post-quantum isogeny signatures, explained in 30 memes or less
summary
Compact post‑quantum signatures reuse elliptic curve math: public keys are single Montgomery coefficients (about 64 bytes), secret keys are endomorphism rings, and signatures are a commitment curve plus an isogeny kernel recovery so total size is ~148 bytes (64 B curve + ~84 B response). Security reduces to the supersingular isogeny path / endomorphism ring problems (best known cost ≈ 2^128 classical, quantum best ~fourth root). Key randomization is a pseudorandom isogeny; verification is fairly slow (order millisecond verify) and schemes like ski sign and Prism add extra assumptions and implementation complexity.
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chapters (11)
- 0:00Post-quantum isogeny signatures intro
- 1:11Why isogenies matter
- 2:35Classical elliptic curves role
- 5:57Super singular curves importance
- 10:12Super singular isogeny path problem
- 12:42Endomorphism ring problem
- 15:57Toy signature scheme with isogenies
- 20:57How SIKE Sign works
- 22:00Why SIKE signatures compact
- 27:42Key randomization with isogenies
- 32:19Summary open challenges
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