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Cryptanalysis - RSA e=3 Broadcast Attack
Mission
broadcast.json contains the same plaintext encrypted with unpadded RSA e=3 under three pairwise-coprime moduli. Recover it with the Chinese Remainder Theorem and an integer cube root.
Hints
Hint 1 Show
Combine the three (c,n) pairs with the Chinese Remainder Theorem
Hint 2 Show
Under the challenge bounds the combined value is the exact m^3 before reduction modulo N
Hint 3 Show
Compute an integer cube root without floating point and convert to big-endian bytes