1,crypto
related：
The title seems to be one prng Random number generator , It's actually an investigation RSA, After reading the source code, we found several valid equations ：
flag=state1+state2+state3
state1^17modn=10607235400098586699994392584841806592000660816191315008947917773605476365884572056544621466807636237415893192966935651590312237598366247520986667580174438232591692369894702423377081613821241343307094343575042030793564118302488401888197517625333923710172738913771484628557310164974384462856047065486913046647133386246976457961265115349103039946802386897315176633274295410371986422039106745216230401123542863714301114753239888820442112538285194875243192862692290859625788686421276234445677411280606266052059579743874849594812733193363406594409214632722438592376518310171297234081555028727538951934761726878443311071990
state2^17modn=2665348075952836665455323350891842781938471372943896177948046901127648217780657532963063228780230203325378931053293617434754585479452556620021360669764370971665619743473463613391689402725053682169256850873752706252379747752552015341379702582040497607180172854652311649467878714425698676142212588380080361100526614423533767196749274741380258842904968147508033091819979042560336703564128279527380969385330845759998657540777339113519036552454829323666242269607225156846084705957131127720351868483375138773025602253783595007177712673092409157674720974653789039702431795168654387038080256838321255342848782705785524911705
state1^17modn=4881225713895414151830685259288740981424662400248897086365166643853409947818654509692299250960938511400178276416929668757746679501254041354795468626916196040017280791985239849062273782179873724736552198083211250561192059448730545500442981534768431023858984817288359193663144417753847196868565476919041282010484259630583394963580424358743754334956833598351424515229883148081492471874232555456362089023976929766530371320876651940855297249474438564801349160584279330339012464716197806221216765180154233949297999618011342678854874769762792918534509941727751433687189532019000334342211838299512315478903418642056097679717
(65537 * state0 - 66666 * state1 + 12345 * state2 ) mod n =
10607235400098586699994392584841806592000660816191315008947917773605476365884572056544621466807636237415893192966935651590312237598366247520986667580174438232591692369894702423377081613821241343307094343575042030793564118302488401888197517625333923710172738913771484628557310164974384462856047065486913046647133386246976457961265115349103039946802386897315176633274295410371986422039106745216230401123542863714301114753239888820442112538285194875243192862692290859625788686421276234445677411280606266052059579743874849594812733193363406594409214632722438592376518310171297234081555028727538951934761726878443311071990
state0+state1+state2=280513550110197745829890567436265496990
We use sage lower groebner_basis Solution to linear transformation of variables in equation ( It is similar to solving algebraic equation ), You can get it flag
N =
16084923760264169099484353317952979348361855860935256157402027983349457021767614332173154044206967015252105109115289920685657394517879177103414348487477378025259589760996270909325371731433876289897874303733424115117776042592359041482059737708721396118254756778152435821692154824236881182156000806958403005506732891823555324800528934757672719379501318525189471726279397236710401497352477683714139039769105043411654493442696289499967521222951945823233371845110807469944602345293068346574630273539870116158817556523565199093874587097230314166365220290730937380983228599414137341498205967870181640370981402627360812251649
Cs =
[10607235400098586699994392584841806592000660816191315008947917773605476365884572056544621466807636237415893192966935651590312237598366247520986667580174438232591692369894702423377081613821241343307094343575042030793564118302488401888197517625333923710172738913771484628557310164974384462856047065486913046647133386246976457961265115349103039946802386897315176633274295410371986422039106745216230401123542863714301114753239888820442112538285194875243192862692290859625788686421276234445677411280606266052059579743874849594812733193363406594409214632722438592376518310171297234081555028727538951934761726878443311071990L,
2665348075952836665455323350891842781938471372943896177948046901127648217780657532963063228780230203325378931053293617434754585479452556620021360669764370971665619743473463613391689402725053682169256850873752706252379747752552015341379702582040497607180172854652311649467878714425698676142212588380080361100526614423533767196749274741380258842904968147508033091819979042560336703564128279527380969385330845759998657540777339113519036552454829323666242269607225156846084705957131127720351868483375138773025602253783595007177712673092409157674720974653789039702431795168654387038080256838321255342848782705785524911705L,
4881225713895414151830685259288740981424662400248897086365166643853409947818654509692299250960938511400178276416929668757746679501254041354795468626916196040017280791985239849062273782179873724736552198083211250561192059448730545500442981534768431023858984817288359193663144417753847196868565476919041282010484259630583394963580424358743754334956833598351424515229883148081492471874232555456362089023976929766530371320876651940855297249474438564801349160584279330339012464716197806221216765180154233949297999618011342678854874769762792918534509941727751433687189532019000334342211838299512315478903418642056097679717L,
12534425973458061280573013378054836248888335198966169076118474130362704619767247747943108676623695140384169222126709673116428645230760767457471129655666350250668322899568073246541508846438634287249068036901665547893655280767196856844375628177381351311387888843222307448227990714678010579304867547658489581752103225573979257011139236972130825730306713287107974773306076630024338081124142200612113688850435053038506912906079973403207309246156198371852177700671999937121772761984895354214794816482109585409321157303512805923676416467315573673701738450569247679912197730245013539724493780184952584813891739837153776754362L]
s = 280513550110197745829890567436265496990 e = 17 l = len(Cs) PR =
PolynomialRing( Zmod(N), 'x', l ) x = PR.gens() f1 = (65537*x[0] - 66666*x[1] +
12345*x[2] - x[3]) f2 = x[0] + x[1] + x[2] - s Fs = [f1, f2] Fs.extend( [
(x[i]**e - Cs[i]) for i in range(l) ] ) I = Ideal(Fs) B = I.groebner_basis() m
= '' for b in B[:-1][::-1]: assert b.degree() == 1 mi = ZZ( -b(0,0,0,0) ) print
mi
2. Smart alice
We get the data encrypted with similar plaintext 4 Group ciphertext , But the two sets of public keys are 3, The two sets of public keys are 5, So we have the following equation
We restructure it , Square one or two , Three or four times one x, The polynomial of the same power can be obtained ,
The Chinese remainder theorem is used to combine them sage Of small_roots Solving equations ：
#!/usr/bin/sage -python from sage.all import * from Crypto.Util import number
from Crypto.PublicKey import RSA from hashlib import sha256 Usernames =
['Alice', 'Bob', 'Carol', 'Dan', 'Erin'] A = sha256( b'Alice' ).hexdigest() PKs
= [] Ciphers = [] B = [] for i in range(4): name = Usernames[i+1] pk =
open(name+'Public.pem', 'rb').read() PKs.append( RSA.importKey(pk) ) cipher =
open(name+'Cipher.enc', 'rb').read() Ciphers.append(
number.bytes_to_long(cipher) ) data = '{"from": "'+A+'", "msg":
"'+'\x00'*95+'", "to": "'+sha256( name.encode() ).hexdigest()+'"}' B.append(
number.bytes_to_long(data) ) PR = PolynomialRing(ZZ, 'x') x = PR.gen() Fs = []
for i in range(4): f = PR( ( 2**608*x + B[i] )**PKs[i].e - Ciphers[i] ) ff =
f.change_ring( Zmod(PKs[i].n) ) ff = ff.monic() f = ff.change_ring(ZZ)
Fs.append(f) F = crt( [ Fs[0]**2, Fs[1]**2, x*Fs[2], x*Fs[3] ], [ PKs[i].n for
i in range(4) ] ) M = reduce( lambda x, y: x * y, [ PKs[i].n for i in range(4)
] ) FF = F.change_ring( Zmod(M) ) m = FF.small_roots(X=2**760, beta=7./8)[0]
print 'msg: ' + number.long_to_bytes(m)
3.xx
We are here ida Used in findcrypt The plug-in found one in the middle xx_tea Encryption function of , The key is the first four digits of the input , Then the encrypted ciphertext is converted to plaintext , Now we can get the reverse of it ：
import xxtea v20=[0xce, 0xbc, 0x40, 0x6b, 0x7c, 0x3a, 0x95, 0xc0, 0xef, 0x9b,
0x20, 0x20, 0x91, 0xf7, 0x02, 0x35, 0x23, 0x18, 0x02, 0xc8, 0xe7, 0x56, 0x56,
0xfa] for i in xrange(len(v20)-1,0,-1): j=0 while j<i/3: v20[i]=v20[i]^v20[j]
j+=1 v19=[] for i in xrange(24): v19.append(0) for i in xrange(6):
v19[4*i+2]=v20[4*i+0] v19[4*i+0]=v20[4*i+1] v19[4*i+3]=v20[4*i+2]
v19[4*i+1]=v20[4*i+3] ss="" for i in v19: ss=ss+chr(i) key = "flag"
decrypt_data = xxtea.decrypt(ss, key) print decrypt_data
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