Isn't this circular reasoning? If you do that, you have another constant to justify: the offset into pi you used. Go find BADA55 in Pi, and relay back to us what the offset is.†
You don't need lotteries to break this logjam. You just demand the minimal parameters that satisfy the security a/o performance considerations for your problem. LaMacchia and Costello did this for NUMS without even needing recourse to constants: they just start with the target security level, find the minimal prime for that security level, and then the minimal suitable (given, for instance, SafeCurves) d for an Edwards curve.
You don't need lotteries to break this logjam. You just demand the minimal parameters that satisfy the security a/o performance considerations for your problem. LaMacchia and Costello did this for NUMS without even needing recourse to constants: they just start with the target security level, find the minimal prime for that security level, and then the minimal suitable (given, for instance, SafeCurves) d for an Edwards curve.
† My friend Peter found it: http://pi.nersc.gov/cgi-bin/pi.cgi?word=BADA55&format=hex --- so: justify the binary offset "2733181964". :)