Number & MeasureGreek → English
Isogeny
/aɪˈsɒdʒəni/noun
A structure-preserving map between algebraic groups, such as elliptic curves, that is onto and has a finite kernel.
The Greek roots
ἴσος
ísos
equal, same
γένος
génos
birth, origin, kind
Literally: “same origin”
The story of the word
Nineteenth-century biology used isogeny loosely for sameness of descent before algebraic geometers took the word over in the mid-twentieth century and gave it a precise job. Curves linked by an isogeny share their essential arithmetic while looking different, which is why cryptographers built key exchange on the difficulty of finding the connecting map. One such scheme, SIKE, was broken in 2022 by an attack that took a laptop about an hour.
- How it travelled
- Ancient Greek → mathematical coinage → English
- First recorded
- 20th century
Same family
isotopeisomorphismgenesisgenushomogeneous
In a sentence
The two curves are isogenous, so their point counts agree over every finite field.