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{{Computational hardness assumptions}} [[Category:Computational hardness assumptions]] ...

...s conjecture''' or '''2-cycle conjecture''' is an unproven [[computational hardness assumption]] asserting that solving the 1-vs-2 cycles problem in the [[mass ...similar communication [[lower bound]]s for several other problems in this computational model, including [[single-linkage clustering]]{{r|yv}} and geometric [[mini ...

...xity theory]], a '''fine-grained reduction''' is a transformation from one computational problem to another, used to relate the difficulty of improving the time bou Let <math>A</math> and <math>B</math> be computational problems, specified as the desired output for each possible input. ...

...the '''planted clique conjecture'''; it has been used as a [[computational hardness assumption]]. ...e a graph, by the following random process:<ref name="ab">{{citation|title=Computational Complexity: A Modern Approach|first1=Sanjeev|last1=Arora|author1-link=Sanje ...

{{Short description|Computational hardness assumption}} ...small set expanders. This assumption implies the hardness of several other computational problems, and the optimality of certain known [[approximation algorithm]]s. ...

...yclic lattices, and efficient one-way functions from worst-case complexity assumptions.] Foundations of Computer Science, 2002. Proceedings. The 43rd Annual IEEE ...nsky, Lenny, and Xun Sun. [On the geometry of cyclic lattices.] Discrete & Computational Geometry 52.2 (2014): 240–259.</ref> ...

...606347 |issn=0004-5411}}</ref> In more technical terms, it refers to the [[computational problem]] of inferring a linear <math>n</math>-ary function <math>f</math> ...ly, the LWE problem has been used as a [[Computational hardness assumption|hardness assumption]] to create [[Public-key cryptography|public-key cryptosystems]] ...

...ure) had to wait until Jain, Lin, and Sahai (2020). (Even so, one of these assumptions used in the 2020 proposal is not secure against [[quantum computers]].) {{Broader|Computational indistinguishability}} ...

{{short description|Unproven computational hardness assumption}} ...NP problem|P ≠ NP]], but it is a stronger statement. It implies that many computational problems are equivalent in complexity, in the sense that if one of them has ...

...[[Computational hardness assumption|assumption]] that certain well-studied computational [[lattice problem]]s cannot be solved efficiently. ...ographic hash function]] whose security is equivalent to the computational hardness of SIS. ...

...a basis for extremely secure cryptographic schemes. The use of worst-case hardness in such schemes makes them among the very few schemes that are very likely ...{{cite journal |author-link=Subhash Khot |first=Subhash |last=Khot |title=Hardness of approximating the shortest vector problem in lattices |journal=J. ACM |v ...

...''n'')-Ideal-SVP). The average-case collision-finding problem is a natural computational problem called Ideal-SIS, which has been shown to be as hard as the worst-c ...] [[Cryptographic hash function|hash functions]] can be built based on the hardness of finding an approximate [[Lattice problem|shortest vector]] in such latti ...

...are [[Computational hardness assumption|computational assumptions]]. Such assumptions consists of two parts. First, one assumes that a particular problem is diff ...ptography]] physical assumptions appear, which do not rely on any hardness assumptions, but merely assume a limit on some other resource. In classical cryptograph ...

{{short description|Computational problem possibly useful for post-quantum cryptography}} ...uantum cryptography]], '''ring learning with errors''' ('''RLWE''') is a [[computational problem]] which serves as the foundation of new cryptographic [[algorithm]] ...

...nditional to appropriate [[Computational hardness assumption|cryptographic assumptions]]):<ref name=":0" /> ...

...key, provided the appropriate [[Computational hardness assumption|hardness assumptions]] are satisfied of course, and provided the PURB is padded to one of the al ...

...is a type of [[algorithm]] that aims to find approximate solutions to [[NP-hardness|NP-hard]] [[optimization problem]]s in polynomial time in the input size an ...n |date=2020 |title=A Survey on Approximation in Parameterized Complexity: Hardness and Algorithms |journal=Algorithms |language=en |volume=13 |issue=6 |pages= ...

{{Short description|Economical computational problem}} ...ve equilibrium computation''' or '''clearing-prices computation''') is a [[computational problem]] in the intersection of [[economics]] and [[computer science]]. Th ...

...solved in polynomial time for arbitrary graphs unless [[P = NP]]. Stronger hardness results are also known showing that it is difficult to [[approximation algo ==NP-hardness== ...

...t effective method for finding discrete logarithms, consists of four large computational steps, of which the first three depend only on the order of the group G, no [[Category:Computational hardness assumptions]] ...