RedPwn 2021 - Blecc [Crypto]
CTF: RedPwn 2021
Challenge information:
Name: Blecc
Category: Crypto
Description: Blecc! What are all these numbers? This doesn't look like RSA...
Author: AdnanSlef
Points: 119
Solves: 146 out of 1418 teams
Flag: flag{m1n1_3cc}
The challenge contains a file named blecc.txt with the following content:
p = 17459102747413984477
a = 2
b = 3
G = (15579091807671783999, 4313814846862507155)
Q = (8859996588597792495, 2628834476186361781)
d = ???
Can you help me find d
?
Decode it as a string and wrap in flag format.
Writeup:
The description, the file contents and the challenge's name itself Blecc gives us a big hint "ECC" regarding Elliptic-Curve Cryptography. We are given:p
the prime modulus. a, b, G and Q
Usually a capital letter contains the point on the elliptic curve and lowercase letters mean integer scalar.
Once we understand the information given, we are ready to compute d
. I am using SageMath to do the maths. The finite field can be defined as F = GF(P)
, and we can define an Elliptic Curve E
in Sage using the EllipticCurve
command: E = EllipticCurve(GF(p),[a, b])
.
In this case Q = k*G
so Q = d*G
or Q = GF(p)*G
, and solve d
from the equation d = G.discrete_log(Q)
.

We can use long_to_bytes
from pycryptodome
or use x.to_bytes((x.bit_length() + 7)//8, 'big')
to convert 7868191182322623331
to a string format:

And the flag for this crypto challenge is flag{m1n1_3cc}
.