Convert polynomial to integer value ?

asked 2019-03-23 22:06:57 -0500

Hello everyone, I'm a totally newer to sage. I encountered some minor problems in the process of implementing RSA encryption algorithm with sage. The code has been passed to the attachment, This algorithm is implemented using finite fields and polynomial rings. There is a line c_poly = pow(m_poly, e, n) in the code, but m_poly and n are not integers. Instead, sage.rings.polynomial.polynomial_gf2x.Polynomial_GF2X, I want to convert these two quantities into integers, but it always fails. Can someone provide any method? Grateful.

    pubkey.py


from sage.all import GF,PolynomialRing

P=PolynomialRing(GF(2),'x') 
e = 31337

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')

rsa.sage

#!/usr/bin/env sage
# coding=utf-8

from pubkey import P, n, e

from os import urandom
flag = "flag"
R.<a> = GF(2^2049)  

def encrypt(m):
global n
assert len(m) <= 256
m_int = Integer(m.encode('hex'), 16)
m_poly = P(R.fetch_int(m_int)) #canshubianhuan?

c_poly = pow(m_poly, e, n)

c_int = R(c_poly).integer_representation()  
c = format(c_int, '0256x').decode('hex')
return c

if __name__ == '__main__':
    ptext = flag + os.urandom(256-len(flag))
    ctext = encrypt(ptext)
    with open('flag.enc', 'wb') as f:
        f.write(ctext)
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Comments

1

Please isolate the problem with minimal code. We have for instance no chance to know what is the flag. It may be also useful to use a debug environment like eclipse or PyCharm. So please insert a minimal line with explicit constants (no variables), which is not working, possibly with polynomials of decent degrees.

dan_fulea gravatar imagedan_fulea ( 2019-03-24 10:58:05 -0500 )edit