[Verse 1] In the realm of cryptography so strong RSA has protected us for long Large integers multiply with ease But factoring them brings us to our knees Classical computers take too long to find The secret primes hidden in design [Chorus] Shor's the door that quantum computing opens wide Period finding is the key that breaks the RSA hide Superposition searches all the paths at once Fourier transforms reveal what classical methods can't When qubits dance in quantum parallelism The fortress falls to Shor's algorithm [Verse 2] Start with N, the number we must break Find a random number A we'll take If they share a factor, we are done But usually that battle's never won So we search for periods in the math Quantum mechanics shows us the path [Chorus] Shor's the door that quantum computing opens wide Period finding is the key that breaks the RSA hide Superposition searches all the paths at once Fourier transforms reveal what classical methods can't When qubits dance in quantum parallelism The fortress falls to Shor's algorithm [Bridge] A to the power R mod N equals one When R is even, then the race is run A to the R over two, plus or minus one Use Euclid's method till the factors come What takes forever on machines today In polynomial time just fades away [Verse 3] First we build the quantum register wide Hadamard gates spread amplitudes inside Modular exponentiation takes the stage Quantum Fourier transform turns the page Measurement collapses all the spinning states Revealing periods that seal RSA's fate [Chorus] Shor's the door that quantum computing opens wide Period finding is the key that breaks the RSA hide Superposition searches all the paths at once Fourier transforms reveal what classical methods can't When qubits dance in quantum parallelism The fortress falls to Shor's algorithm [Outro] The quantum threat is more than just a dream When fault-tolerant qubits join the scheme Post-quantum crypto must prepare the way For Shor's algorithm's coming day
← Classical vs Quantum Computing Power | Period Finding in Quantum Computing →