This problem involves finding the polynomial functions for the given equations whose roots are known, having the least degree. Since it is not mentioned whether the coefficients are real or unreal, to make the function with the least degree...
造Copper解决: #sageimportgmpy2fromCrypto.Util.numberimport*gift=46635322848619790584491725916282901439691751328335921415278638528896063068132242718070261114525516272650970256270551306096774004921902972838212903368063625872c=10138304635644733642662379847053069544836170879873138223874756710806723624125138408940150632074181508102435290815646687790742420388892396564731814...
next() #p4 = 0x81a722c9fc2b2ed061fdab737e3893506eae71ca6415fce14c0f9a45f8e2300711119fa0a5135a053e654fead010b96e987841e47db586a55e3d4494613aa0cc4e4ab59fc6a958b5 kbits = pbits - 576 p4 = p4 << kbits PR.<x> = PolynomialRing(Zmod(n)) f = x + p4 x0 = f.small_roots(X=2...
(1-2*delta) * m) # optimization from Herrmann and May X = 2*floor(N^delta) # this _might_ be too much Y = floor(N^(1/2)) # correct if p, q are ~ same size # # Don't touch anything below # # Problem put in equation P.<x,y> = PolynomialRing(ZZ) A = int((N+1)...
方程分解 $N$. #!/usr/bin/sage -python from sageall import * from Crypto.Util.numberimport long_to_bytes import gmpy2 _p = p0 - (p0&(2**668-2**444)) PR = PolynomialRing(Zmod(N1), 'x') x = PR.gen() f = 2**444 * x + _p f = f.monic() r = f.small_roots(X...
PR.<x> = PolynomialRing(Zmod(n)) nbits = n.nbits() f = 2^kbits*x + p0 f = f.monic() roots = f.small_roots(X=2^(nbits//2-kbits), beta=0.3) # find root < 2^(nbits//2-kbits) with factor >= n^0.3 if roots: ...
This example shows how to write class-based unit tests to qualify the correctness of a function defined in a file in your current folder. ThequadraticSolverfunction takes as inputs the coefficients of a quadratic polynomial and returns the roots of that polynomial. If the coefficients are specifi...
2066740540367638744157494110844029055193511998422999596748975390734628418184477450856691002269702533884505178634105672240426552752649855510423531462598366536500750787631689349504137087 import itertools R.<x,y> = PolynomialRing(Zmod(p)) f = (r1-r2)*(d1+x)*(d2+y)-(d2+y-d1-x) ans = small_roots(f, bounds=(2^246,2^...
append(root) return roots return [] def boneh_durfee(): print('Boneh Durfee') beta = 0.397 bounds = (floor(N^beta) // 2, floor(N^0.5)) R = Integers(e) P.<k, s> = PolynomialRing(R) f = k * (N^2 + N*2*s+(2*s)^2-N+2*s+1) + 1 print(small_roots(f, bounds, ...
CTF-小学生这个平台,也是风大搭建的,大部分题目都是自己出的,题目难度非常友好。稍微难点的题目在风大的B站上都有讲解。 本文主要收录一下自己的解题过程。这些题目用风大的工具来解如同砍瓜切菜般流畅。 风二西_RSA1 题目:e=1 (风二西原创题) importgmpy2importlibnumimportuuid ...