[HALtheWise]

Feeding random inputs to a crypto function is not guaranteed to exercise all the weird paths that an attacker providing intentionally malicious input could access. For example, a loop comparing against secret data in 32 bit chunks will take constant time 99.99999999% of the time, but is still a security hole because an attacker learns a lot from the one case where it returns faster. Crypto vulnerabilities often take the form of very specifically crafted inputs that exploit some mathematical property that's very unlikely from random data.