841 research outputs found
A tight security reduction in the quantum random oracle model for code-based signature schemes
Quantum secure signature schemes have a lot of attention recently, in
particular because of the NIST call to standardize quantum safe cryptography.
However, only few signature schemes can have concrete quantum security because
of technical difficulties associated with the Quantum Random Oracle Model
(QROM). In this paper, we show that code-based signature schemes based on the
full domain hash paradigm can behave very well in the QROM i.e. that we can
have tight security reductions. We also study quantum algorithms related to the
underlying code-based assumption. Finally, we apply our reduction to a concrete
example: the SURF signature scheme. We provide parameters for 128 bits of
quantum security in the QROM and show that the obtained parameters are
competitive compared to other similar quantum secure signature schemes
Quantum attacks on Bitcoin, and how to protect against them
The key cryptographic protocols used to secure the internet and financial
transactions of today are all susceptible to attack by the development of a
sufficiently large quantum computer. One particular area at risk are
cryptocurrencies, a market currently worth over 150 billion USD. We investigate
the risk of Bitcoin, and other cryptocurrencies, to attacks by quantum
computers. We find that the proof-of-work used by Bitcoin is relatively
resistant to substantial speedup by quantum computers in the next 10 years,
mainly because specialized ASIC miners are extremely fast compared to the
estimated clock speed of near-term quantum computers. On the other hand, the
elliptic curve signature scheme used by Bitcoin is much more at risk, and could
be completely broken by a quantum computer as early as 2027, by the most
optimistic estimates. We analyze an alternative proof-of-work called Momentum,
based on finding collisions in a hash function, that is even more resistant to
speedup by a quantum computer. We also review the available post-quantum
signature schemes to see which one would best meet the security and efficiency
requirements of blockchain applications.Comment: 21 pages, 6 figures. For a rough update on the progress of Quantum
devices and prognostications on time from now to break Digital signatures,
see https://www.quantumcryptopocalypse.com/quantum-moores-law
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
The problem with the SURF scheme
There is a serious problem with one of the assumptions made in the security
proof of the SURF scheme. This problem turns out to be easy in the regime of
parameters needed for the SURF scheme to work.
We give afterwards the old version of the paper for the reader's convenience.Comment: Warning : we found a serious problem in the security proof of the
SURF scheme. We explain this problem here and give the old version of the
paper afterward
CRYSTALS-Dilithium: A lattice-based digital signature scheme
In this paper, we present the lattice-based signature scheme Dilithium, which is a component of the CRYSTALS (Cryptographic Suite for Algebraic Lattices) suite that was submitted to NIST’s call for post-quantum cryptographic standards. The design of the scheme avoids all uses of discrete Gaussian sampling and is easily implementable in constant-time. For the same security levels, our scheme has a public key that is 2.5X smaller than the previously most efficient lattice-based schemes that did not use Gaussians, while having essentially the same signature size. In addition to the new design, we significantly improve the running time of the main component of many lattice-based constructions – the number theoretic transform. Our AVX2-based implementation results in a speed-up of roughly a factor of 2 over the previously best algorithms that appear in the literature. The techniques for obtaining this speed-up also have applications to other lattice-based schemes
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