745 research outputs found
Random Oracles in a Quantum World
The interest in post-quantum cryptography - classical systems that remain
secure in the presence of a quantum adversary - has generated elegant proposals
for new cryptosystems. Some of these systems are set in the random oracle model
and are proven secure relative to adversaries that have classical access to the
random oracle. We argue that to prove post-quantum security one needs to prove
security in the quantum-accessible random oracle model where the adversary can
query the random oracle with quantum states.
We begin by separating the classical and quantum-accessible random oracle
models by presenting a scheme that is secure when the adversary is given
classical access to the random oracle, but is insecure when the adversary can
make quantum oracle queries. We then set out to develop generic conditions
under which a classical random oracle proof implies security in the
quantum-accessible random oracle model. We introduce the concept of a
history-free reduction which is a category of classical random oracle
reductions that basically determine oracle answers independently of the history
of previous queries, and we prove that such reductions imply security in the
quantum model. We then show that certain post-quantum proposals, including ones
based on lattices, can be proven secure using history-free reductions and are
therefore post-quantum secure. We conclude with a rich set of open problems in
this area.Comment: 38 pages, v2: many substantial changes and extensions, merged with a
related paper by Boneh and Zhandr
Tensor-based trapdoors for CVP and their application to public key cryptography
We propose two trapdoors for the Closest-Vector-Problem in lattices (CVP) related to the lattice tensor product. Using these trapdoors we set up a lattice-based cryptosystem which resembles to the McEliece scheme
Wave: A New Family of Trapdoor One-Way Preimage Sampleable Functions Based on Codes
We present here a new family of trapdoor one-way Preimage Sampleable
Functions (PSF) based on codes, the Wave-PSF family. The trapdoor function is
one-way under two computational assumptions: the hardness of generic decoding
for high weights and the indistinguishability of generalized -codes.
Our proof follows the GPV strategy [GPV08]. By including rejection sampling, we
ensure the proper distribution for the trapdoor inverse output. The domain
sampling property of our family is ensured by using and proving a variant of
the left-over hash lemma. We instantiate the new Wave-PSF family with ternary
generalized -codes to design a "hash-and-sign" signature scheme which
achieves existential unforgeability under adaptive chosen message attacks
(EUF-CMA) in the random oracle model. For 128 bits of classical security,
signature sizes are in the order of 15 thousand bits, the public key size in
the order of 4 megabytes, and the rejection rate is limited to one rejection
every 10 to 12 signatures.Comment: arXiv admin note: text overlap with arXiv:1706.0806
Computational Indistinguishability between Quantum States and Its Cryptographic Application
We introduce a computational problem of distinguishing between two specific
quantum states as a new cryptographic problem to design a quantum cryptographic
scheme that is "secure" against any polynomial-time quantum adversary. Our
problem, QSCDff, is to distinguish between two types of random coset states
with a hidden permutation over the symmetric group of finite degree. This
naturally generalizes the commonly-used distinction problem between two
probability distributions in computational cryptography. As our major
contribution, we show that QSCDff has three properties of cryptographic
interest: (i) QSCDff has a trapdoor; (ii) the average-case hardness of QSCDff
coincides with its worst-case hardness; and (iii) QSCDff is computationally at
least as hard as the graph automorphism problem in the worst case. These
cryptographic properties enable us to construct a quantum public-key
cryptosystem, which is likely to withstand any chosen plaintext attack of a
polynomial-time quantum adversary. We further discuss a generalization of
QSCDff, called QSCDcyc, and introduce a multi-bit encryption scheme that relies
on similar cryptographic properties of QSCDcyc.Comment: 24 pages, 2 figures. We improved presentation, and added more detail
proofs and follow-up of recent wor
Constructing Permutation Rational Functions From Isogenies
A permutation rational function is a rational function
that induces a bijection on , that is, for all
there exists exactly one such that . Permutation
rational functions are intimately related to exceptional rational functions,
and more generally exceptional covers of the projective line, of which they
form the first important example.
In this paper, we show how to efficiently generate many permutation rational
functions over large finite fields using isogenies of elliptic curves, and
discuss some cryptographic applications. Our algorithm is based on Fried's
modular interpretation of certain dihedral exceptional covers of the projective
line (Cont. Math., 1994)
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