例句與造句

1. Moreover, worst-case hardness of some lattice problems have been used to create secure cryptographic schemes.
2. The above lattice problems are easy to solve if the algorithm is provided with a " good " basis.
3. In 1925, Onsager was able to get an exact solution to a two-dimensional ( 2D ) lattice problem at the critical density.
4. Many lattice problems have been conjectured or proven to be average-case hard, making them an attractive class of problems to base cryptographic schemes on.
5. It is widely believed that solving SVP ( and all other lattice problems ) in ideal lattices is as hard as in regular lattices . ""
6. It's difficult to find lattice problems in a sentence. 用lattice problems造句挺難的
7. However, this belief was challenged when in the late 1990s, several new results on the hardness of lattice problems were obtained, starting with the result of Ajtai.
8. The second type admits strong provable security guarantees based on the worst-case hardness of lattice problems, but only a few of them are sufficiently efficient to be used in practice.
9. DMFT maps the lattice problem onto a single-site problem, but the latter fundamentally remains a N-body problem which captures the temporal fluctuations due to electron-electron correlations.
10. They also arise in applied mathematics in connection with coding theory, in cryptography because of conjectured computational hardness of several lattice problems, and are used in various ways in the physical sciences.
11. Attempts to solve general lattice problems by quantum algorithms have been made since Shor s discovery of the quantum factoring algorithm in the mid-1990s, but have so far met with little success if any at all.
12. In 2005, Regev showed that the decision version of LWE is hard assuming quantum hardness of the lattice problems GapSVP _ \ gamma ( for \ gamma as above ) and SIVP _ { t } with t = ?( n / \ alpha ).
13. In his seminal papers, Ajtai showed that the SVP problem was NP-hard and discovered some connections between the worst-case complexity and average-case complexity of some lattice problems . thus making it the first result to have used worst-case hardness to create secure systems.
14. He writes : " " There is a mathematical proof that the " " only " " way to break the cryptosystem ( within some formal attack model ) on its random instances is by being able to solve the underlying lattice problem in the " " worst case " " ( emphasis in the original ).
15. State of the art factoring implementations work in a manner similar to Zassenhaus, except that the combinatorial problem is translated to a lattice problem that is then solved by LLL . In this approach, LLL is not used to compute coefficients of factors, instead, it is used to compute vectors with r entries in { 0, 1 } that encode the subsets of f _ 1 ( x ), . . ., f _ r ( x ) that correspond to the irreducible " true " factors.