235,304 research outputs found
Simpler Proofs of Quantumness
A proof of quantumness is a method for provably demonstrating (to a classical
verifier) that a quantum device can perform computational tasks that a
classical device with comparable resources cannot. Providing a proof of
quantumness is the first step towards constructing a useful quantum computer.
There are currently three approaches for exhibiting proofs of quantumness: (i)
Inverting a classically-hard one-way function (e.g. using Shor's algorithm).
This seems technologically out of reach. (ii) Sampling from a
classically-hard-to-sample distribution (e.g. BosonSampling). This may be
within reach of near-term experiments, but for all such tasks known
verification requires exponential time. (iii) Interactive protocols based on
cryptographic assumptions. The use of a trapdoor scheme allows for efficient
verification, and implementation seems to require much less resources than (i),
yet still more than (ii).
In this work we propose a significant simplification to approach (iii) by
employing the random oracle heuristic. (We note that we do not apply the
Fiat-Shamir paradigm.) We give a two-message (challenge-response) proof of
quantumness based on any trapdoor claw-free function. In contrast to earlier
proposals we do not need an adaptive hard-core bit property. This allows the
use of smaller security parameters and more diverse computational assumptions
(such as Ring Learning with Errors), significantly reducing the quantum
computational effort required for a successful demonstration.Comment: TQC 202
“Not Like a Big Gap, Something We Could Handle”: Facilitating Shifts in Paradigm in the Supervision of Mathematics Graduates upon Entry into Mathematics Education
Mathematics is the discipline that a significant majority of most incoming researchers in mathematics education have prior qualifications and experience in. Upon entry into the field of mathematics education research, these newcomers–often students on a postgraduate programme in mathematics education–need a broadened understanding on how to read, converse, write and conduct research in the largely unfamiliar territory of mathematics education. The intervention into the practices of post-graduate teaching and supervision in the field of mathematics education that I describe here aims at fostering this broadened understanding and thus facilitating newcomers’ participation in the practices of the mathematics education research community. Here I outline the theoretical underpinnings of the intervention and exemplify one of its parts (an Activity Set designed to facilitate incoming students’ engagement with the mathematics education research literature). I supplement the discussion of the intervention with comments sampled from student interview and student written evaluation data as well as observations of the activities’ implementation. The main themes touched upon include: learning how to identify appropriate mathematics education literature; reading increasingly more complex writings in mathematics education; coping with the complexity of literate mathematics education discourse; working towards a contextualised understanding of literate mathematics education discourse. I conclude with indicating the directions that the intervention, and its evaluation, is currently taking and a brief discussion of broader implications, theoretical as well as concerning the supervision and teaching of post-graduate students in mathematics education
Gaming security by obscurity
Shannon sought security against the attacker with unlimited computational
powers: *if an information source conveys some information, then Shannon's
attacker will surely extract that information*. Diffie and Hellman refined
Shannon's attacker model by taking into account the fact that the real
attackers are computationally limited. This idea became one of the greatest new
paradigms in computer science, and led to modern cryptography.
Shannon also sought security against the attacker with unlimited logical and
observational powers, expressed through the maxim that "the enemy knows the
system". This view is still endorsed in cryptography. The popular formulation,
going back to Kerckhoffs, is that "there is no security by obscurity", meaning
that the algorithms cannot be kept obscured from the attacker, and that
security should only rely upon the secret keys. In fact, modern cryptography
goes even further than Shannon or Kerckhoffs in tacitly assuming that *if there
is an algorithm that can break the system, then the attacker will surely find
that algorithm*. The attacker is not viewed as an omnipotent computer any more,
but he is still construed as an omnipotent programmer.
So the Diffie-Hellman step from unlimited to limited computational powers has
not been extended into a step from unlimited to limited logical or programming
powers. Is the assumption that all feasible algorithms will eventually be
discovered and implemented really different from the assumption that everything
that is computable will eventually be computed? The present paper explores some
ways to refine the current models of the attacker, and of the defender, by
taking into account their limited logical and programming powers. If the
adaptive attacker actively queries the system to seek out its vulnerabilities,
can the system gain some security by actively learning attacker's methods, and
adapting to them?Comment: 15 pages, 9 figures, 2 tables; final version appeared in the
Proceedings of New Security Paradigms Workshop 2011 (ACM 2011); typos
correcte
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