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Qu'est-ce (qui) est periodicity assumption - définition

THEOREM ON HOMOTOPY GROUPS

Bott periodicity; Bott element; Bott's periodicity theorem

XDH assumption

External Diffie-Hellman assumption; XDH Assumption

The external Diffie–Hellman (XDH) assumption is a computational hardness assumption used in elliptic curve cryptography. The XDH assumption holds that there exist certain subgroups of elliptic curves which have useful properties for cryptography.

https://en.wikipedia.org/wiki/XDH_assumption

Open-world assumption

FORMAL-LOGIC ASSUMPTION THAT THE TRUTH-VALUE OF A STATEMENT IS INDEPENDENT OF WHETHER IT IS KNOWN BY ANY SINGLE OBSERVER OR AGENT TO BE TRUE

Open World Assumption; Open World assumption; Open world assumption; Open-world semantics; Partial-closed world assumption

In a formal system of logic used for knowledge representation, the open-world assumption is the assumption that the truth value of a statement may be true irrespective of whether or not it is known to be true. It is the opposite of the closed-world assumption, which holds that any statement that is true is also known to be true.

https://en.wikipedia.org/wiki/Open-world_assumption

Decisional Diffie–Hellman assumption

Decision Diffie-Hellman problem; Decisional Diffie-Hellman assumption; DDH assumption

The decisional Diffie–Hellman (DDH) assumption is a computational hardness assumption about a certain problem involving discrete logarithms in cyclic groups. It is used as the basis to prove the security of many cryptographic protocols, most notably the ElGamal and Cramer–Shoup cryptosystems.

https://en.wikipedia.org/wiki/Decisional_Diffie–Hellman_assumption

Wikipédia

Bott periodicity theorem

In mathematics, the Bott periodicity theorem describes a periodicity in the homotopy groups of classical groups, discovered by Raoul Bott (1957, 1959), which proved to be of foundational significance for much further research, in particular in K-theory of stable complex vector bundles, as well as the stable homotopy groups of spheres. Bott periodicity can be formulated in numerous ways, with the periodicity in question always appearing as a period-2 phenomenon, with respect to dimension, for the theory associated to the unitary group. See for example topological K-theory.

There are corresponding period-8 phenomena for the matching theories, (real) KO-theory and (quaternionic) KSp-theory, associated to the real orthogonal group and the quaternionic symplectic group, respectively. The J-homomorphism is a homomorphism from the homotopy groups of orthogonal groups to stable homotopy groups of spheres, which causes the period 8 Bott periodicity to be visible in the stable homotopy groups of spheres.

https://en.wikipedia.org/wiki/Bott periodicity theorem