> For the complete documentation index, see [llms.txt](https://giongfnef.gitbook.io/giongfnef/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://giongfnef.gitbook.io/giongfnef/writeup-ctf/crypto/page-1.md).

# Securinets CTF Quals 2022

### Escrime

challenge

```
from Crypto.Util.number import getStrongPrime, getPrime, isPrime, bytes_to_long

FLAG = b"Securinets{REDACTED}"

def genPrime(prime):
    while True:
        a = getPrime(256)
        p = 2*prime*a + 1
        if isPrime(p):
            break
    while True:
        b = getPrime(256)
        q = 2*prime*b + 1
        if isPrime(q):
            break
    return p, q

prime = getStrongPrime(512)
p1, q1 = genPrime(prime)
p2, q2 = genPrime(prime)
assert p1 != p2 != q1 != q2

n1 = p1*q1
n2 = p2*q2
e = 65537

m1 = bytes_to_long(FLAG[:len(FLAG)//2])
m2 = bytes_to_long(FLAG[len(FLAG)//2:])

c1 = pow(m1, e, n1)
c2 = pow(m2, e, n2)

print(f"n1 = {n1}")
print(f"n2 = {n2}")
print(f"e = {e}")
print(f"c1 = {c1}")
print(f"c2 = {c2}")

# n1 = 5285941989924581490741575774796326221790301948671605967204654261159288826022690654909746856601734294076351436205238123432817696904524845143908229601315593896823359605609172777227518764838488130850768836467030938547486936412484230693105639039311878853055295612388722273133638524917106191321503530749409311343663516633298043891444321772817485480644504762143353706512690041092791539952154332856635651319630479019844011333570438615137628705917690349203588170944935681
# n2 = 5512656145670579765357132887430527554149315293720001536465226567777071834432904027590899542293511871806792894769506962601330354553170015126601443256295513753986998761021594415121386822360537570074896704547101502955980189351257681515387379761554807684880212096397524725819607628411147885452294832392886405475830663300445429053365129797792206619514994944481130684176571005780217091773969415001961227566026934419626425934895777818074251010427154279687683891897394401
# e = 65537
# c1 = 3792561290017712418676552700903779226679678307521013229152018077539055935181708693237786486418411190513573593312739874489485768872374239333562352570689090751306553033406629945001093355613620844532659507519582518955178617942044813600181673015763469247380587771641089223066734168709065596269187564842646397647564064090886856491267151338586218098150720579275673440512159074650632829004798635425409766385176472514086448897744502264325566940224093583630788193949908215
# c2 = 3222093169881176821995152873609430742364413196826316856495679228145853706169389758246323802005549827444022148276365869623395771621464376723299960525487777645386674088866891887984766934440527885549168365996216682223515034398685244541695223412679979637178695229351272286453267599205874775267533781360269542834699741976380260822746797186755978820611721151719635986648586937891954519919600047846994285652165076540057377973800029963140392459328016771048953153246246886
```

solve

```
from Crypto.Util.number import *

prime=12397002878565866184412236037259205021945058505472864688501145731895119789392433217522880454989374040698621943547773164450323280239641723319936790061247301
n1 = 5285941989924581490741575774796326221790301948671605967204654261159288826022690654909746856601734294076351436205238123432817696904524845143908229601315593896823359605609172777227518764838488130850768836467030938547486936412484230693105639039311878853055295612388722273133638524917106191321503530749409311343663516633298043891444321772817485480644504762143353706512690041092791539952154332856635651319630479019844011333570438615137628705917690349203588170944935681
n2 = 5512656145670579765357132887430527554149315293720001536465226567777071834432904027590899542293511871806792894769506962601330354553170015126601443256295513753986998761021594415121386822360537570074896704547101502955980189351257681515387379761554807684880212096397524725819607628411147885452294832392886405475830663300445429053365129797792206619514994944481130684176571005780217091773969415001961227566026934419626425934895777818074251010427154279687683891897394401
e = 65537
K = Zmod(n1)
P.<a1,b1> = PolynomialRing(K)
f =((2*prime*a1+1)*(2*prime*b1+1)-n1)
load("coppersmith.sage")
a1,b1 = small_roots(f, (1 << 256, 1 << 256))[0]
c1 = 3792561290017712418676552700903779226679678307521013229152018077539055935181708693237786486418411190513573593312739874489485768872374239333562352570689090751306553033406629945001093355613620844532659507519582518955178617942044813600181673015763469247380587771641089223066734168709065596269187564842646397647564064090886856491267151338586218098150720579275673440512159074650632829004798635425409766385176472514086448897744502264325566940224093583630788193949908215
c2 = 3222093169881176821995152873609430742364413196826316856495679228145853706169389758246323802005549827444022148276365869623395771621464376723299960525487777645386674088866891887984766934440527885549168365996216682223515034398685244541695223412679979637178695229351272286453267599205874775267533781360269542834699741976380260822746797186755978820611721151719635986648586937891954519919600047846994285652165076540057377973800029963140392459328016771048953153246246886
prime=12397002878565866184412236037259205021945058505472864688501145731895119789392433217522880454989374040698621943547773164450323280239641723319936790061247301
p1=2*prime*a1 + 1
q1=2*prime*b1 + 1
phi1=(p1-1)*(q1-1)
d1=pow(e,-1,phi1)

L = Zmod(n2)
P.<a2,b2> = PolynomialRing(L)
f =((2*prime*a2+1)*(2*prime*b2+1)-n2)
load("coppersmith.sage")
a2,b2 = small_roots(f, (1 << 256, 1 << 256))[0]
p2=2*prime*a2 + 1
q2=2*prime*b2 + 1
phi2=(p2-1)*(q2-1)
d2=pow(e,-1,phi2)
print(long_to_bytes(pow(c1,d1,n1))+long_to_bytes(pow(c2,d2,n2)))
```

Thanks for reading. Have a good day :heart: !

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