[Verse 1] Peter Shor discovered something wild in ninety-four A quantum trick that cuts through numbers like never before RSA encryption thinks it's safe behind its wall But Shor's algorithm makes those giant factors fall [Chorus] Find the period, then we factorize Quantum computers break the secret ties Shor's the key that opens every door Classical crypto ain't secure no more Period finding leads to factorization Quantum speed beats every calculation [Verse 2] Take a number like fifteen, we'll break it down today Find a base that's coprime, let's say we choose the way Of using two as our foundation, raise it to each power Modulo fifteen cycles in a predictable hour [Chorus] Find the period, then we factorize Quantum computers break the secret ties Shor's the key that opens every door Classical crypto ain't secure no more Period finding leads to factorization Quantum speed beats every calculation [Bridge] Two to the one is two Two squared gives us four Two cubed becomes eight Two to the fourth is one once more The cycle repeats every four steps clean That's the period hiding in between [Verse 3] Once we know the period, the magic can begin Use Euclid's greatest common divisor to win Half the period gives us two, subtract one makes it one GCD of one and fifteen means we're not quite done [Verse 4] But add one to our half-period, now we've got three GCD of three and fifteen gives us victory Three divides both numbers, so we found our factor Five times three makes fifteen, Shor's our benefactor [Final Chorus] Find the period, then we factorize Quantum computers break the secret ties Shor's the key that opens every door Classical crypto ain't secure no more RSA trembles when the qubits dance Shor's algorithm ends the old romance
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