The Complexity of Black-Box Ring Problems
نویسندگان
چکیده
We study the complexity of some computational problems on finite black-box rings whose elements are encoded as strings of a given length and the ring operations are performed by a black-box oracle. We give a polynomial-time quantum algorithm to compute a basis representation for a given black-box ring. Using this result we obtain polynomial-time quantum algorithms for several natural computational problems over black-box rings.
منابع مشابه
Lower Bounds on Black-Box Ring Extraction
The black-box ring extraction problem is the problem of extracting a secret ring element from a black-box by performing only the ring operations and testing for equality of elements. An efficient algorithm for the black-box ring extraction problem implies the equivalence of the discrete logarithm and the Diffie-Hellman problem. At the same time this implies the inexistence of secure ring-homomo...
متن کاملA New Framework for the Valuation of Algorithms for Black-Box Optimization
Black-box optimization algorithms optimize a fitness function f without knowledge of the specific parameters of the problem instance. Their run time is measured as the number of f -evaluations. This implies that the usual algorithmic complexity of a problem cannot be applied in the black-box scenario. Therefore, a new framework for the valuation of algorithms for black-box optimization is prese...
متن کاملUniversity of Dortmund
Black-box optimization algorithms cannot use the specific parameters of the problem instance, i.e., of the fitness function f . Their run time is measured as the number of f -evaluations. This implies that the usual algorithmic complexity of a problem cannot be used in the black-box scenario. Therefore, a new framework for the valuation of algorithms for black-box optimization is presented allo...
متن کاملQuantum Query Complexity of Multilinear Identity Testing
Motivated by the quantum algorithm for testing commutativity of black-box groups (Magniez and Nayak, 2007), we study the following problem: Given a black-box finite ring by an additive generating set and a multilinear polynomial over that ring, also accessed as a black-box function (we allow the indeterminates of the polynomial to be commuting or noncommuting), we study the problem of testing i...
متن کاملOn Black-Box Ring Extraction and Integer Factorization
The black-box extraction problem over rings has (at least) two important interpretations in cryptography: An efficient algorithm for this problem implies (i) the equivalence of computing discrete logarithms and solving the Diffie-Hellman problem and (ii) the in-existence of secure ring-homomorphic encryption schemes. In the special case of a finite field, Boneh/Lipton [BL96] and Maurer/Raub [MR...
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:
دوره شماره
صفحات -
تاریخ انتشار 2006