Pythonによる楕円曲線・ペアリング暗 号ライブラリの実装とアプリケーショ ンPython March 30, 2016 1 / 30 who? @elliptic shiho 0x10 , CTF March 30, 2016 2 / 30 why? Python sage1 , , 1 NumPy, Cython Python March 30, 2016 3 / 30 why? , . - , - , , March 30, 2016 4 / 30 , E : y2 = x3 + ax + b 3 - 2, 3 Fp( ) March 30, 2016 5 / 30 , P = (x, y) , Q = (r, s) = P + P ℓ = 3x2 + a 2y r = ℓ2 − 2x s = y + ℓ(r − x) , Q = nP , P, Q n ( (ECDLP)) - , ECDLP March 30, 2016 6 / 30 n , nP = O
