Information om | Engelska ordet SUPERSINGULAR

Exempel på hur man kan använda SUPERSINGULAR i en mening

• Arnold Pizer proved that the supersingular isogeny graphs are Ramanujan, although they tend to have lower girth than the graphs of Lubotzky, Phillips, and Sarnak.
• In positive characteristic it is possible for the endomorphism ring to be even larger: it can be an order in a quaternion algebra of dimension 4, in which case the elliptic curve is supersingular.
• The classic reason (due to Serre) is that if X is a supersingular elliptic curve, then its endomorphism ring is a maximal order in a quaternion algebra B over Q ramified at p and ∞.
• Among the more well-known representatives of this field are the Diffie–Hellman-like key exchange CSIDH, which can serve as a straightforward quantum-resistant replacement for the Diffie-Hellman and elliptic curve Diffie–Hellman key-exchange methods that are in widespread use today, and the signature scheme SQISign which is based on the categorical equivalence between supersingular elliptic curves and maximal orders in particular types of quaternion algebras.

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