Search results

...sure computationally intractable problems exist. Cryptographers thus make assumptions as to which problems are ''hard''. It is commonly believed that if ''m'' is {{Computational hardness assumptions}} ...

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

{{Short description|Computational hardness assumption used in elliptic curve cryptography}} ...'''external Diffie–Hellman (XDH) assumption''' is a [[computational hardness assumption]] used in [[elliptic curve cryptography]]. The XDH assumption h ...

The '''computational Diffie–Hellman (CDH) assumption''' is a [[computational hardness assumption]] about the [[Diffie–Hellman problem]].<ref>{{Citation | last1=B ...change]] as well as the security of the [[ElGamal encryption]] rely on the hardness of the DDH problem. ...

The '''decisional Diffie–Hellman (DDH) assumption''' is a [[computational hardness assumption]] about a certain problem involving [[discrete logarithm]]s in [ ==Relation to other assumptions== ...

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

{{Short description|Problem in computational number theory}} ...78-1-4419-5906-5_429|isbn=978-1-4419-5905-8 |doi-access=free}}</ref>) in [[computational number theory]] is to decide, given [[integer]]s <math>a</math> and <math>N ...

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

{{short description|Hypothesis in computational complexity theory}} ...lly relate the hardness of a new or complicated problem to a computational hardness assumption about a problem that is better-understood. ...

== Computational complexity == ...Sometimes the DHP is called the [[Computational Diffie–Hellman assumption|computational Diffie–Hellman problem]] (CDHP) to more clearly distinguish it from the DDH ...

...|ElGamal]], base their security on the [[computational hardness assumption|hardness assumption]] that the discrete logarithm problem (DLP) over carefully chose ...//link.springer.com/book/10.1007/978-3-0348-8295-8 |title=Cryptography and Computational Number Theory |author-last2=Shparlinski |author-last3=Wang |author-last4=Xi ...

{{Short description|Unsolved problem in computational complexity theory}} ...|computational complexity]]. It has broad applications in the theory of [[hardness of approximation]]. If the unique games conjecture is true and P&nbsp;≠&nbs ...

In [[computational complexity theory]], the [[complexity class]] '''TFNP''' is the class of to ...re are no known unconditional intractability results or results showing NP-hardness of TFNP problems. TFNP is not believed to have any complete problems.<ref n ...

...aim of the proof is to show that the attacker must solve the underlying [[Computational complexity theory#Hard|hard problem]] in order to break the security of the ...omputational hardness assumption|assumptions about the hardness of certain computational tasks]] hold. An early example of such requirements and proof was given by ...

...e is in a certain sense equivalent to (unproven) circuit lower bounds in [[computational complexity theory]]. ...s of Boolean circuits of a given size rests on currently unproven hardness assumptions. ...

...le confidential channels are known to exist under [[computational hardness assumptions]] based on [[hybrid encryption]] and a [[public key infrastructure]].<ref>W ...

...mal language|language]] or not. The prover is assumed to possess unlimited computational resources but cannot be trusted, while the verifier has bounded computation ...ive proof systems solve problems not believed to be in '''NP''', but under assumptions about the existence of [[one-way function]]s, a prover can convince the ver ...

..., '''proof complexity''' is the field aiming to understand and analyse the computational resources that are required to prove or refute statements. Research in proo ...e basic definition of a propositional proof system from the perspective of computational complexity. Specifically Cook and Reckhow observed that proving proof size ...

In [[Computational complexity theory|computational complexity]], problems that are in the [[complexity class]] [[NP (complexit ...of the [[discrete logarithm problem]] and others related to cryptographic assumptions ...

They are typically used when the proof cannot be carried out using weaker assumptions on the [[cryptographic hash function]]. A system that is proven secure when ...behavior from the oracle, or solve some mathematical problem believed [[NP-hardness|hard]] in order to break it. However, it only proves such properties in the ...