Monero adversarial spammer privacy impact

adversary-controlled-decoys-DSA.R

# When current.height = 3100144,
# start.spam.height = 3097308, and
# spam.share <- 0.75
# 59% of the probability mass function of the DSA are outputs created by the suspected spammer

# Formula for the exact Monero Decoy Selection Algorithm (DSA) probability mass function is based on:
# jeffro256 (2023) "Implementing Monero Decoy Selection"
# https://github.com/jeffro256/monero/blob/decoy_selection_md/docs/DECOY_SELECTION.md
# and
# Rucknium (2023) "Closed-form expression of the wallet2 Decoy Selection Algorithm"
# https://www.overleaf.com/read/ndbtkwrbrdjq

# Must be able to connect to a monero node. Specify URL below.

# Must install these R packages:
install.packages(c("RJSONIO", "RCurl", "actuar"))

# These variables can be edited:

# Input the node's URL here. This should be correct for
# a local node using standard ports:'
url.rpc <- "http://127.0.0.1:18081/json_rpc"

current.height <- 3100144 # About 22:00 UTC March 7, 2024
start.spam.height <- 3097308 # First block of March 4, 2024 UTC
spam.share <- 0.75





calculate_average_output_flow <- function(crod) {
    # 1
    num_blocks_to_consider_for_flow = min(c(length(crod), BLOCKS_IN_A_YEAR))

    # 2
    if (length(crod) > num_blocks_to_consider_for_flow) {
        num_outputs_to_consider_for_flow = crod[length(crod)] - crod[ length(crod) - num_blocks_to_consider_for_flow ]
        # R indexes from 1
    } else {
        num_outputs_to_consider_for_flow = crod[length(crod)] # R indexes from 1
    }

    # 3
    average_output_flow = DIFFICULTY_TARGET_V2 * num_blocks_to_consider_for_flow / num_outputs_to_consider_for_flow

    return(average_output_flow)
}

calculate_num_usable_rct_outputs <- function(crod) {
    # 1
    num_usable_crod_blocks = length(crod) - (CRYPTONOTE_DEFAULT_TX_SPENDABLE_AGE - 1)

    # 2
    num_usable_rct_outputs = crod[num_usable_crod_blocks] # R indexes from 1

    return(num_usable_rct_outputs)
}




# Modified from TownforgeR::tf_rpc_curl function
xmr.rpc <- function(
    url.rpc = "http://127.0.0.1:18081/json_rpc",
  method = "",
  params = list(),
  userpwd = "",
  num.as.string = FALSE,
  nonce.as.string = FALSE,
  keep.trying.rpc = FALSE,
  curl = RCurl::getCurlHandle(),
  ...
){

  json.ret <- RJSONIO::toJSON(
    list(
      jsonrpc = "2.0",
      id = "0",
      method = method,
      params = params
    ), digits = 50
  )

  rcp.ret <- 	tryCatch(RCurl::postForm(url.rpc,
    .opts = list(
      userpwd = userpwd,
      postfields = json.ret,
      httpheader = c('Content-Type' = 'application/json', Accept = 'application/json')
      # https://stackoverflow.com/questions/19267261/timeout-while-reading-csv-file-from-url-in-r
    ),
    curl = curl
  ), error = function(e) {NULL})

  if (keep.trying.rpc && length(rcp.ret) == 0) {
    while (length(rcp.ret) == 0) {
      rcp.ret <- 	tryCatch(RCurl::postForm(url.rpc,
        .opts = list(
          userpwd = userpwd,
          postfields = json.ret,
          httpheader = c('Content-Type' = 'application/json', Accept = 'application/json')
          # https://stackoverflow.com/questions/19267261/timeout-while-reading-csv-file-from-url-in-r
        ),
        curl = curl
      ), error = function(e) {NULL})
    }
  }

  if (is.null(rcp.ret)) {
    stop("Cannot connect to monerod. Is monerod running?")
  }

  if (num.as.string) {
    rcp.ret <- gsub("(: )([-0123456789.]+)([,\n\r])", "\\1\"\\2\"\\3", rcp.ret )
  }

  if (nonce.as.string & ! num.as.string) {
    rcp.ret <- gsub("(\"nonce\": )([-0123456789.]+)([,\n\r])", "\\1\"\\2\"\\3", rcp.ret )
  }

  RJSONIO::fromJSON(rcp.ret, asText = TRUE) # , simplify = FALSE
}


CRYPTONOTE_DEFAULT_TX_SPENDABLE_AGE = 10
DIFFICULTY_TARGET_V2 = 120
DEFAULT_UNLOCK_TIME = CRYPTONOTE_DEFAULT_TX_SPENDABLE_AGE * DIFFICULTY_TARGET_V2
RECENT_SPEND_WINDOW = 15 * DIFFICULTY_TARGET_V2

SECONDS_IN_A_YEAR =  60 * 60 * 24 * 365
BLOCKS_IN_A_YEAR = SECONDS_IN_A_YEAR / DIFFICULTY_TARGET_V2



crod <- xmr.rpc(url.rpc = url.rpc, method = "get_output_distribution",
  params = list(amounts = list(0), from_height = 0, to_height = current.height, binary = FALSE, cumulative = TRUE))

crod <- crod$result$distributions[[1]]$distribution

average_output_flow <- calculate_average_output_flow(crod)

num_usable_rct_outputs <- calculate_num_usable_rct_outputs(crod)


GAMMA_SHAPE = 19.28
GAMMA_RATE = 1.61
# GAMMA_SCALE = 1 / GAMMA_RATE





G <- function(x) {
  actuar::plgamma(x, shapelog = GAMMA_SHAPE, ratelog = GAMMA_RATE)
}



G_star <- function(x) {
  (0 <= x*v & x*v <= 1800) *
  (G(x*v + 1200) - G(1200) +
     ( (x*v)/(1800) ) * G(1200)
  )/G(z*v + 1200) +
    (x*v > 1800) * G(x*v + 1200)/G(z*v + 1200)
}



v <- average_output_flow
z <- num_usable_rct_outputs

usable.outputs <- 1:num_usable_rct_outputs

crod.reversed <- cumsum(abs(diff(rev(crod)))[-(1:9)])
# Remove first 9 blocks before cumsum() since cant spend from those outputs

crod.reversed <- c(0, crod.reversed)

y_0 <- crod.reversed[-length(crod.reversed)] + 1
y_1 <- crod.reversed[-1]
pmf.decoy.crod <- (G_star(y_1 + 1) - G_star(y_0)) / (y_1 + 1 - y_0)


pmf.decoy <- rep(pmf.decoy.crod, times = diff(crod.reversed))


start.spam.relative.output.index <- crod.reversed[ (current.height - 9) - start.spam.height]

# Final result
sum(spam.share * pmf.decoy[1:start.spam.relative.output.index] )