1,880 research outputs found
Asymptotically Efficient Lattice-Based Digital Signatures
We present a general framework that converts certain types of linear collision-resistant hash
functions into one-time signatures. Our generic construction can be instantiated based on both
general and ideal (e.g. cyclic) lattices, and the resulting signature schemes are provably secure
based on the worst-case hardness of approximating the shortest vector (and other standard
lattice problems) in the corresponding class of lattices to within a polynomial factor. When
instantiated with ideal lattices, the time complexity of the signing and verification algorithms,
as well as key and signature size is almost linear (up to poly-logarithmic factors) in the dimension
n of the underlying lattice. Since no sub-exponential (in n) time algorithm is known to solve
lattice problems in the worst case, even when restricted to ideal lattices, our construction gives
a digital signature scheme with an essentially optimal performance/security trade-off
Making Existential-Unforgeable Signatures Strongly Unforgeable in the Quantum Random-Oracle Model
Strongly unforgeable signature schemes provide a more stringent security
guarantee than the standard existential unforgeability. It requires that not
only forging a signature on a new message is hard, it is infeasible as well to
produce a new signature on a message for which the adversary has seen valid
signatures before. Strongly unforgeable signatures are useful both in practice
and as a building block in many cryptographic constructions.
This work investigates a generic transformation that compiles any
existential-unforgeable scheme into a strongly unforgeable one, which was
proposed by Teranishi et al. and was proven in the classical random-oracle
model. Our main contribution is showing that the transformation also works
against quantum adversaries in the quantum random-oracle model. We develop
proof techniques such as adaptively programming a quantum random-oracle in a
new setting, which could be of independent interest. Applying the
transformation to an existential-unforgeable signature scheme due to Cash et
al., which can be shown to be quantum-secure assuming certain lattice problems
are hard for quantum computers, we get an efficient quantum-secure strongly
unforgeable signature scheme in the quantum random-oracle model.Comment: 15 pages, to appear in Proceedings TQC 201
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
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
Solving the Shortest Vector Problem in Lattices Faster Using Quantum Search
By applying Grover's quantum search algorithm to the lattice algorithms of
Micciancio and Voulgaris, Nguyen and Vidick, Wang et al., and Pujol and
Stehl\'{e}, we obtain improved asymptotic quantum results for solving the
shortest vector problem. With quantum computers we can provably find a shortest
vector in time , improving upon the classical time
complexity of of Pujol and Stehl\'{e} and the of Micciancio and Voulgaris, while heuristically we expect to find a
shortest vector in time , improving upon the classical time
complexity of of Wang et al. These quantum complexities
will be an important guide for the selection of parameters for post-quantum
cryptosystems based on the hardness of the shortest vector problem.Comment: 19 page
A Survey on Exotic Signatures for Post-quantum Blockchain: Challenges and Research Directions
Blockchain technology provides efficient and secure solutions to various online activities by utilizing a wide range of cryptographic tools. In this article, we survey the existing literature on post-quantum secure digital signatures that possess exotic advanced features and that are crucial cryptographic tools used in the blockchain ecosystem for (1) account management, (2) consensus efficiency, (3) empowering scriptless blockchain, and (4) privacy. The exotic signatures that we particularly focus on in this work are the following: multi-/aggregate, threshold, adaptor, blind, and ring signatures. Herein the term "exotic"refers to signatures with properties that are not just beyond the norm for signatures, e.g., unforgeability, but also imbue new forms of functionalities. Our treatment of such exotic signatures includes discussions on existing challenges and future research directions in the post-quantum space. We hope that this article will help to foster further research to make post-quantum cryptography more accessible so that blockchain systems can be made ready in advance of the approaching quantum threats
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