Simulates the probability of a double-spend attack succeeding over a 10 minute interval, with 10 minute vs 1 minute target block interval times

blockchain-attack-w-modified-target-time.R

# Simulations carried out by the R statistical language: https://www.r-project.org/

set.seed(314)
# Set the random seed to make the results reproducible
current.target.block.time <- 10
modified.target.block.time <- 1
hashpower.honest.miners <- 0.70
hashpower.malicious.miner <- 0.30

n.simulations <- 1000000
# One million simulations

normal.operations <- rexp(n.simulations) * current.target.block.time / (hashpower.honest.miners + hashpower.malicious.miner)
# Draw n.simulations from an exponential distribution, scaled by block time and hashpower

mean(normal.operations)
# 10.00411
# Mean block time is 10.00411 minutes

honest.blocks.attack.current <- rexp(n.simulations) * current.target.block.time / hashpower.honest.miners
malicious.blocks.attack.current <- rexp(n.simulations) * current.target.block.time / hashpower.malicious.miner
# Now, split the hashpower by honest and malicious miners

mean(honest.blocks.attack.current)
# 14.32075
# Mean time between blocks found by the honest miners is 14.32075
mean(malicious.blocks.attack.current)
# 33.2966
# Mean time between blocks found by the malicious miner is 33.2966

mean(malicious.blocks.attack.current < honest.blocks.attack.current)
# 0.300555
# On average, the malicious miner finds a block before the honest miners in 30.0555% of cases

##########################################################################################
# Now, simulate a one-minute block time
# How often will the malicious miner find 10 blocks before the honest miners find 10 blocks?
##########################################################################################

honest.blocks.sum.v <- vector("numeric", length = n.simulations)
malicious.blocks.sum.v <- vector("numeric", length = n.simulations)

for (i in seq_len(n.simulations)) {
  
  honest.blocks.attack.modified <- rexp(current.target.block.time) * modified.target.block.time / hashpower.honest.miners
  malicious.blocks.attack.modified <- rexp(current.target.block.time) * modified.target.block.time / hashpower.malicious.miner
  # Draw 10 values from an exponential distribution for both honest and malicious miners
  
  honest.blocks.sum.v[i] <- sum(honest.blocks.attack.modified)
  malicious.blocks.sum.v[i] <- sum(malicious.blocks.attack.modified)
  # Take the sums. This is the total time it took each set of miners to find 10 blocks
  
}

mean(malicious.blocks.sum.v < honest.blocks.sum.v)
# 0.032736
##########################################################################################
# KEY RESULT:
# In 3.2736% of cases, the malicious miner finds 10 blocks before the honest miners finds 10 blocks
##########################################################################################


mean(honest.blocks.sum.v/current.target.block.time)
# 1.429406
# Mean time between blocks found by the honest miners is 1.429406 minutes
mean(malicious.blocks.sum.v/current.target.block.time)
# 3.334569
# Mean time between blocks found by the malicious miner is 3.334569 minutes