Another Example of Higher Order Randomness
نویسندگان
چکیده
We consider the notion of algorithmic randomness relative to an oracle. We prove that the probability that a program for infinite computations (a program that never halts) outputs a cofinite set is random in the second jump of the halting problem. Indeed, we prove that is exactly as random as the halting probability of a universal machine equipped with an oracle for the second jump of the halting problem, in spite of the fact that is defined without considering oracles.
منابع مشابه
CDMTCS Research Report Series Another Example of Higher Order Randomness
We consider the notion of randomness relative to an oracle: a real number is random in A if and only if its initial segments are algorithmically incompressible in a self-delimiting universal machine equipped with an oracle A. We prove that the probability that a program for infinite computations outputs a cofinite set is random in the second jump of the halting problem.
متن کاملWall Effect in 3D Simulation Of Same Sized Particles Packing
In this paper, the effects of container size on the porosity of random loose packing of mono size particles have been investigated using an Event Dynamics (ED) based model. Simultaneous effects of square container walls on particles packing and their order are also investigated. Our simulation results indicate higher container size will increase the total packing factor and high density regions...
متن کاملA note on the security of Higher-Order Threshold Implementations
At ASIACRYPT 2014, Bilgin et al. describe higher-order threshold implementations: a masking countermeasure claiming resistance against higher-order differential power analysis attacks. In this note, we point out that higher-order threshold implementations do not necessarily provide higher-order security. We give as counterexamples two concrete higher-order threshold implementations that exhibit...
متن کاملAn Efficient Side-Channel Protected AES Implementation with Arbitrary Protection Order
Passive physical attacks, like power analysis, pose a serious threat to the security of digital circuits. In this work, we introduce an efficient sidechannel protected Advanced Encryption Standard (AES) hardware design that is completely scalable in terms of protection order. Therefore, we revisit the private circuits scheme of Ishai et al. [13] which is known to be vulnerable to glitches. We d...
متن کاملAffine Equivalence and Its Application to Tightening Threshold Implementations
Motivated by the development of Side-Channel Analysis (SCA) countermeasures which can provide security up to a certain order, defeating higher-order attacks has become amongst the most challenging issues. For instance, Threshold Implementation (TI) which nicely solves the problem of glitches in masked hardware designs is able to avoid firstorder leakages. Hence, its extension to higher orders a...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Fundam. Inform.
دوره 51 شماره
صفحات -
تاریخ انتشار 2002