Efficient Reconstruction of Euler's Totient Function from Carmichael's Function in Semiprime RSA Moduli

We present a direct and efficient algorithm to reconstruct Euler’s totient function φ(N) from the Carmichael function λ(N), under the assumption that N=pq is a semiprime. This method avoids explicit computation of gcd⁡(p−1,q−1) and enables immediate recovery of p and q via a single quadratic equation. The algorithm has been experimentally validated across over a million semiprime combinations and has potential applications in RSA analysis, quantum algorithm post-processing, and number-theoretical education.