research/whisper_scalability/whisper.py

# Util and format functions
#-----------------------------------------------------------

class bcolors:
    HEADER = '\033[95m'
    OKBLUE = '\033[94m'
    OKGREEN = '\033[92m'
    WARNING = '\033[93m'
    FAIL = '\033[91m'
    ENDC = '\033[0m'
    BOLD = '\033[1m'
    UNDERLINE = '\033[4m'

# https://web.archive.org/web/20111010015624/http://blogmag.net/blog/read/38/Print_human_readable_file_size
# TODO: Get rid of bytes and KB, always print as as MB and above, then %3.1f
def sizeof_fmt(num):
    for x in ['bytes','KB','MB','GB','TB']:
        if num < 1024.0:
            return "%6.1f%s" % (num, x)
        num /= 1024.0

def magnitude_fmt(num):
    for x in ['','k','m']:
        if num < 1000:
            return "%2d%s" % (num, x)
        num /= 1000

# Color format based on daily bandwidth usage
# <10mb/d = good, <30mb/d ok, <100mb/d bad, 100mb/d+ fail.
def load_color_prefix(load):
    if load < (1024 * 1000 * 10):
        color_level = bcolors.OKBLUE
    elif load < (1024 * 1000 * 30):
        color_level = bcolors.OKGREEN
    elif load < (1024 * 1000 * 100):
        color_level = bcolors.WARNING
    else:
        color_level = bcolors.FAIL
    return color_level

def load_color_fmt(load, string):
    return load_color_prefix(load) + string + bcolors.ENDC

def print_header(string):
    print bcolors.HEADER + string + bcolors.ENDC + "\n"

def print_assumptions(xs):
    print "Assumptions:"
    for x in xs:
        print x
    print ""

def usage_str(load_users_fn, n_users):
    load = load_users_fn(n_users)
    return load_color_fmt(load, "For " + magnitude_fmt(n_users) + " users, receiving bandwidth is " + sizeof_fmt(load_users_fn(n_users)) + "/day")

def print_usage(load_users):
    print usage_str(load_users, 100)
    print usage_str(load_users, 100 * 100)
    print usage_str(load_users, 100 * 100 * 100)
    print ""

# Assumptions
#-----------------------------------------------------------

# We assume a node is not relaying messages, but only sending
#
# Goal:
# - make it user-bound, not network-bound
# - reasonable bw and fetch time
# ~1GB per month, ~ 30 mb per day, ~1 mb per hour

envelope_size = 1024 # 1kb

# Due to negotiation, data sync, etc
# Rough assumed overhead, constant factor
envelopes_per_message = 10

received_messages_per_day = 100

# Assume half of all messages are in 1:1 and group chat
# XXX: Implicitly assume message/envelope ratio same for 1:1 and public,
# probably not true due to things like key negotiation and data sync
private_message_proportion = 0.5

# Number of partitions for partition topic
n_partitions = 5000

# On Bloom filter, false positive rate:
#
# Bloom logic
# f: in_set?(s, x) => (maybe, no)
# if false_positive high => lots of maybe => direct hits
# test happens at routing node and depends on what filter preference peer has,
# OR what request mailserver receives
#
bloom_size = 512     # size of filter, m
bloom_hash_fns = 3   # number of hash functions, k
bloom_elements = 100 # elements in set, n
# assuming optimal number of hash functions, i.e. k=(m/n)ln 2
# (512/100)*math.log(2) ~ 3.46
# Note that this is very sensitive, so if 200 element you want 1 hash fn, and
# if 50 topics you want 7. Understanding the implications using a suboptimal
# number of hash function is left as an exercise to the reader.
#
# Implied false positive rate (https://hur.st/bloomfilter/?n=100&p=&m=512&k=3)
# p=~0.087, roughly.
bloom_false_positive = 0.1 # false positive rate, p
# Sensitivity to n:
# n=50 => p=1%, n=100 => p=10%, n=200 => 30%
#
# Note that false positivity has two faces, one is in terms of extra bandwidth usage
# The other is in terms of anonymity / plausible deniability for listening on topic
# I.e. N envelopes go to node => 1% false positive rate => 1% of N goes to recipient node
# Even if they only wanted 1 message!
#
# The false positive is a factor of total network traffic

# Assumption strings
a1 = "- A1. Envelope size (static): " + str(envelope_size) + "kb"
a2 = "- A2. Envelopes / message (static): " + str(envelopes_per_message)
a3 = "- A3. Received messages / day (static): " + str(received_messages_per_day)
a4 = "- A4. Only receiving messages meant for you"
a5 = "- A5. Received messages for everyone"
a6 = "- A6. Proportion of private messages (static): " + str(private_message_proportion)
a7 = "- A7. Public messages only received by relevant recipients (static)"
a8 = "- A8. All private messages are received by everyone (same topic) (static)"
a9 = "- A9. Private messages are partitioned evenly across partition shards (static), n=" + str(n_partitions)
a10 = "- A10. Bloom filter size (m) (static): " + str(bloom_size)
a11 = "- A11. Bloom filter hash functions (k) (static): " + str(bloom_hash_fns)
a12 = "- A12. Bloom filter elements, i.e. topics, (n) (static): " + str(bloom_elements)
a13 = "- A13. Bloom filter optimal k choice (sensitive to m, n)"
a14 = "- A14. Bloom filter false positive proportion of full traffic, p=" + str(bloom_false_positive)

# Cases
#-----------------------------------------------------------

# Case 1: only receiving messages meant for you
def case1():
    def load_users(n_users):
        return envelope_size * envelopes_per_message * \
            received_messages_per_day

    print_header("Case 1. Only receiving messages meant for you")
    print_assumptions([a1, a2, a3, a4])
    print_usage(load_users)
    print("------------------------------------------------------------")

# Case 2: receiving all messages
def case2():

    def load_users(n_users):
        return envelope_size * envelopes_per_message * \
            received_messages_per_day * n_users

    print_header("Case 2. Receiving messages for everyone")
    print_assumptions([a1, a2, a3, a5])
    print_usage(load_users)
    print("------------------------------------------------------------")

# Case 3: all private messages go over one discovery topic
def case3():

    # Public scales per usage, all private messages are received
    # over one discovery topic
    def load_users(n_users):
        load_private = envelope_size * envelopes_per_message * \
            received_messages_per_day * n_users
        load_public = envelope_size * envelopes_per_message * \
            received_messages_per_day
        total_load = load_private * private_message_proportion + \
            load_public * (1 - private_message_proportion)
        return total_load

    print_header("Case 3. All private messages go over one discovery topic")
    print_assumptions([a1, a2, a3, a6, a7, a8])
    print_usage(load_users)
    print("------------------------------------------------------------")

# Case 4: all private messages are partitioned into shards
def case4():

    def load_users(n_users):
        if n_users < n_partitions:
            # Assume spread out, not colliding
            factor_load = 1
        else:
            # Assume spread out evenly, collides proportional to users
            factor_load = n_users / n_partitions
        load_private = envelope_size * envelopes_per_message * \
            received_messages_per_day * factor_load
        load_public = envelope_size * envelopes_per_message * \
            received_messages_per_day
        total_load = load_private * private_message_proportion + \
            load_public * (1 - private_message_proportion)
        return total_load

    print_header("Case 4. All private messages are partitioned into shards")
    print_assumptions([a1, a2, a3, a6, a7, a9])
    print_usage(load_users)
    print("------------------------------------------------------------")

# Case 5: all messages are passed through a bloom filter with a certain false positive rate
def case5():

    def load_users(n_users):
        if n_users < n_partitions:
            # Assume spread out, not colliding
            factor_load = 1
        else:
            # Assume spread out evenly, collides proportional to users
            factor_load = n_users / n_partitions
        load_private = envelope_size * envelopes_per_message * \
            received_messages_per_day * factor_load
        load_public = envelope_size * envelopes_per_message * \
            received_messages_per_day
        total_load = load_private * private_message_proportion + \
            load_public * (1 - private_message_proportion)

        # false positive total network traffic, assuming full node relaying
        network_load = envelope_size * envelopes_per_message * \
            received_messages_per_day * n_users
        false_positive_load = network_load * bloom_false_positive

        return total_load + false_positive_load

    print_header("Case 5. Case 4 + All messages are passed through bloom filter with false positive rate")
    print_assumptions([a1, a2, a3, a6, a7, a9, a10, a11, a12, a13, a14])
    print_usage(load_users)
    print("------------------------------------------------------------")


# Run cases
#-----------------------------------------------------------
case1()
case2()
case3()
case4()
case5()

# Misc notes
#-----------------------------------------------------------

# What did I observe? I observed 15GB/m = 500mb per day.

# Things to encode:
# - Noisy topic
# - Duplicate messages
# - Bloom filter false positives
# - Bugs / invalid messages
# - Offline case dominant

# Now getting somewhere, still big discrepency though. I.e.
# Case 3. All private messages go over one discovery topic

# Assumptions:
# - A1. Envelope size (static): 1024kb
# - A2. Envelopes / message (static): 10
# - A3. Received messages / day (static): 100
# - A4. Proportion of private messages (static): 0.5
# - A5. All private messages are received by everyone (same topic) (static)
# - A6. Public messages only received by relevant recipients (static)

# For 100 users, receiving bandwidth is  49MB/day
# For 10k users, receiving bandwidth is   5GB/day
# For  1m users, receiving bandwidth is 477GB/day

# 50mb*30 = 1.5GB, I see 15GB so x10. What's missing?
# Heavy user, and duplicate messages (peers), Envelope size?
# Say * 4 (size) * 2 (duplicates) * 2 (usage) then it is within x8-16.
# Also missing bloom filter here

# I am also assuming we are roughly 100 users today, is this accurate?
# How many unique public keys have we seen in common chats the last month?

# TODO: It'd be neat if you could encode assumptions set

# Ok, problem. We know case 4 is inaccurate. Ish.
# Duplicate messages, bloom filter. Need to encode these.
# Also heavy usage etc.

# More factors:
# percentage_offline
# - impacts mailservers
# - and also data sync
# duplication_factor
# bad_envelopes

# Ask feedback:
# Which of these assumptions are false?
# Any assumptions or conditions not accurately captured?
# Which are most interesting to you?
# Which do we want to verify, and what metrics do we need to verify?

# If we x100 users tomorrow, how can we move the partition topic?
# Path we are on today, and alternative path

# Also not captured: fallover of relaying node, if it exceeds bandwidth link