supersingular isogeny diffie-hellman · originally ffdh: key = gab mod p exchange integers then...
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Deirdre Connolly@durumcrustulum
Supersingular Isogeny Diffie-Hellman
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Shor’s Algorithm
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Diffie-Hellman Key Exchange
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Diffie-Hellman Key Exchange
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Diffie-Hellman Key Exchange
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Diffie-Hellman Key Exchange
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Diffie-Hellman Key Exchange
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Diffie-Hellman Key Exchange
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Diffie-Hellman Key Exchange
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Originally FFDH: key = gab mod p
Exchange integers
Diffie-Hellman Key Exchange
![Page 12: Supersingular Isogeny Diffie-Hellman · Originally FFDH: key = gab mod p Exchange integers Then ECDH: key = abP mod p Exchange points on curve Now SIDH: key = ϕ′ a (ϕ b (E)) =](https://reader033.vdocument.in/reader033/viewer/2022060400/5f0e040b7e708231d43d33af/html5/thumbnails/12.jpg)
Originally FFDH: key = gab mod p
Exchange integers
Then ECDH: key = abP mod p
Exchange points on curve
Diffie-Hellman Key Exchange
![Page 13: Supersingular Isogeny Diffie-Hellman · Originally FFDH: key = gab mod p Exchange integers Then ECDH: key = abP mod p Exchange points on curve Now SIDH: key = ϕ′ a (ϕ b (E)) =](https://reader033.vdocument.in/reader033/viewer/2022060400/5f0e040b7e708231d43d33af/html5/thumbnails/13.jpg)
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Originally FFDH: key = gab mod p
Exchange integers
Diffie-Hellman Key Exchange
![Page 23: Supersingular Isogeny Diffie-Hellman · Originally FFDH: key = gab mod p Exchange integers Then ECDH: key = abP mod p Exchange points on curve Now SIDH: key = ϕ′ a (ϕ b (E)) =](https://reader033.vdocument.in/reader033/viewer/2022060400/5f0e040b7e708231d43d33af/html5/thumbnails/23.jpg)
Originally FFDH: key = gab mod p
Exchange integers
Then ECDH: key = abP mod p
Exchange points on curve
Diffie-Hellman Key Exchange
![Page 24: Supersingular Isogeny Diffie-Hellman · Originally FFDH: key = gab mod p Exchange integers Then ECDH: key = abP mod p Exchange points on curve Now SIDH: key = ϕ′ a (ϕ b (E)) =](https://reader033.vdocument.in/reader033/viewer/2022060400/5f0e040b7e708231d43d33af/html5/thumbnails/24.jpg)
Originally FFDH: key = gab mod p
Exchange integers
Then ECDH: key = abP mod p
Exchange points on curve
Diffie-Hellman Key Exchange
![Page 25: Supersingular Isogeny Diffie-Hellman · Originally FFDH: key = gab mod p Exchange integers Then ECDH: key = abP mod p Exchange points on curve Now SIDH: key = ϕ′ a (ϕ b (E)) =](https://reader033.vdocument.in/reader033/viewer/2022060400/5f0e040b7e708231d43d33af/html5/thumbnails/25.jpg)
Originally FFDH: key = gab mod p
Exchange integers
Then ECDH: key = abP mod p
Exchange points on curve
Diffie-Hellman Key Exchange
![Page 26: Supersingular Isogeny Diffie-Hellman · Originally FFDH: key = gab mod p Exchange integers Then ECDH: key = abP mod p Exchange points on curve Now SIDH: key = ϕ′ a (ϕ b (E)) =](https://reader033.vdocument.in/reader033/viewer/2022060400/5f0e040b7e708231d43d33af/html5/thumbnails/26.jpg)
Originally FFDH: key = gab mod p
Exchange integers
Then ECDH: key = abP mod p
Exchange points on curve
Now SIDH:
key = ϕ′a(ϕb(E)) = ϕ′B(ϕA(E))
Exchange whole curves
Diffie-Hellman Key Exchange
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Grover’s Algorithm
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Best known attacks
Classical:
Quantum:
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Alice Bob
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Alice Bob
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Alice Bob
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Alice Bob
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Alice Bob
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Alice Bob
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Alice Bob
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Alice Bob
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Alice
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Alice
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Alice
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Alice
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Alice
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Alice
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Alice
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Alice
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Alice
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Alice
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Alice
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Alice
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Alice
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Alice
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Alice
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Alice
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Alice
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Alice
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Alice
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Alice
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Alice
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Alice
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2.9X!
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Towards quantum-resistant cryptosystems from supersingular elliptic curve isogeniesLuca De Feo and David Jao and Jérôme Plût, 2011
Efficient algorithms for supersingular isogeny Diffie-HellmanCraig Costello and Patrick Longa and Michael Naehrig, 2016
On the Security of Supersingular Isogeny CryptosystemsSteven D. Galbraith and Christophe Petit and Barak Shani and Yan Bo Ti, 2016
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Deirdre Connolly@durumcrustulum
Supersingular Isogeny Diffie-Hellman