Crypton VS CTFNote

n = 56438641309774959123579452414864548345708278641778632906871133633348990457713200426806112132039095059800662176837023585166134224681069774331148738554157081531312104961252755406614635488382297434171375724135403083446853715913787796744272218693049072693460001363598351151832646947233969595478647666992523249343972394051106514947235445828889363124242280013397047951812688863313932909903047 e = 2 B = 263063435253385937926984981365320113271 c1= 429546912004731012886527767254149694574730322956287028161761007271362927652041138366004560890773167255588200792979452452 c2= 29903904396126887576044949247400308530425862142675118500848365445245957090320752747039056821346410855821626622960719507094119542088455732058232895757115241568569663893434035594991241152575495936972994239671806350060725033375704703416762794475486000391074743029264587481673930383986479738961452214727157980946 delta = (B + n) >> 1 c1 = (c1 + delta^2) % n c2 = (c2 + delta^2) % n # Source: https://github.com/ashutosh1206/Crypton/blob/master/RSA-encryption/Attack-Franklin-Reiter/exploit.sage def gcd(a, b): while b: a, b = b, a % b return a.monic() def franklinreiter(C1, C2, e, N, a, b): P. = PolynomialRing(Zmod(N)) g1 = (a*X + b)^e - C1 g2 = X^e - C2 result = -gcd(g1, g2).coefficients()[0] return result def int_to_bytes(x: int) -> bytes: return x.to_bytes((x.bit_length() + 7) // 8, 'big') bg = 0x272727272727272727272727272727272727272727272727272727272727272727272727272727 soln = franklinreiter(c2, c1, e, n, 1 << 312, bg + delta - (delta << 312)) - delta print(int_to_bytes(int(soln)))

I suck at taking notes lol but a useful tool I have used with my team for collaboration is CTFNote. You may need to deploy and manage the server yourself but it is a pretty good tool.

Sure! If you're working with a team it makes it much easier for someone to assist you if there is a summary of what you did and tried (eg. using https://github.com/TFNS/CTFNote during a CTF). Afterwards it's also a good way to structure and distil a bit the solution, and make a good reference for the future if you stumble upon a similar problem. Lots of people publish their writeups.