[Verse 1] Hidden patterns lurk beneath the surface of integers vast Factorization seems impossible when numbers grow so fast But quantum superposition holds the secret we desire Find the period, crack the code, set cryptography on fire [Chorus] Period finding, period finding In the quantum realm we search Modular arithmetic's heartbeat Powers cycling, powers cycling Through their mathematical church Shor's foundation runs so deep [Verse 2] Take your number N to factor, choose a random base called A Raise it to increasing powers, watch the sequence start to play A to one, A squared, A cubed, modulo N they dance Till the pattern starts repeating, quantum gives us our chance [Chorus] Period finding, period finding In the quantum realm we search Modular arithmetic's heartbeat Powers cycling, powers cycling Through their mathematical church Shor's foundation runs so deep [Bridge] Quantum Fourier Transform reveals What classical computers cannot steal The period R where A to R Equals one mod N so far Greatest common divisor splits The factors fall in perfect bits [Verse 3] Hadamard gates create the superposition state we need Controlled operations build the function that will feed The inverse QFT extraction pulls the frequency from noise Integer factorization bows before our quantum voice [Chorus] Period finding, period finding In the quantum realm we search Modular arithmetic's heartbeat Powers cycling, powers cycling Through their mathematical church Shor's foundation runs so deep [Outro] When the period's found at last RSA encryption's past Quantum threat has found its mark In the mathematics dark
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