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1 Python March 30, / 30
2 shiho 0x10, CTF March 30, / 30
3 why? Python sage 1,, 1 NumPy, Cython Python March 30, / 30
4 why?,. -, -,, March 30, / 30
5 , E : y 2 = x 3 + ax + b 3-2, 3 F p ( ) March 30, / 30
6 , P = (x, y), Q = (r, s) = P + P l = 3x2 + a 2y r = l 2 2x s = y + l(r x), Q = np, P, Q n ( (ECDLP)) -, ECDLP March 30, / 30
7 n, np = O P E n E[n], mod p 1 m µ m F p - F p F p March 30, / 30
8 , e n : E[n] E[n] µ n. -,, Weil Tate η - Optimal Ate Weil Tate. March 30, / 30
9 ? -, P, Q, R E n, e(p, Q) = g e(p + Q, R) = e(p, Q) + e(r, Q) e(p, Q + R) = e(p, Q) + e(p, R) e(ap, Q) = e(p, aq) e(ap, bq) = e(bp, aq) = e(p, Q) a = g ab March 30, / 30
10 ,... long, - F = FiniteField (7); F(2) + F(5) == F(0) Python,... March 30, / 30
11 , µ n F p -, -, 2 2, March 30, / 30
12 ,,... March 30, / 30
13 ...!... [+] 141 Test(s) finished. 141 Test(s) success, 0 Test(s ) fail. real user sys 0m8.717s 0m8.718s 0m0.004s March 30, / 30
14 高速化 流石になんとか高速化したい - 調べてみると, Call graph というものを取ってみると良いらしい, と いうことで使ってみた ツールの影響ですごく時間がかかるので, ツールの挟まれた時間での 計測結果 緑川 志穂 サイボウズ ラボユース 成果報告 March 30, / 30
15 -,? March 30, / 30
16 -,, Fermat... March 30, / 30
17 Fermat -, : Python - Eval - VM March 30, / 30
18 , CPU line profile, PEP8 Python - March 30, / 30
19 Tate, real 0m8.717s user 0m8.718s sys 0m0.004s real 0m2.823s user 0m2.815s sys 0m0.008s 3? - time,... March 30, / 30
20 ? -, timeit 100 weil: usec/pass tate: usec/pass weil: usec/pass tate: usec/pass March 30, / 30
21 sage sage: %timeit P.weil_pairing(Q, l) 10 loops, best of 3: 48.1 ms per loop sage: %timeit P.tate_pairing(Q, l, 2) 10 loops, best of 3: 24.1 ms per loop Tate? -, sage Cython (Pure Python ) March 30, / 30
22 , PyPy(Python JIT )... Python PyPy JIT Numpy Cython Pure Python, C++. March 30, / 30
23 ,. - ID-based Encryption - Boneh-Lynn-Shacham(BLS) Short Signature March 30, / 30
24 ID-Based Encryption ID,,,. - ID, -, ID,. -,, ID. -,... DEMO March 30, / 30
25 Boneh-Lynn-Shacham Short Signature, ECDLP - 512bit,...? F 3 k, 2, 3,. DEMO March 30, / 30
26 Boneh-Lynn-Shacham Short Signature E, P, k E, P, kp. m, k MapT op oint(m). sig m, a = ê(p, sig), b = ê(kp, MapT op oint(m )), a = b, a b. -, ê(, ) ê(, ) = e(, ϕ( )) a = ê(p, sig) = ê(p, MapT op oint(m)) k, b = ê(kp, MapT op oint(m )) = ê(p, MapT op oint(m )) k m = m a = b. ( ) March 30, / 30
27 Python. -,, sage.,., C++. Github: elliptic-shiho/ecpy March 30, / 30
28 - -,,,,,, / The Arithmetic of Elliptic Curve - J.H.Silverman - J.H.Silverman, J.T.Tate 1 - March 30, / 30
29 Pairing for beginners - Craig Costello Short Signature from the Weil Pairing - Dan Boneh, Ben Lynn, Hovav Shacham Identity-Based Encryption from the Weil Pairing - Dan Boneh, Matthew Franklin Bilinear Pairings in Cryptography - Dennis Meffert Square root computation over even extension fields - Gora Adj, Francisco Rodriguez-Henriquez Pairing-Based Cryptography - Martijn Maas Weak Curve In Elliptic Curve Cryptography - Peter Novotney Adleman-Manders-Miller Root Extraction Method Revisited - Zhengjun Cao, Qian Sha, Xiao Fan -,, - - March 30, / 30
30 . March 30, / 30
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MATLAB/Simulink による現代制御入門 サンプルページ この本の定価 判型などは, 以下の URL からご覧いただけます. http://www.morikita.co.jp/books/mid/9241 このサンプルページの内容は, 初版 1 刷発行当時のものです. i MATLAB/Simulink MATLAB/Simulink 1. 1 2. 3. MATLAB/Simulink
Super perfect numbers and Mersenne perefect numbers /2/22 1 m, , 31 8 P = , P =
Super perfect numbers and Mersenne perefect numbers 3 2019/2/22 1 m, 2 2 5 3 5 4 18 5 20 6 25 7, 31 8 P = 5 35 9, 38 10 P = 5 39 1 1 m, 1: m = 28 m = 28 m = 10 height48 2 4 3 A 40 2 3 5 A 2002 2 7 11 13