPU has constant size. Therefore the code of the
program to be executed is stored on the disk, i.e., we consider a von Neumann architecture. The
most prominent consequence of this is that the code of the program executed will be subject to
tampering.
We construct a compiler for this architecture which transforms any keyed primitive into a
RAM program where the key is encoded and stored on the disk along with the program to
evaluate the primitive on that key. Our compiler only assumes the existence of a so-called
continuous non-malleable code, and it only needs black-box access to such a code. No further
(cryptographic) assumptions are needed. This in particular means that given an information
theoretic code, the overall construction is information theoretic secure.
Although it is required that the CPU is tamper and leakage proof, its design is independent
of the actual primitive being computed and its internal storage is non-persistent, i.e., all secret
registers are reset between invocations. Hence, our result can be interpreted as reducing the
problem of shielding arbitrary complex computations to protecting a single, simple yet universal
component
Quantum Lazy Sampling and Game-Playing Proofs for Quantum Indifferentiability
Game-playing proofs constitute a powerful framework for non-quantum
cryptographic security arguments, most notably applied in the context of
indifferentiability. An essential ingredient in such proofs is lazy sampling of
random primitives. We develop a quantum game-playing proof framework by
generalizing two recently developed proof techniques. First, we describe how
Zhandry's compressed quantum oracles~(Crypto'19) can be used to do quantum lazy
sampling of a class of non-uniform function distributions. Second, we observe
how Unruh's one-way-to-hiding lemma~(Eurocrypt'14) can also be applied to
compressed oracles, providing a quantum counterpart to the fundamental lemma of
game-playing. Subsequently, we use our game-playing framework to prove quantum
indifferentiability of the sponge construction, assuming a random internal
function
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