Double RSA Encryption
Given that the encryption standard used is double RSA(the ciphertext is: (message.modpow(publicKey, p1 * p2)).modpow(publicKey, p1 * p2)
and that:
Prime1: 674449898029343324125960129133546398445125248717227189998338836783749268316413874740981320946394895958236124946 6543851799181419398634666415720501042963439
Prime2: 7399242666256222901758159458924085668213750831886997251154683823178450493770217795394523647215822445235626521227 175898733431769288278973766158509318240987
Public key: 256112118095161323042115893555881913125629750852196125735323701395646157334486733585297926242410415964844054150772 80942879367081987594548286248076221422382553854553641938680588196852210279319435539974962399870256652476447043 613041280228303364831412960922600050744288703260423917496698951898392551430899733471
BitLength: 1024
Decrypt the message(converted from string to byte array to number): 23392616345555313605919167058644699120876025356161555809878654111923815810333435486107302640167526508195510207553 020347927571834118867368930145349608665245242658400060659182084710747843682293187303114663413862533201735882997 013110042926297727429690462831240065112067037916859821064295439236630706338604397539
The decrypted text should contain: "Type the following number as answer: (type this 4-digit number)."
The answer is 1948.
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1 solution
Since we know that the public key(call it e) is 256112118...., the private key is simply publicKey.modInverse(euler's totient function of (p * q)). Private Key: 241099571348380347560930789816789335374739804197650008476275058186473634017679324068656900645741025815772782554941083952347468992142929658 8987762196086344097126564481180543184085456849284915490456274428765928978720539554588055122363864882658479332863933450964277770421643534 966367482868657273129471917586675.
We know that the ciphertext was encrypted twice using: message.modPow(publicKey, p1 p2).modPow(publicKey, p1 p2), so we need to "decrypt" it twice using: cipherText.modPow(privateKey, p1 p2).modPow(privateKey, p1 p2).
Thus, we get: 180436161883203116951344620698953437415119327943762475837025298219289260780175534445659668291859512, which can be converted into a byte array and back into the original message.
Byte Array of Message: [84, 121, 112, 101, 32, 116, 104, 101, 32, 102, 111, 108, 108, 111, 119, 105, 110, 103, 32, 110, 117, 109, 98, 101, 114, 32, 97, 115, 32, 97, 110, 115, 119, 101, 114, 58, 32, 49, 57, 52, 56]
You can paste the array above into a converter online like this one: https://onlineutf8tools.com/convert-bytes-to-utf8 converter to get the answer.
Message from byte array: "Type the following number as answer: 1948"