Tags: sagemath rsa
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# Insights
## Source
Boundary attacks on RSA involve manipulating the input values at specific boundaries to exploit vulnerabilities in the encryption system's implementation. As one of the most widely used encryption systems, RSA provides insights into secure communications through its reliance on the difficulty of factoring large prime numbers. However, it is crucial to implement RSA correctly with robust key management and secure implementations to ensure its effectiveness in protecting sensitive information.
## Encryption
The only function of importance here is:
```
def genKey(L, nbit):
p, q = [genPrime(L, nbit) for _ in '__']
n = p * q
d = next_prime(pow(n, 0.2919))
phi = (p - 1) * (q - 1)
e = inverse(d, phi)
pubkey, privkey = (n, e), (p, q)
return pubkey, privkey
```
- It's a basic RSA and it's flawed because of the line of code `d = next_prime(pow(n, 0.2919))`
- We have been given `n` so we can get `d` by running the same code. We have `d`,`n` and `c`, so we can simply get `m = pow(c,d,n)`
## Decryption
```
n = 12765231982257032754070342601068819788671760506321816381988340379929052646067454855779362773785313297204165444163623633335057895252608396010414744222572161530653104640020689896882490979790275711854268113058363186249545193245142912930804650114934761299016468156185416083682476142929968501395899099376750415294540156026131156551291971922076435528869024742993840057342092865203064721826362149723366381892539617642364692012936270150691803063945919154346756726869466855557344213050973081755499746750276623648407677639812809665472258655462846021403503851719008687214848550916999977775070011121527941755954255781343103086789
d = next_prime(pow(n, 0.2919))
c = 10992248752412909788626396175372747713079469256270100576886987393986576680666320383209810005318254336440105142571546847427454822405793626080251363454531982746373841267986148332456716023293306870382809568309620264499225135226626560298741596462262513921032733814032790312163314776421380481083058518893602887082464123177575742160690315666730642727773288362853901330620841098230284739614618790097180848133698381487679399364400048499041582830157094876815030301231505774900176910650887780842536610942820066913075027528705150102760422836458745949063992228680293226303245265232017738712226154128654682937687199768621565945171
m = pow(c,d,n)
flag=bytes.fromhex(hex(m)[2:]).decode()
print(flag)
```
By running this code in Sage we can get the flag
## Flag
The flag is CCTF{RSA_N3w_rEc0rd5_4Nd_nEw_!nSi9h75!}
