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September 2025

I Analyzed 6TB of Raw Stock Market Data to Uncover the 30 Most Consistently Traded Stocks — Here’s What I Found

What if you could replay the last 9 years of market activity — every quote, every trade — and figure out which stocks have never left the party?


Stock Selection Last Friday, a quiet challenge came up in a conversation. Someone with a sharp mathematical mind and a preference for staying behind the scenes posed a deceptively simple question: "Which stocks have been traded the most, consistently, from 2016 to today?" That one question sent me down a 27-hour rabbit hole…

We had the data: 6TB of IEX tick captures spanning 2'187 PCAP files and over 22'119 unique symbols. We had the tools: an HDF5-backed firehose built for high-frequency analytics in pure C++23.

What followed was a misadventure in semantics. I first averaged trade counts across all dates — a rookie mistake. Turns out, averaging doesn’t guarantee consistency — some stocks burn bright for a while, then disappear. That oversight cost me half a day of CPU time and a good chunk of humility. The fix? A better idea: walk backwards from today and look for the longest uninterrupted streak of trading activity for each stock. Luckily, the 12 hours spent building the index weren’t wasted — that heavy lifting could be recycled for the new logic. Implementation time? 30 minutes. Execution time? 5 seconds. Victory? Priceless.

Here’s what we found.


Step 1 — Convert PCAPs into Stats with IEX2H5

Before we can rank stocks, we need summary statistics from the raw IEX market data feeds. That’s where iex2h5 comes in — a high-performance HDF5-based data converter purpose-built for handling PCAP dumps from IEX.

To extract stats only (and skip writing any tick data), we use the --command none mode. We'll name the output file something meaningful like statistics.h5, and pass in a file glob — the glorious Unix-era invention (from B at Bell Labs) — pointing to our compressed dataset, e.g. /lake/iex/tops/*.pcap.gz.

Of course, we’re all lazy, so let’s use the short forms -c, -o, and let iex2h5 do its thing:

steven@saturn:~/shared-tmp$ iex2h5 -c none -o statistics.h5 /lake/iex/tops/*.pcap.gz
[iex2h5] Converting 2194 files using backend: hdf5  using 1 thread  © Varga Consulting, 2017–2025
[iex2h5] Visit https://vargaconsulting.github.io/iex2h5/  Star it, Share it, Support Open Tools ⭐️
 2016-12-13 14:30:00 21:00:00  2016-12-14 14:30:00 21:00:00  2016-12-15 17:31:52 21:00:00 [...]
 2025-08-22 14:30:00 21:00:00  2025-08-25 14:30:00 21:00:00  2025-08-26 14:30:00 21:00:00 benchmark: 259159357724 events in 44087097ms  5.9Mticks/s, 0.170000µs/tick latency, 5758.33 GiB input converted into 733.97 MiB output
[iex2h5] Conversion complete  all files processed successfully 
[iex2h5] Market data © IEX  Investors Exchange. Attribution required. See https://iextrading.com

What you get is a compact HDF5 file containing:

  • /instruments → all unique stock symbols (22,119)
  • /trading_days → the full trading calendar (2,187 days)
  • /stats → per-symbol statistics across all days (e.g. trade volume, trade count, first/last seen)

On the performance side:

  • Raw storage throughput (ZFS): ~254 MB/s
  • End-to-end pipeline throughput: 5.76 TB of compressed PCAP input in 44,087 s → ~130 MB/s effective
  • Event rate: ~5.9 million ticks/sec sustained

From here you’re ready to rank, filter, and extract the top performers. The best part? A full 6 TB dataset was processed in ~12 hours — on a single desktop workstation, using a single-threaded execution model. No cluster, no parallel jobs.

These results form a solid baseline: the upcoming commercial version will extend the engine to a multi-process, multi-threaded execution model, scaling performance well beyond what a single core can deliver.

Step 2 — digest the statistics
Top-K Trade Streak Filter for Julia
using HDF5

base = homedir() * "/scratch"
input_file, output_file = base * "/index.h5", base * "/top30.h5"
cutoff_limit, lower_bound = 30, 50_000

fd = h5open(input_file, "r";  swmr=true)
function trailing_streak(x::AbstractVector{<:Real}, min::Real)
    count = 0
    for val in Iterators.reverse(x)
        val > min ? (count += 1) : break
    end
    return count
end

dates = String.(read(fd["/trading_days.txt"]))
instruments = String.(read(fd["/instruments.txt"]))

D, I = length(dates), length(instruments)
A = zeros(Float64, D, I)

for (day, date) in enumerate(dates)
    path = "/stats/$date/trade_size"
    if haskey(fd, path)
        count = vec(read(fd[path]))
        A[day, 1:length(count)] .= count
    end
end

# Step 2: Compute trailing streak length for each instrument
streak_lengths = [trailing_streak(A[:,i], lower_bound) for i in 1:I]

# Step 3: Rank instruments by streak length
order = sortperm(streak_lengths, rev=true)
selection = order[1:cutoff_limit]
h5_instruments = instruments[selection]
h5_trading_days = dates[end - minimum(streak_lengths[selection]) + 1:end]

# Step 4: Write result
h5open(output_file, "w") do fd
    write(fd, "/instruments.txt", h5_instruments)
    write(fd, "/trading_days.txt", h5_trading_days)
end
Top-K Trade Streak Filter for Python
#!/usr/bin/env python3
import numpy as np
import h5py
from pathlib import Path

base = Path.home() / "scratch"
input_file  = base / "index.h5"
output_file = base / "top30.h5"
cutoff_limit, lower_bound = 30, 50_000

fd = h5py.File(input_file, "r", swmr=True)
def trailing_streak(x: np.ndarray, min_val: float) -> int:
    cnt = 0
    for v in x[::-1]:
        if v > min_val:
            cnt += 1
        else:
            break
    return cnt

dates = fd["/trading_days.txt"][:].astype(str)
instruments = fd["/instruments.txt"][:].astype(str)

D, I = len(dates), len(instruments)
A = np.zeros((D, I), dtype=np.float64)

for day, date in enumerate(dates):
    path = f"/stats/{date}/trade_size"
    if path in fd:
        count = np.asarray(fd[path][()]).ravel()
        n = min(I, count.size)
        A[day, :n] = count[:n]

# Step 2: Compute trailing streak length for each instrument
streak_lengths = np.array([trailing_streak(A[:, i], lower_bound) for i in range(A.shape[1])])

# Step 3: Rank instruments by streak length
# DO NOT USE: it is not a stable sort, will diverge from julia implementation
#     order = np.argsort(-streak_lengths) 
order = np.lexsort((np.arange(len(streak_lengths)), -streak_lengths))

selection = order[:cutoff_limit]
h5_instruments = instruments[selection]
h5_trading_days = dates[-streak_lengths[selection].min():]

# Step 4: write result
str_dtype = h5py.string_dtype(encoding="utf-8")
with h5py.File(output_file, "w") as fd_out:
    fd_out.create_dataset("/instruments.txt", data=h5_instruments.astype(object), dtype=str_dtype)
    fd_out.create_dataset("/trading_days.txt", data=h5_trading_days.astype(object), dtype=str_dtype)
HDF5 data dump h5dump topk.h5
HDF5 "top30.h5" {
GROUP "/" {
   DATASET "instruments.txt" {
      DATATYPE  H5T_STRING {
         STRSIZE H5T_VARIABLE;
         STRPAD H5T_STR_NULLTERM;
         CSET H5T_CSET_UTF8;
         CTYPE H5T_C_S1;
      }
      DATASPACE  SIMPLE { ( 30 ) / ( 30 ) }
      DATA {
      (0): "EEM", "AAL", "HBAN", "TLT", "SQQQ", "CMCSA", "QQQ", "EWZ", "SPY",
      (9): "XLP", "CCL", "TSLA", "PLUG", "AMD", "NVDA", "XLF", "MU", "HYG",
      (18): "CSCO", "XLE", "IWM", "AAPL", "EFA", "TSM", "PCG", "INTC",
      (26): "VALE", "LQD", "FXI", "PBR"
      }
   }
   DATASET "trading_days.txt" {
      DATATYPE  H5T_STRING {
         STRSIZE H5T_VARIABLE;
         STRPAD H5T_STR_NULLTERM;
         CSET H5T_CSET_UTF8;
         CTYPE H5T_C_S1;
      }
      DATASPACE  SIMPLE { ( 980 ) / ( 980 ) }
      DATA {
      (0): "2021-09-13", "2021-09-14", "2021-09-15", "2021-09-16",
      (4): "2021-09-17", "2021-09-20", "2021-09-21", "2021-09-22",
      (972): "2025-08-15", "2025-08-18", "2025-08-19", "2025-08-20",
      (976): "2025-08-21", "2025-08-22", "2025-08-25", "2025-08-26"
      }
   }
}
}
Julia Plot
using Printf, Format
import GRUtils: oplot, plot, legend, xlabel, ylabel, title, savefig

colorscheme("solarized light")

thresholds = [20_000, 30_000, 40_000, 50_000, 60_000, 80_000, 100_000]
cutoff_limit,max = 30, 100

compute_streaks(A, min_val) = [trailing_streak(A[:, i], min_val) for i in 1:size(A, 2)]
sorted_streaks_per_threshold = Dict()
for t in thresholds
    streaks = compute_streaks(A, t)
    sorted_streaks_per_threshold[t] = sort(streaks, rev = true)[1:max]
end
plot([cutoff_limit, cutoff_limit], [0, 1000], "-r";
    linewidth=4, linestyle=:dash, xlim=(0, max), xticks=(10, 3), label=" 30")

for t in thresholds[1:end]
    oplot(1:length(sorted_streaks_per_threshold[t]),
          sorted_streaks_per_threshold[t]; label = format("{:>8}",format(t, commas=true)), lw = 2)
end

legend("")
xlabel("Top-N Instruments")
ylabel("Trailing Days Over Threshold")
title("Trailing Active Streaks by Trade Threshold")
Step 3 — Reprocess the Tick Data for the Top 30 Stocks

Now that we’ve identified the most consistently active stocks, it’s time to zoom in and reprocess just the relevant PCAP files. If you already have tick-level HDF5 output, you’re set. But if not, here's a neat trick: use good old Unix GLOB patterns to cherry-pick just the days you need — no need to touch all 6TB again.

For example, let’s reconstruct a trading window around September 2021:

iex2h5 -c irts -o top30.h5 /lake/iex/tops/TOPS-2021-09-1{3,4,5,6,7,8,9}.pcap.gz  # fractional start
iex2h5 -c irts -o top30.h5 /lake/iex/tops/TOPS-2021-09-{2,3}?.pcap.gz            # rest of the month

And then stitch together additional months or years:

iex2h5 -c irts -o top30.h5 /lake/iex/tops/TOPS-2021-1{0,1,2}-??.pcap.gz
iex2h5 -c irts -o top30.h5 /lake/iex/tops/TOPS-202{2,3,4,5}-??-??.pcap.gz

These globs target specific slices of the timeline while keeping file-level parallelism open for future optimization. And of course, you can always batch them via xargs.

Top-K Trade Streak Filter for Julia
using HDF5

base = homedir() * "/scratch"
input_file, output_file = base * "/index.h5", base * "/top30.h5"
cutoff_limit, lower_bound = 30, 50_000

fd = h5open(input_file, "r";  swmr=true)
function trailing_streak(x::AbstractVector{<:Real}, min::Real)
    count = 0
    for val in Iterators.reverse(x)
        val > min ? (count += 1) : break
    end
    return count
end

dates = String.(read(fd["/trading_days.txt"]))
instruments = String.(read(fd["/instruments.txt"]))

D, I = length(dates), length(instruments)
A = zeros(Float64, D, I)

for (day, date) in enumerate(dates)
    path = "/stats/$date/trade_size"
    if haskey(fd, path)
        count = vec(read(fd[path]))
        A[day, 1:length(count)] .= count
    end
end

# Step 2: Compute trailing streak length for each instrument
streak_lengths = [trailing_streak(A[:,i], lower_bound) for i in 1:I]

# Step 3: Rank instruments by streak length
order = sortperm(streak_lengths, rev=true)
selection = order[1:cutoff_limit]
h5_instruments = instruments[selection]
h5_trading_days = dates[end - minimum(streak_lengths[selection]) + 1:end]

# Step 4: Write result
h5open(output_file, "w") do fd
    write(fd, "/instruments.txt", h5_instruments)
    write(fd, "/trading_days.txt", h5_trading_days)
end
System Specs — Single Desktop Workstation (ZFS-backed)

This entire pipeline was executed on a single desktop workstation — no cluster, no GPU, no cloud — just efficient C++ and smart data layout:

  • CPU: Intel Core i7‑11700K @ 3.60 GHz (8 cores / 16 threads)
  • RAM: 64 GiB DDR4
  • Scratch Disk: 3.6 TB NVMe SSD (/mnt)
  • Main Archive: 15 TB ZFS pool (/lake), spanned 2× 8 TB HDDs
    • Pool name: lake, Dataset: lake/stock, Compression: off (default), Recordsize: 128K (default), Deduplication: off
  • 🐧 OS: Ubuntu 22.04 LTS
Read performance of ZFS based Lake 254MB/s sustained
steven@saturn:~$ sudo fio --name=zfs_seq_read_real --filename=/lake/fio-read-test.bin
    --rw=read --bs=1M --size=100G --numjobs=1 --ioengine=psync --direct=1 --group_reporting

zfs_seq_read_real: (g=0): rw=read, bs=(R) 1024KiB-1024KiB, (W) 1024KiB-1024KiB, (T) 1024KiB-1024KiB, ioengine=psync, iodepth=1
fio-3.28
Starting 1 process
zfs_seq_read_real: Laying out IO file (1 file / 102400MiB)
Jobs: 1 (f=1): [R(1)][100.0%][r=180MiB/s][r=180 IOPS][eta 00m:00s]
zfs_seq_read_real: (groupid=0, jobs=1): err= 0: pid=2897558: Sat Aug 30 16:40:16 2025
read: IOPS=242, BW=243MiB/s (254MB/s)(100GiB/422156msec)
    clat (usec): min=103, max=326105, avg=4118.30, stdev=8610.69
    lat (usec): min=104, max=326105, avg=4118.72, stdev=8610.67
    clat percentiles (usec):
    |  1.00th=[   208],  5.00th=[   229], 10.00th=[   277], 20.00th=[   824],
    | 30.00th=[   865], 40.00th=[   914], 50.00th=[  4146], 60.00th=[  4817],
    | 70.00th=[  5276], 80.00th=[  5800], 90.00th=[  6587], 95.00th=[  7767],
    | 99.00th=[ 33817], 99.50th=[ 61080], 99.90th=[102237], 99.95th=[139461],
    | 99.99th=[299893]
bw (  KiB/s): min=16384, max=395264, per=100.00%, avg=248505.24, stdev=59429.03, samples=843
iops        : min=   16, max=  386, avg=242.68, stdev=58.04, samples=843
lat (usec)   : 250=8.07%, 500=4.03%, 750=2.97%, 1000=28.82%
lat (msec)   : 2=1.16%, 4=3.06%, 10=49.77%, 20=0.87%, 50=0.56%
lat (msec)   : 100=0.60%, 250=0.08%, 500=0.03%
cpu          : usr=0.21%, sys=15.68%, ctx=58582, majf=0, minf=270
IO depths    : 1=100.0%, 2=0.0%, 4=0.0%, 8=0.0%, 16=0.0%, 32=0.0%, >=64=0.0%
    submit    : 0=0.0%, 4=100.0%, 8=0.0%, 16=0.0%, 32=0.0%, 64=0.0%, >=64=0.0%
    complete  : 0=0.0%, 4=100.0%, 8=0.0%, 16=0.0%, 32=0.0%, 64=0.0%, >=64=0.0%
    issued rwts: total=102400,0,0,0 short=0,0,0,0 dropped=0,0,0,0
    latency   : target=0, window=0, percentile=100.00%, depth=1

Run status group 0 (all jobs):
READ: bw=243MiB/s (254MB/s), 243MiB/s-243MiB/s (254MB/s-254MB/s), io=100GiB (107GB), run=422156-422156msec 
Read performance of NVME scratch disk 4GB/s sustained
steven@saturn:~$ sudo fio --name=nvme_seq_read_real --filename=/home/steven/scratch/fio-read-test.bin
    --rw=read --bs=1M --size=100G --numjobs=1 --ioengine=psync --direct=1 --group_reporting
nvme_seq_read_real: (g=0): rw=read, bs=(R) 1024KiB-1024KiB, (W) 1024KiB-1024KiB, (T) 1024KiB-1024KiB, ioengine=psync, iodepth=1
fio-3.28
Starting 1 process
nvme_seq_read_real: Laying out IO file (1 file / 102400MiB)
Jobs: 1 (f=1): [R(1)][100.0%][r=3203MiB/s][r=3203 IOPS][eta 00m:00s]
nvme_seq_read_real: (groupid=0, jobs=1): err= 0: pid=3047825: Sat Aug 30 18:28:21 2025
read: IOPS=3847, BW=3848MiB/s (4035MB/s)(100GiB/26613msec)
    clat (usec): min=180, max=3871, avg=259.65, stdev=79.55
    lat (usec): min=180, max=3871, avg=259.68, stdev=79.56
    clat percentiles (usec):
    |  1.00th=[  198],  5.00th=[  200], 10.00th=[  202], 20.00th=[  202],
    | 30.00th=[  202], 40.00th=[  204], 50.00th=[  206], 60.00th=[  237],
    | 70.00th=[  310], 80.00th=[  318], 90.00th=[  371], 95.00th=[  400],
    | 99.00th=[  502], 99.50th=[  529], 99.90th=[  660], 99.95th=[  676],
    | 99.99th=[ 1106]
bw (  MiB/s): min= 2774, max= 4912, per=100.00%, avg=3852.79, stdev=798.23, samples=53
iops        : min= 2774, max= 4912, avg=3852.79, stdev=798.23, samples=53
lat (usec)   : 250=60.44%, 500=38.55%, 750=0.99%, 1000=0.01%
lat (msec)   : 2=0.01%, 4=0.01%
cpu          : usr=0.09%, sys=8.43%, ctx=102484, majf=0, minf=267
IO depths    : 1=100.0%, 2=0.0%, 4=0.0%, 8=0.0%, 16=0.0%, 32=0.0%, >=64=0.0%
    submit    : 0=0.0%, 4=100.0%, 8=0.0%, 16=0.0%, 32=0.0%, 64=0.0%, >=64=0.0%
    complete  : 0=0.0%, 4=100.0%, 8=0.0%, 16=0.0%, 32=0.0%, 64=0.0%, >=64=0.0%
    issued rwts: total=102400,0,0,0 short=0,0,0,0 dropped=0,0,0,0
    latency   : target=0, window=0, percentile=100.00%, depth=1

Run status group 0 (all jobs):
READ: bw=3848MiB/s (4035MB/s), 3848MiB/s-3848MiB/s (4035MB/s-4035MB/s), io=100GiB (107GB), run=26613-26613msec

Disk stats (read/write):
nvme0n1: ios=220152/422, merge=0/15, ticks=44398/64, in_queue=44537, util=99.70     
Write performance of NVME scratch disk 2GB/s sustained
steven@saturn:~$ sudo fio --name=nvme_seq_write_real --filename=/home/steven/scratch/fio-write-test.bin
    --rw=write --bs=1M --size=100G --numjobs=1 --ioengine=psync --direct=1 --group_reporting

nvme_seq_write_real: (g=0): rw=write, bs=(R) 1024KiB-1024KiB, (W) 1024KiB-1024KiB, (T) 1024KiB-1024KiB, ioengine=psync, iodepth=1
fio-3.28
Starting 1 process
nvme_seq_write_real: Laying out IO file (1 file / 102400MiB)
Jobs: 1 (f=1): [W(1)][100.0%][w=1410MiB/s][w=1410 IOPS][eta 00m:00s]
nvme_seq_write_real: (groupid=0, jobs=1): err= 0: pid=3048070: Sat Aug 30 18:44:43 2025
write: IOPS=1989, BW=1990MiB/s (2087MB/s)(100GiB/51460msec); 0 zone resets
    clat (usec): min=211, max=232270, avg=462.02, stdev=3175.40
    lat (usec): min=232, max=232302, avg=502.00, stdev=3176.05
    clat percentiles (usec):
    |  1.00th=[   217],  5.00th=[   221], 10.00th=[   225], 20.00th=[   227],
    | 30.00th=[   229], 40.00th=[   233], 50.00th=[   241], 60.00th=[   281],
    | 70.00th=[   318], 80.00th=[   375], 90.00th=[   529], 95.00th=[   693],
    | 99.00th=[  1762], 99.50th=[  4883], 99.90th=[ 27132], 99.95th=[ 50070],
    | 99.99th=[149947]
bw (  MiB/s): min=  534, max= 3574, per=100.00%, avg=1997.23, stdev=784.43, samples=102
iops        : min=  534, max= 3574, avg=1997.15, stdev=784.48, samples=102
lat (usec)   : 250=52.21%, 500=36.83%, 750=6.89%, 1000=1.85%
lat (msec)   : 2=1.34%, 4=0.31%, 10=0.22%, 20=0.14%, 50=0.17%
lat (msec)   : 100=0.02%, 250=0.03%
cpu          : usr=8.02%, sys=23.04%, ctx=102593, majf=0, minf=14
IO depths    : 1=100.0%, 2=0.0%, 4=0.0%, 8=0.0%, 16=0.0%, 32=0.0%, >=64=0.0%
    submit    : 0=0.0%, 4=100.0%, 8=0.0%, 16=0.0%, 32=0.0%, 64=0.0%, >=64=0.0%
    complete  : 0=0.0%, 4=100.0%, 8=0.0%, 16=0.0%, 32=0.0%, 64=0.0%, >=64=0.0%
    issued rwts: total=0,102400,0,0 short=0,0,0,0 dropped=0,0,0,0
    latency   : target=0, window=0, percentile=100.00%, depth=1

Run status group 0 (all jobs):
WRITE: bw=1990MiB/s (2087MB/s), 1990MiB/s-1990MiB/s (2087MB/s-2087MB/s), io=100GiB (107GB), run=51460-51460msec

Disk stats (read/write):
nvme0n1: ios=6052/319248, merge=0/35, ticks=4761/121381, in_queue=138161, util=95.95%

Lessons from the Data Trenches

Stock Selection As this series of experiments suggests, there’s more to large-scale market data processing than meets the eye. It’s tempting to think of backtesting as a clean, deterministic pipeline — but in practice, the data fights back. You’ll encounter missing or corrupted captures, incomplete trading days, symbols that appear midstream, and others that vanish without warning. Stocks get halted, merged, delisted, or IPO mid-cycle — all of which silently affect continuity, volume, and strategy logic. Even more subtly, corporate actions like stock splits can distort price series unless explicitly accounted for. For example, Nvidia’s 10-for-1 stock split on June 7, 2024, caused a sudden drop in share price purely due to adjustment — not market dynamics. Without proper normalization, strategies can misinterpret these events as volatility or crashes. Even a simple idea like “find the most consistently traded stocks” turns out to depend on how you define consistency, and how well you understand the structure of your own dataset.

Radix64 Encoding: Order-Preserving Strings in 64 Bits

Problem: Compact, Order-Preserving Identifiers for Short Symbols

In domains like high-frequency trading, structured storage, or financial indexing, identifiers such as stock symbols (e.g., "AAPL", "GOOG", "TSLA") are:

  • Short — typically ≤ 8 characters
  • Drawn from a small alphabet — ~32 to 40 printable characters
  • Compared lexicographically — e.g., "ABC" < "XYZ" must hold

These structural constraints can be exploited to encode each symbol into a compact, fixed-width binary key while preserving their natural sort order.

Specifically, such systems often need:

  • Lexicographic ordering — to maintain sorted maps, symbol trees, or search indices
  • Fixed-size keys — for CPU- and cache-friendly performance
  • Support for variable-length symbols — without breaking ordering
  • Ability to pack extra metadata — like 16-bit contract IDs or timestamps

But typical representations fall short:

  • std::string / char[] are variable-length and inefficient as keys
  • strcmp is slow, branching, and non-SIMD friendly
  • Standard Base64 isn't order-preserving
  • Hashes destroy ordering and increase collision risk

Radix64 encoding solves this by leveraging the symbol structure — short, constrained, ordered strings — to pack lex-order-preserving representations into just 64 bits.

Solution: Order-Preserving Radix64 Encoding

Radix64 solves this by:

  • Encoding up to 8 characters as a 48-bit big-endian base-64 integer
  • Padding shorter strings with the lowest code to preserve prefix order
  • Optionally combining a 16-bit integer (e.g., contract ID) in the LSBs
  • Making unsigned integer comparison exactly match lexicographic order

So you can now represent things like:

"AAPL"    → 48-bit radix64 prefix
contract  → 16-bit index
key       → 64-bit sortable, compact ID

Used as keys in:

  • Fast symbol lookup tables
  • Order books and trading systems
  • Encoded identifiers for datasets or HDF5 groups
  • Key-value stores, B-trees, or radix trees

Read the full radix64 guide

From Curve to Signature: A Hands-on Guide to ECDSA

ECDSA operates on elliptic curve groups over finite fields.
In the most common form, the curve is defined by the Weierstrass equation:\(E(\mathbb{F}_p):\; y^2 \equiv x^3 + ax + b \pmod p,\) where \(a, b\) are curve parameters and \(p\) is a prime defining the field \(\mathbb{F}_p\). In production systems, the curve is fixed by cryptographers — for example, secp256k1 in Ethereum — but nothing prevents you from experimenting with your own, especially for learning, prototyping, or testing with small primes.

Generate a toy Weierstrass curve

This example searches for a curve over primes \(\pi \in (97,103)\), with parameters \(a \in (10,15)\), \(b \in (2,7)\). It selects the first candidate that is non-singular, whose group of points has prime order, and that admits a generator spanning the group.

using TinyCrypto

curve = Weierstrass(97:103, 10:15, 2:7)
Weierstrass{𝔽₉₇}:  =  + 10x + 3 | 𝔾(0,10), q = 101, h = 1, #E = 101
Here, \(q\) is the order of the generator \(\mathbb{G} (0𝔽₉₇,10𝔽₉₇)\), \(h\) the cofactor, and \(\#E = q \cdot h\) the total number of points on the curve.

Sign a Message (ECDSA)
priv, pub = genkey(curve)             # Generate private/public key pair
msg = "hello ethereum"                # The message to sign
signature = sign(curve, priv, msg)    # → (r, s, v)

The result is a NamedTuple:

(r = ..., s = ..., v = ...)

Here, \((r,s)\) are the ECDSA signature scalars, and \(v\) is the recovery identifier — letting you reconstruct the signer’s public key from the signature and message alone. This is exactly how Ethereum transactions prove authenticity without revealing the private key.

Verify the Signature
is_valid = verify(curve, pub, signature, msg)
@assert is_valid

Verification checks that the signature \((r,s)\) was produced with the private key corresponding to the public key pub, on the exact message msg. If the check passes, you know the message is authentic and unaltered — the essence of digital signatures in action.

Recover the Public Key (like Ethereum)
recovered = ecrecover(curve, msg, signature)
@assert pub == recovered

ECDSA with recovery adds a small extra bit \(v\) to the signature, making it possible to reconstruct the signer’s public key directly from (msg, signature). This is how Ethereum avoids shipping full public keys inside every transaction: the network can derive them on the fly, saving space while still proving who signed what.

Summary

TinyCrypto.jl makes it easy to:

  • Define toy elliptic curves over small prime fields
  • Generate key pairs and sign messages with ECDSA
  • Verify signatures to ensure authenticity and integrity
  • Recover public keys from signatures (à la Ethereum)

Perfect for learning, prototyping, or experimenting with elliptic curve cryptography — without the overhead of production-grade libraries.

🔗 Source code on GitHub