How the eMudrha certificate debacle might have happened

You may have seen references to a password being the number 4. There are countless allusions to this online, but they don’t give the context. As I mentioned in an earlier post, eMudrha was using the numbers 4, 56, 115, 155, 156, 230, and 237 as secret keys. I haven’t seen details of how this happened, but in this post I’ll give a plausible account of how it might have happened, what someone could have done to produce those results. I’m not trying to do forensic analysis on this specific incident, just exploring what someone might do. eMudrha was using the NIST elliptic curve P-384, and a secret key should be a random number chosen between 1 and 2384. That upper bound isn’t exactly correct, but it’s close. See this post if you want to know the exact number. Someone might have chosen numbers up to 384 rather than 2384 out of ignorance. Or they might done so by a typo. Maybe they generated a random value that might have been larger than 2384 and then intended to reduce the number mod…