RSA--低加密指数广播攻击例子

最新推荐文章于 2025-06-26 00:20:59 发布

xuqi7

最新推荐文章于 2025-06-26 00:20:59 发布

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分类专栏： ctf python 文章标签： RSA 低加密指数广播攻击

本文链接：https://blog.youkuaiyun.com/xuqi7/article/details/75578414

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本文介绍了一种针对RSA加密系统的低加密指数广播攻击方法，并通过Python2和Python3提供了具体实现案例。当使用相同较小的加密指数给多个接收者发送相同消息时，这种攻击变得可行。

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RSA—低加密指数广播攻击例子

如果选取的加密指数较小，并且使用了相同的加密指数给一群接收者发送相同的信息，那么可以进行广播攻击得到明文

python2的一个例子

# coding:utf8
# python2

'''
安装依赖：
sudo apt install libgmp-dev
pip install gmpy
'''

from struct import pack,unpack
import zlib
import gmpy

def my_parse_number(number):
    string = "%x" % number
    erg = []
    while string != '':
        erg = erg + [chr(int(string[:2], 16))]
        string = string[2:]
    return ''.join(erg)

def extended_gcd(a, b):
    x,y = 0, 1
    lastx, lasty = 1, 0
    while b:
        a, (q, b) = b, divmod(a,b)
        x, lastx = lastx-q*x, x
        y, lasty = lasty-q*y, y
    return (lastx, lasty, a)

def chinese_remainder_theorem(items):
    N = 1
    for a, n in items:
        N *= n
    result = 0
    for a, n in items:
        m = N/n
        r, s, d = extended_gcd(n, m)
        if d != 1:
            N=N/n
            continue
            #raise "Input not pairwise co-prime"
        result += a*s*m
    return result % N, N

sessions=[{"c": 7366067574741171461722065133242916080495505913663250330082747465383676893970411476550748394841437418105312353971095003424322679616940371123028982189502042, "e": 10, "n": 25162507052339714421839688873734596177751124036723831003300959761137811490715205742941738406548150240861779301784133652165908227917415483137585388986274803},
{"c": 21962825323300469151795920289886886562790942771546858500842179806566435767103803978885148772139305484319688249368999503784441507383476095946258011317951461, "e": 10, "n": 23976859589904419798320812097681858652325473791891232710431997202897819580634937070900625213218095330766877190212418023297341732808839488308551126409983193},
{"c": 6569689420274066957835983390583585286570087619048110141187700584193792695235405077811544355169290382357149374107076406086154103351897890793598997687053983, "e": 10, "n": 18503782836858540043974558035601654610948915505645219820150251062305120148745545906567548650191832090823482852604346478335353784501076761922605361848703623},
{"c": 4508246168044513518452493882713536390636741541551805821790338973797615971271867248584379813114125478195284692695928668946553625483179633266057122967547052, "e": 10, "n": 23383087478545512218713157932934746110721706819077423418060220083657713428503582801909807142802647367994289775015595100541168367083097506193809451365010723},
{"c": 22966105670291282335588843018244161552764486373117942865966904076191122337435542553276743938817686729554714315494818922753880198945897222422137268427611672, "e": 10, "n": 31775649089861428671057909076144152870796722528112580479442073365053916012507273433028451755436987054722496057749731758475958301164082755003195632005308493},
{"c": 17963313063405045742968136916219838352135561785389534381262979264585397896844470879023686508540355160998533122970239261072020689217153126649390825646712087, "e": 10, "n": 22246342022943432820696190444155665289928378653841172632283227888174495402248633061010615572642126584591103750338919213945646074833823905521643025879053949},
{"c": 1652417534709029450380570653973705320986117679597563873022683140800507482560482948310131540948227797045505390333146191586749269249548168247316404074014639, "e": 10, "n": 25395461142670631268156106136028325744393358436617528677967249347353524924655001151849544022201772500033280822372661344352607434738696051779095736547813043},
{"c": 15585771734488351039456631394040497759568679429510619219766191780807675361741859290490732451112648776648126779759368428205194684721516497026290981786239352, "e": 10, "n": 32056508892744184901289413287728039891303832311548608141088227876326753674154124775132776928481935378184756756785107540781632570295330486738268173167809047},
{"c": 8965123421637694050044216844523379163347478029124815032832813225050732558524239660648746284884140746788823681886010577342254841014594570067467905682359797, "e": 10, "n": 52849766269541827474228189428820648574162539595985395992261649809907435742263020551050064268890333392877173572811691599841253150460219986817964461970736553},
{"c": 13560945756543023008529388108446940847137853038437095244573035888531288577370829065666320069397898394848484847030321018915638381833935580958342719988978247, "e": 10, "n": 30415984800307578932946399987559088968355638354344823359397204419191241802721772499486615661699080998502439901585573950889047918537906687840725005496238621}]
 
data = []
for session in sessions:
    e=session['e']
    n=session['n']
    msg=session['c']
    data = data + [(msg, n)]
print("Please wait, performing CRT")
x, n = chinese_remainder_theorem(data)
e=session['e']
realnum = gmpy.mpz(x).root(e)[0].digits()
result = my_parse_number(int(realnum))
print(result)

# flag{wo0_th3_tr4in_i5_leav1ng_g3t_on_it}

python3的一个例子

# coding:utf8
# python3

'''
安装依赖：
sudo apt install libgmp-dev
sudo apt install libmpfr-dev
sudo apt install libmpc-dev
pip install sympy gmpy2
'''

from sympy.ntheory.modular import crt
from gmpy2 import iroot

e = 3
N = [86812553978993, 81744303091421, 83695120256591]
C = [8875674977048, 70744354709710, 29146719498409]

resultant, mod = crt(N,C)
value, is_perfect = iroot(resultant,e)
print(bytes.fromhex(str(value)).decode())

# h45t4d

参考链接：

Code300脚本: http://bobao.360.cn/ctf/detail/162.html
低加密指数广播攻击: http://www.tuicool.com/articles/iYBZBfy
python3例子: https://dunsp4rce.github.io/csictf-2020/crypto/2020/07/21/Quick-Math.html

2018/6/5