UNCTF2020-crypto：简单的RSA

题目：

e= 18437613570247445737704630776150775735509244525633303532921813122997549954741828855898842356900537746647414676272022397989161180996467240795661928117273837666615415153571959258847829528131519423486261757569454011940318849589730152031528323576997801788206457548531802663834418381061551227544937412734776581781
n= 147282573611984580384965727976839351356009465616053475428039851794553880833177877211323318130843267847303264730088424552657129314295117614222630326581943132950689147833674506592824134135054877394753008169629583742916853056999371985307138775298080986801742942833212727949277517691311315098722536282119888605701
c= 140896698267670480175739817539898638657099087197096836734243016824204113452987617610944986742919793506024892638851339015015706164412994514598564989374037762836439262224649359411190187875207060663509777017529293145434535056275850555331099130633232844054767057175076598741233988533181035871238444008366306956934

给了e、n、c求明文，使用前辈写的脚本：

import gmpy2
import time
def continuedFra(x, y):
    cF = []
    while y:
        cF += [x / y]
        x, y = y, x % y
    return cF
def Simplify(ctnf):
    numerator = 0
    denominator = 1
    for x in ctnf[::-1]:
        numerator, denominator = denominator, x * denominator + numerator
    return (numerator, denominator)
def calculateFrac(x, y):
    cF = continuedFra(x, y)
    cF = map(Simplify, (cF[0:i] for i in xrange(1, len(cF))))
    return cF
def solve_pq(a, b, c):
    par = gmpy2.isqrt(b * b - 4 * a * c)
    return (-b + par) / (2 * a), (-b - par) / (2 * a)
def wienerAttack(e, n):
    for (d, k) in calculateFrac(e, n):
        if k == 0: continue
        if (e * d - 1) % k != 0: continue
        phi = (e * d - 1) / k
        p, q = solve_pq(1, n - phi + 1, n)
        if p * q == n:
            return abs(int(p)), abs(int(q))
    print 'not find!'
time.clock()
e= 18437613570247445737704630776150775735509244525633303532921813122997549954741828855898842356900537746647414676272022397989161180996467240795661928117273837666615415153571959258847829528131519423486261757569454011940318849589730152031528323576997801788206457548531802663834418381061551227544937412734776581781
n= 147282573611984580384965727976839351356009465616053475428039851794553880833177877211323318130843267847303264730088424552657129314295117614222630326581943132950689147833674506592824134135054877394753008169629583742916853056999371985307138775298080986801742942833212727949277517691311315098722536282119888605701
c= 140896698267670480175739817539898638657099087197096836734243016824204113452987617610944986742919793506024892638851339015015706164412994514598564989374037762836439262224649359411190187875207060663509777017529293145434535056275850555331099130633232844054767057175076598741233988533181035871238444008366306956934
p, q = wienerAttack(e, n)
print '[+]Found!'
print '  [-]p =',p
print '  [-]q =',q
print '  [-]n =',p*q
d = gmpy2.invert(e,(p-1)*(q-1))
print '  [-]d =', d
print '  [-]m is:' + '{:x}'.format(pow(c,d,n)).decode('hex')
print '
[!]Timer:', round(time.clock(),2), 's'
print '[!]All Done!'