Why RSA replaced Euler's totient function with Carmichael

RSA implementations gradually shifted from using Euler's totient function φ(n) to Carmichael's totient function λ(n) for computing private keys. While Carmichael's function produces smaller private keys and faster decryption, experiments show the efficiency gain is minimal—typically just a factor of 2 or 4. The gcd of (p-1) and (q-1) rarely exceeds small values, making the performance improvement trivial. Greater efficiency gains can be achieved through alternative approaches like Garner's algorithm.