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Pairing Friendly Elliptic Curves of Prime Order with Embedding degree 12

Pairing Friendly Elliptic Curves of Prime Order with Embedding degree 12. Paulo Barreto and Michael Naehrig Presented by Mike Scott. BN Curves. An elliptic curve E: y 2 =x 3 +B mod p, where #E=p+1-t, and defined by p(x) = 36x 4 +36x 3 +24x 2 +6x+1 #E(x)=36x 4 +36x 3 +18x 2 +6x+1

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Pairing Friendly Elliptic Curves of Prime Order with Embedding degree 12

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  1. Pairing Friendly Elliptic Curves of Prime Order with Embedding degree 12 Paulo Barreto and Michael Naehrig Presented by Mike Scott

  2. BN Curves An elliptic curve E: y2=x3+B mod p, where #E=p+1-t, and defined by p(x) = 36x4+36x3+24x2+6x+1 #E(x)=36x4+36x3+18x2+6x+1 t(x)= 6x2+1

  3. BN Curves • … has an embedding degree of 12 • … has a CM discriminant of 3 • … facilitates pairings at the 128-bit level of security • … is good for all pairing applications (including short signature) • … supports a sextic twist, so the P and Q parameters of the pairing can be over Fp2and Fp respectively

  4. BN Curves • … supports pairing compression • … is efficient for both the Tate and Ate pairings (half length loop) • … curves are plentiful and are easily found. • … I could go on…  • … The End

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