Crypto
拿到3个文件，rsa.sage，pubkey.py和flag.enc。
其中pubkey.py给出了公钥(n,e)，但是发现n为多项式。
再看rsa.sage
从代码里可以看到，对明文进行了RSA加密。
在kali里安装数学软件sage
sudo apt-get install sagemath
我们知道整数的RSA加密，对应的欧拉函数为
phi = (p-1)*(q-1)
需要注意的是，多项式的欧拉函数为
phi = (2**p.degree()-1)*(2**q.degree()-1)
其中p.degree()为多项式p的最大幂。
编写如下sage代码进行解密：
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file = open("flag.enc","rb")
c = file.read()
file.close()
R.<a> = GF(2^2049)
P = PolynomialRing(GF(2),'x')
c_int = Integer(c.encode('hex'), 16)
c_poly = P(R.fetch_int(c_int))
n = P('x^2048 + x^2046 + x^2043 + x^2040 + x^2036 + x^2035 + x^2034 + x^2033 + x^2031 + x^2029 + x^2025 + x^2024 + x^2022 + x^2019 + x^2018 + x^2017 + x^2012 + x^2007 + x^2006 + x^2004 + x^2000 + x^1999 + x^1998 + x^1997 + x^1993 + x^1992 + x^1991 + x^1986 + x^1982 + x^1981 + x^1979 + x^1978 + x^1977 + x^1975 + x^1970 + x^1964 + x^1963 + x^1962 + x^1961 + x^1960 + x^1959 + x^1958 + x^1955 + x^1954 + x^1952 + x^1951 + x^1949 + x^1947 + x^1942 + x^1939 + x^1938 + x^1936 + x^1934 + x^1933 + x^1932 + x^1930 + x^1928 + x^1927 + x^1923 + x^1922 + x^1919 + x^1918 + x^1915 + x^1914 + x^1913 + x^1912 + x^1911 + x^1910 + x^1908 + x^1903 + x^1902 + x^1900 + x^1899 + x^1897 + x^1893 + x^1891 + x^1890 + x^1886 + x^1881 + x^1880 + x^1879 + x^1878 + x^1875 + x^1874 + x^1873 + x^1872 + x^1871 + x^1870 + x^1869 + x^1865 + x^1863 + x^1862 + x^1860 + x^1856 + x^1855 + x^1853 + x^1852 + x^1845 + x^1841 + x^1839 + x^1837 + x^1836 + x^1835 + x^1833 + x^1832 + x^1829 + x^1828 + x^1827 + x^1826 + x^1824 + x^1823 + x^1822 + x^1821 + x^1820 + x^1819 + x^1818 + x^1817 + x^1813 + x^1812 + x^1810 + x^1809 + x^1808 + x^1807 + x^1803 + x^1799 + x^1797 + x^1796 + x^1794 + x^1792 + x^1790 + x^1786 + x^1783 + x^1782 + x^1779 + x^1778 + x^1776 + x^1775 + x^1774 + x^1772 + x^1767 + x^1766 + x^1765 + x^1764 + x^1763 + x^1762 + x^1759 + x^1757 + x^1756 + x^1754 + x^1753 + x^1752 + x^1750 + x^1749 + x^1741 + x^1734 + x^1730 + x^1729 + x^1726 + x^1725 + x^1723 + x^1722 + x^1721 + x^1716 + x^1714 + x^1713 + x^1712 + x^1710 + x^1709 + x^1706 + x^1705 + x^1703 + x^1702 + x^1700 + x^1698 + x^1693 + x^1692 + x^1691 + x^1690 + x^1683 + x^1682 + x^1681 + x^1680 + x^1679 + x^1677 + x^1672 + x^1670 + x^1669 + x^1666 + x^1663 + x^1662 + x^1661 + x^1659 + x^1655 + x^1653 + x^1651 + x^1649 + x^1648 + x^1647 + x^1646 + x^1644 + x^1643 + x^1642 + x^1640 + x^1639 + x^1638 + x^1634 + x^1633 + x^1628 + x^1620 + x^1619 + x^1618 + x^1616 + x^1614 + x^1611 + x^1610 + x^1608 + x^1605 + x^1604 + x^1603 + x^1599 + x^1597 + 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x^337 + x^336 + x^335 + x^334 + x^332 + x^330 + x^328 + x^327 + x^326 + x^324 + x^320 + x^318 + x^316 + x^315 + x^309 + x^302 + x^298 + x^292 + x^291 + x^290 + x^289 + x^287 + x^286 + x^285 + x^284 + x^281 + x^279 + x^278 + x^276 + x^274 + x^273 + x^272 + x^271 + x^267 + x^266 + x^264 + x^263 + x^262 + x^260 + x^259 + x^256 + x^254 + x^253 + x^252 + x^251 + x^249 + x^248 + x^247 + x^245 + x^244 + x^241 + x^239 + x^235 + x^234 + x^233 + x^232 + x^231 + x^230 + x^226 + x^224 + x^221 + x^219 + x^218 + x^216 + x^215 + x^214 + x^209 + x^207 + x^206 + x^202 + x^201 + x^198 + x^197 + x^194 + x^193 + x^192 + x^191 + x^189 + x^188 + x^183 + x^182 + x^181 + x^180 + x^179 + x^178 + x^177 + x^175 + x^172 + x^169 + x^168 + x^166 + x^165 + x^164 + x^163 + x^158 + x^157 + x^153 + x^152 + x^149 + x^147 + x^146 + x^144 + x^140 + x^139 + x^136 + x^128 + x^127 + x^126 + x^124 + x^123 + x^122 + x^121 + x^116 + x^115 + x^113 + x^112 + x^109 + x^108 + x^107 + x^106 + x^104 + x^103 + x^102 + x^101 + x^100 + x^99 + x^97 + x^95 + x^94 + x^93 + x^92 + x^87 + x^84 + x^83 + x^82 + x^80 + x^79 + x^78 + x^76 + x^73 + x^70 + x^69 + x^68 + x^67 + x^66 + x^65 + x^63 + x^60 + x^59 + x^57 + x^55 + x^52 + x^51 + x^47 + x^46 + x^45 + x^43 + x^42 + x^40 + x^36 + x^35 + x^30 + x^29 + x^28 + x^27 + x^23 + x^20 + x^17 + x^14 + x^9 + x^7 + x^3 + 1')
p,q = n.factor()
p,q = p[0],q[0]
phi = (2**p.degree()-1)*(2**q.degree()-1)
e = 31337
d = inverse_mod(e,phi)
flag_poly = pow(c_poly,d,n)
flag_int = R(flag_poly).integer_representation()
flag = format(flag_int, '0256x').decode('hex')
print flag
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运行得到flag
