# Script For Calculating Byzantine Resistance

Script that calculated probability of successful Byzantine attack. This provided the data presented in "Consensus Among Computer Networks"

#!/usr/bin/python #This script was written by Darren Tapp and optimized by thephez from decimal import Decimal from math import log from math import factorial as fac from math import log1p from math import exp def binom(x, y): try: binom = fac(x) // fac(y) // fac(x - y) except ValueError: binom = 0 return binom ###This function takes inputs and outputs the probability #of success in one trial #pcalc is short for probability calculation def pcalc(masternodes,quorumsize,attacksuccess,Byznodes): SampleSpace = binom(masternodes,quorumsize) pctemp=0 for x in range(attacksuccess, quorumsize+1): pctemp = pctemp + binom(Byznodes,x)*binom(masternodes-Byznodes,quorumsize-x) #at this juncture the answer is pctemp/SampleSpace #but that will produce an overflow error. We use logarithms to #calculate this value return 10 ** (log(pctemp,10)- log(SampleSpace,10)) #Takes the probability of success in one trial and outputs the probability of success in 730 septillion trials #730 septillion trials requires a septillion years of masternode quorum formation. def ZettaYear(probability): trials = 2*365*10 ** 21 return 1-exp(trials * log1p(-probability)) def MegaYear(probability): trials = 2*365*10 ** 6 return 1-exp(trials * log1p(-probability)) ##We evaluate the function pcalc(10,5,3,4) ##print pcalc(10,5,3,4) ##as a test vector ##The answer would be [binom(3,4)*binom(2,6)+(binom(4,4)*binom(1,6)]/binom(10,5) ##[4*15+1*6]/252 = 66/252 ##print float(66)/252 qs = 400 ##Number of masternodes mn = 5000 ##Number of Byzantine nodes assuming 5000 nodes Bft = [250,500,1000,1500,1700,2000,2500] ##Threshold out of quorum of 400 thresh = 161 for j in range(0,7): print "For ", mn, " masternodes with ", Bft[j],"Byzantine the chance of withholding a ChainLock in one trial is ", pcalc(mn,qs,thresh,Bft[j]) ##Now change the # threshold thresh = 240 print "\n" for j in range(0,7): print "For ", mn, " masternodes with ", Bft[j],"Byzantine the chance of producing a malicious ChainLock is ", pcalc(mn,qs,thresh,Bft[j]) print "\n" ##quorum size for InstantSend qs = 50 ##Number of masternodes mn = 5000 ##Number of Byzantine nodes assuming 5000 nodes Bft = [250,500,1000,1500,1700,2000,2500] ##Threshold out of quorum of 400 thresh = 21 for j in range(0,7): print "For ", mn, " masternodes with ", Bft[j],"Byzantine the chance of withholding an InstantSend lock in one trial is ", pcalc(mn,qs,thresh,Bft[j]) ##Now change the # threshold thresh = 30 print "\n" for j in range(0,7): print "For ", mn, " masternodes with ", Bft[j],"Byzantine the chance of producing a malicious InstantSend lock is ", pcalc(mn,qs,thresh,Bft[j])