1,588 research outputs found
Portable random number generators
Computers are deterministic devices, and a computer-generated random number is a contradiction in terms. As a result, computer-generated pseudorandom numbers are fraught with peril for the unwary. We summarize much that is known about the most well-known pseudorandom number generators: congruential generators. We also provide machine-independent programs to implement the generators in any language that has 32-bit signed integers-for example C, C++, and FORTRAN. Based on an extensive search, we provide parameter values better than those previously available.Programming (Mathematics) ; Computers
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
Why Philosophers Should Care About Computational Complexity
One might think that, once we know something is computable, how efficiently
it can be computed is a practical question with little further philosophical
importance. In this essay, I offer a detailed case that one would be wrong. In
particular, I argue that computational complexity theory---the field that
studies the resources (such as time, space, and randomness) needed to solve
computational problems---leads to new perspectives on the nature of
mathematical knowledge, the strong AI debate, computationalism, the problem of
logical omniscience, Hume's problem of induction, Goodman's grue riddle, the
foundations of quantum mechanics, economic rationality, closed timelike curves,
and several other topics of philosophical interest. I end by discussing aspects
of complexity theory itself that could benefit from philosophical analysis.Comment: 58 pages, to appear in "Computability: G\"odel, Turing, Church, and
beyond," MIT Press, 2012. Some minor clarifications and corrections; new
references adde
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An Improved Pseudorandom Generator Based on Hardness of Factoring
We present a simple to implement and efficient pseudorandom generator based on the factoring assumption. It outputs more than pn/2 pseudorandom bits per p exponentiations, each with the same base and an exponent shorter than n/2 bits. Our generator is based on results by Hastad, Schrift and Shamir
[HSS93], but unlike their generator and its improvement by Goldreich and Rosen [GR00], it does not use hashing or extractors, and is thus simpler and somewhat more efficient.
In addition, we present a general technique that can be used to speed up pseudorandom generators based on iterating one-way permutations. We construct our generator by applying this technique to results of [HSS93]. We also show how the generator given by Gennaro [Gen00] can be simply derived from results of Patel and Sundaram [PS98a] using our technique.Engineering and Applied Science
Quantum Copy-Protection and Quantum Money
Forty years ago, Wiesner proposed using quantum states to create money that
is physically impossible to counterfeit, something that cannot be done in the
classical world. However, Wiesner's scheme required a central bank to verify
the money, and the question of whether there can be unclonable quantum money
that anyone can verify has remained open since. One can also ask a related
question, which seems to be new: can quantum states be used as copy-protected
programs, which let the user evaluate some function f, but not create more
programs for f? This paper tackles both questions using the arsenal of modern
computational complexity. Our main result is that there exist quantum oracles
relative to which publicly-verifiable quantum money is possible, and any family
of functions that cannot be efficiently learned from its input-output behavior
can be quantumly copy-protected. This provides the first formal evidence that
these tasks are achievable. The technical core of our result is a
"Complexity-Theoretic No-Cloning Theorem," which generalizes both the standard
No-Cloning Theorem and the optimality of Grover search, and might be of
independent interest. Our security argument also requires explicit
constructions of quantum t-designs. Moving beyond the oracle world, we also
present an explicit candidate scheme for publicly-verifiable quantum money,
based on random stabilizer states; as well as two explicit schemes for
copy-protecting the family of point functions. We do not know how to base the
security of these schemes on any existing cryptographic assumption. (Note that
without an oracle, we can only hope for security under some computational
assumption.)Comment: 14-page conference abstract; full version hasn't appeared and will
never appear. Being posted to arXiv mostly for archaeological purposes.
Explicit money scheme has since been broken by Lutomirski et al
(arXiv:0912.3825). Other quantum money material has been superseded by
results of Aaronson and Christiano (coming soon). Quantum copy-protection
ideas will hopefully be developed in separate wor
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