The telegraph age¶

From the 1840s to 1920: messages that travel by wire and radio, the fall of the "indecipherable" cipher, Africa's talking drums, telegraph codes for Chinese and Japanese, Kerckhoffs's rules, the Okhrana's mail readers, a telegram that helped pull America into a world war, the first code talkers, and the one cipher that can't be broken.

The electric telegraph made it possible to send a message across a continent in minutes, but every message passed through the hands of clerks, and later radio put every military order into the air for anyone with an aerial. At the same time the most trusted cipher of the Renaissance, the keyword cipher wrongly named after Vigenère, was broken by two men who never met. The period ends with a discovery that no later invention has bettered: a cipher that is mathematically unbreakable, if you can live with its rules.

When	Who	What
1837–1844	Cooke and Wheatstone; Morse	electric telegraphs in Britain and the US
1845	Francis O. J. Smith	the first code book for telegraph messages
1843	Edgar Allan Poe	"The Gold-Bug" makes ciphers popular reading
1854	Charles Babbage	breaks the keyword cipher, but doesn't publish
1854	Charles Wheatstone	the Playfair cipher
1861–1865	US Civil War	the first war to lean heavily on telegraph ciphers
1800s–1900s (described)	Central and West Africa	drum and gong languages carry messages for miles
1869–1879	Japan	the telegraph arrives; government code charts, then a cipher wheel
1871–1872	Schjellerup, Viguier	the Chinese telegraph code: four digits per character
1881–1917	the Okhrana	black chambers in Russian post offices
1863	Friedrich Kasiski	publishes the general attack on keyword ciphers
1883	Auguste Kerckhoffs	La cryptographie militaire: only the key is secret
1882	Frank Miller	a one-time pad in a banker's telegraph code
1914	Russian army at Tannenberg	orders sent by radio in clear; a catastrophe
1914–1918	Room 40, London	reads German naval and diplomatic codes
1917	Nigel de Grey and William Montgomery	read the Zimmermann telegram
1917–1919	Gilbert Vernam, Joseph Mauborgne	the teleprinter cipher and the one-time tape
1918	Georges Painvin	breaks Germany's ADFGVX field cipher
1918	Choctaw soldiers, 142nd Infantry	the first code talkers

Wires change everything¶

Codes for a price per word¶

William Fothergill Cooke and Charles Wheatstone patented their electric telegraph in 1837, and their first commercial line, along the Great Western Railway out of London, went into service in 1839. Samuel Morse sent "What hath God wrought" from Washington to Baltimore in 1844. Within a decade, wires linked the big cities of Europe and North America; the first lasting transatlantic cable opened in 1866.

Two problems came with them. Telegrams were charged by the word, so businesses wanted to say more in fewer words. And every telegram was read by at least two clerks, one at each end, so anything private was exposed. The answer to both was the commercial code: a printed book that assigns a short code word to each common phrase. Francis O. J. Smith, Morse's business partner, published the first one for the telegraph in 1845. Hundreds followed. A single invented word like "BAFUZ" might stand for "we accept your offer at the price named, shipment to follow".

These codes kept out a curious clerk but not a determined rival: the books were on sale. Firms that wanted real secrecy bought private codes or added secret arithmetic to the code numbers. That combination, a code book plus encryption on top, became the standard military and diplomatic system of the next hundred years.

Ciphers as entertainment¶

In 1841 Edgar Allan Poe challenged readers of Graham's Magazine to send him substitution ciphers and claimed to solve almost all of them. In 1843 his story "The Gold-Bug", in which a cryptogram leads to buried treasure, explained frequency analysis to a mass audience. Many later cryptologists, including William Friedman, traced their interest back to it.

The keyword cipher falls¶

For three centuries the keyword cipher (see Bellaso and the keyword) had a reputation as le chiffre indéchiffrable. Its flat letter counts defeat simple frequency analysis. Its weakness is the repeating keyword: with a 5-letter key, letters 1, 6, 11, 16 and so on are all shifted by the same amount.

Babbage, 1854¶

Charles Babbage (1791–1871), the inventor of the Difference Engine and the Analytical Engine, was an enthusiastic codebreaker. In 1854 (some accounts say 1853) a Bristol dentist, John Hall Brock Thwaites, presented a "new" cipher in the Journal of the Society of Arts. Babbage pointed out that it was an old keyword cipher. Thwaites challenged him to find the keys he had used on a passage of Shakespeare's The Tempest, and Babbage found them: "two" and "combined". Popular accounts also tell of Babbage solving Tennyson's poem "The Vision of Sin" enciphered with the keyword EMILY; the details of both stories come from secondary retellings of his papers and differ between them.

He never published his method; it was found in his notebooks after his death. Ole Franksen suggested in 1985 that British intelligence kept it quiet during the Crimean War. That is a guess, and an equally likely explanation is that Babbage left many projects unfinished.

Kasiski, 1863¶

Friedrich Wilhelm Kasiski (1805–1881), a retired major of the Prussian infantry, published the same attack in a small book of 95 pages, Die Geheimschriften und die Dechiffrir-Kunst ("Secret Writing and the Art of Deciphering"), in 1863. It attracted little notice; Kasiski turned to archaeology. But it is the method that made the keyword cipher a solved problem.

The Kasiski examination has two steps:

Find the key length. When the same piece of plaintext, such as THE, happens to fall under the same part of the keyword twice, it produces the same ciphertext twice. The distance between the two copies is then a multiple of the key length. Collect the distances between repeated groups; the number that divides most of them is the key length.
Split and solve. Once you know the key is 5 letters, take every fifth letter starting at the first. All of those were shifted by the same key letter, so that column is just a Caesar cipher, and frequency analysis solves it. Do the same for the other four columns.

Trying it¶

The keyword here is EMILY, from the Tennyson story. The program doesn't know it: it finds the key length from the repeats, then picks for each column the shift whose letter counts best match English.

from collections import Counter

A = "ABCDEFGHIJKLMNOPQRSTUVWXYZ"
# How often each letter appears in English, per 1,000 letters
EN = [82, 15, 28, 43, 127, 22, 20, 61, 70, 2, 8, 40, 24,
      67, 75, 19, 1, 60, 63, 91, 28, 10, 24, 2, 20, 1]

def vigenere(text, key, sign=1):
    return "".join(A[(A.index(c) + sign * A.index(key[i % len(key)])) % 26]
                   for i, c in enumerate(text))

plain = ("THE TELEGRAPH CARRIED THE NEWS OF THE WAR FASTER THAN ANY RIDER "
         "COULD AND THE GENERALS SOON LEARNED THAT THE ENEMY COULD READ "
         "THE WIRES AS EASILY AS THEIR OWN CLERKS SO THEY TURNED TO THE "
         "CIPHER THAT EVERY BOOK CALLED UNBREAKABLE AND THE ENEMY SOON "
         "LEARNED TO BREAK THE CIPHER BY LOOKING FOR THE PLACES WHERE THE "
         "SAME WORDS FELL UNDER THE SAME LETTERS OF THE KEY").replace(" ", "")
secret = vigenere(plain, "EMILY")
print(secret[:50])

# Step 1 (Kasiski): find repeated three-letter groups and how far apart they are
spots = {}
for i in range(len(secret) - 2):
    spots.setdefault(secret[i:i + 3], []).append(i)
gaps = [b - a for p in spots.values() for a, b in zip(p, p[1:])]
print(len(gaps), "gaps:", sorted(gaps)[:12], "...")
factors = Counter(f for g in gaps for f in range(2, 13) if g % f == 0)
print(factors.most_common(4))
n = factors.most_common(1)[0][0]       # the factor shared by most gaps

# Step 2: each n-th letter was shifted by the same key letter, so it is a
# Caesar cipher. Pick the shift whose letter counts look most like English.
key = ""
for col in range(n):
    column = secret[col::n]
    counts = Counter(column)
    score = lambda s: sum(counts[A[(i + s) % 26]] * EN[i] for i in range(26))
    key += A[max(range(26), key=score)]
print(key)
print(vigenere(secret, key, -1)[:50])

Output:

XTMECPQOCYTTKLPVUMORLQVPUWANEFIIICDEEBPPXTIYYRKZTB
27 gaps: [25, 25, 35, 35, 35, 35, 47, 60, 65, 65, 65, 70] ...
[(5, 26), (7, 11), (3, 9), (2, 6)]
EMILY
THETELEGRAPHCARRIEDTHENEWSOFTHEWARFASTERTHANANYRID

Of 27 gaps between repeats, 26 are multiples of 5; the odd one, 47, is a chance repeat. Once the key length is known, five small Caesar ciphers fall in an instant. A longer keyword only means more columns, each with fewer letters, so it needs a longer message. In 1920 William Friedman found a purely statistical way to measure key length, the index of coincidence, which needs no repeats at all.

New hand ciphers¶

Playfair, 1854¶

Charles Wheatstone, the same Wheatstone of the telegraph, invented a cipher in 1854 that encrypts letters in pairs. His friend Lyon Playfair, a scientist and politician, promoted it to the British government, so it carries his name. According to Playfair's biographer, the Foreign Office complained it was too complicated; Wheatstone offered to teach it to boys from a nearby school in a quarter of an hour, and an official replied that he could never teach it to attachés.

The key is a word written into a \(5 \times 5\) square, followed by the rest of the alphabet (I and J share a cell). The plaintext is split into pairs, with an X between doubled letters. Each pair is then replaced by the two letters at the other corners of the rectangle it forms in the square, or by the letters to the right if both are in the same row, or below if both are in the same column.

def square(keyword):
    seen = ""
    for ch in keyword + "ABCDEFGHIKLMNOPQRSTUVWXYZ":   # no J: it shares I's cell
        if ch not in seen:
            seen += ch
    return [seen[i:i + 5] for i in range(0, 25, 5)]

def playfair(text, keyword):
    rows = square(keyword)
    where = {ch: (r, c) for r, row in enumerate(rows) for c, ch in enumerate(row)}
    text = text.replace("J", "I")
    pairs, i = [], 0
    while i < len(text):                  # split into pairs
        a = text[i]
        b = text[i + 1] if i + 1 < len(text) else "X"
        if a == b:                        # a doubled letter gets an X between
            b, i = "X", i + 1
        else:
            i += 2
        pairs.append(a + b)
    out = []
    for a, b in pairs:
        (ra, ca), (rb, cb) = where[a], where[b]
        if ra == rb:                      # same row: take the letters to the right
            out.append(rows[ra][(ca + 1) % 5] + rows[rb][(cb + 1) % 5])
        elif ca == cb:                    # same column: take the letters below
            out.append(rows[(ra + 1) % 5][ca] + rows[(rb + 1) % 5][cb])
        else:                             # rectangle: swap the columns
            out.append(rows[ra][cb] + rows[rb][ca])
    return " ".join(pairs), " ".join(out)

for row in square("WHEATSTONE"):
    print(" ".join(row))
pairs, secret = playfair("MEETMEATTHEBRIDGEATNOON", "WHEATSTONE")
print(pairs)
print(secret)

Output:

W H E A T
S O N B C
D F G I K
L M P Q R
U V X Y Z
ME ET ME AT TH EB RI DG EA TN OX ON
PH AW PH TW WE AN QK FI AT EC NV NB

Working on pairs hides single-letter frequencies, and there are 600 possible pairs to count instead of 26 letters. But the same pair always encrypts the same way (ME becomes PH both times above), so with enough text, pair frequencies break it. The British army used Playfair as a field cipher in the Boer War and the First World War, where speed mattered more than strength; a message only had to stay secret for a few hours.

The wheel cipher: Jefferson, Bazeries and the M-94¶

Thomas Jefferson described a "wheel cypher" in his papers, probably in the 1790s: 36 wooden disks, each with the alphabet around its edge in a different scrambled order, threaded on an iron axle. Turn the disks until the message reads along one row, then copy any other row as the ciphertext. The receiver, with the same disks in the same order, sets the ciphertext on one row and looks around the cylinder for the row that makes sense. The order of the disks is the key. The description was found among his papers in 1922; there is no sign he used it much.

The French cryptologist Étienne Bazeries, who later broke the Rossignols' Great Cipher, reinvented it in 1891 with 20 disks. The US Army adopted a version with 25 aluminium disks as the M-94 in 1922 and used it into the Second World War, along with a flat strip version, the M-138-A, used by the State Department, the Army and the Navy.

The US Civil War: the first telegraph war¶

The American Civil War (1861–1865) was the first war in which armies relied heavily on the telegraph; the British and French had used it in the Crimea a few years before. The Union's military telegraph, run by former Western Union men, used route transpositions: the words of a message were written in a grid and read off along a prearranged path, with code words standing in for names and places and dummy words added at the ends. The Confederates never broke them and even printed intercepted messages in newspapers in the hope that a reader could.

The Confederacy used the keyword cipher, often with brass cipher disks, but kept the same few keywords for years ("Manchester Bluff", "Complete Victory" and "Come Retribution" are the ones on record) and sometimes left word spaces in. Three young Union telegraphers in the War Department in Washington solved their messages regularly. One of them, David Homer Bates, later described the work, and Lincoln's frequent visits to the telegraph office, in Lincoln in the Telegraph Office (1907).

China: a number for every character, 1871–1872¶

Morse code was built for alphabets, and Chinese is written with thousands of characters. When the Great Northern Telegraph Company, a Danish firm, opened a cable between Shanghai and Hong Kong in 1871, it needed a way round that. The Danish astronomer Hans Schjellerup drew up a first list, and in 1872 Septime Auguste Viguier published the codebook that replaced it, Dianbao xinshu (電報新書, "New book for the telegraph"). It gave a selection of common characters four-digit numbers from 0001 to 9999, and the clerk sent the digits. Telegraph clerks soon knew the commonest numbers by heart. Zheng Guanying brought out an expanded, reorganised edition in 1881. The code's descendants are still in use; police forces, for example, use the numbers to record Chinese names.

The codebook itself hid nothing, since anyone could buy it. But numbers make secrecy easy to add. The NSA's short history of the code gives 米 (rice) as 4149: add a secret 5555 digit by digit, dropping the carries, and 9694 goes on the wire, and the receiver subtracts the same key. That is the same additive trick the Japanese navy later used on top of its JN-25 code book.

Japan: ciphers for the new telegraph¶

Japan's first telegraph line, from Tokyo to Yokohama, opened in 1869, and by the early 1880s the network reached every major part of the country. Messages went in Wabun code, a Morse code for the kana syllables. The worry, as a National Diet Library essay puts it, was that the telegraph operator could read everything, and coded telegrams were allowed soon after the service began.

Government offices used code charts from about 1875. The papers of the official Mishima Michitsune include charts for messages between the Home Ministry, the Finance Ministry and the prefectural governors. They were simple substitutions, such as running the iroha syllabary from its last syllable instead of its first. From March 1879 the tables were scrambled irregularly, and in November 1879 the government adopted a cipher wheel: a small disk on a larger one, with a window that picked one of five code charts. The notice about the change, from the finance minister Ōkuma Shigenobu to the prefectures, survives in the same papers. It is the same kind of device as Alberti's disk of four centuries earlier, but each setting was still one simple substitution.

Russia: the Okhrana's black chambers¶

Tsarist Russia read mail on a large scale. Under the Okhrana, the political police set up in 1881, black chambers in post offices across the empire opened letters, and ciphered ones went to decipherers. The revolutionary Victor Serge, who saw the Okhrana's files after 1917, wrote that its best decipherer, a man named Zybin, had such a reputation that he was kept on after the revolution of March 1917. Serge's account is partisan, and little else is known about Zybin. The Okhrana read foreign traffic too: one of its officers, Ivan Manasevich-Manuilov, described intercepting and decoding the messages of the Japanese military attaché. Russia's own military ciphers were another matter, as Tannenberg showed in 1914.

Africa: drums that talk¶

In Central and West Africa, people sent messages over miles by drum. In tonal languages, where a word's meaning depends on the pitch of its syllables, a drum or a hollowed log "slit-gong" with two or more tones can copy the tune and rhythm of a sentence. The missionary John Carrington, who lived among the Kele people of the Congo, described the system in The Talking Drums of Africa (1949) and reckoned the messages carried three to seven miles.

The trouble is that many words share the same tones. In Kele, "manioc", "plantain", "above" and "forest" all sound alike on the drum, so each is drummed inside a longer stock phrase: manioc is "the manioc which remains in the fallow ground". The extra words make the message longer but remove the ambiguity, the same trade-off between length and reliability that later engineers would call redundancy. Drum language was not secret: anyone who knew the language and the phrases could follow the simpler messages, though the full art belonged to trained drummers. But it could be used to hide things. Ruth Finnegan notes that during the Nigerian civil war (1967–1970) drum language went out over the radio to reach some listeners and not others.

Kerckhoffs's rules¶

In 1883 Auguste Kerckhoffs (1835–1903), a Dutch-born professor of languages working in France, published La cryptographie militaire in the Journal des sciences militaires. He argued that the telegraph had changed what a military cipher must do. A cipher used by a whole army, with equipment in the hands of thousands of soldiers, would certainly fall into enemy hands. So it had to stay safe even then. He set out six requirements, here in paraphrase:

The system must be practically, if not mathematically, unbreakable.
It must not need to be secret; it must be able to fall into the enemy's hands without harm.
The key must be easy to remember without writing it down, and easy to change.
It must work for telegraph messages.
It must be portable and usable by one person.
It must be easy to use, without strain or a long list of rules.

The second rule is now called Kerckhoffs's principle: the security of a cipher must depend only on the secrecy of the key, never on the secrecy of the method. Claude Shannon put it more bluntly in 1949: "the enemy knows the system". Every algorithm on this site follows it. AES, RSA and ML-KEM are published in full, and anyone may study them. See the FAQ for why secret algorithms tend to fail.

Kerckhoffs also showed how to attack a polyalphabetic cipher by lining up several messages sent with the same key, a method called superimposition. It comes back in the one-time pad story below.

Radio and the First World War¶

Everyone is listening¶

By 1914 armies and navies used Marconi's radio, and radio has no wire to tap: anyone with a receiver in range hears every message. The first great disaster came in the opening weeks. At Tannenberg in August 1914, two Russian armies invading East Prussia were short of code books and sent many orders by radio in plain language. German listeners read them, knew where each Russian corps would be, and destroyed the Second Army. Its commander, Alexander Samsonov, shot himself.

From then on, every major power built signals-intelligence services. The war produced enormous volumes of intercepted traffic, and codebreaking became a large organized profession.

Room 40¶

In August 1914 Sir Alfred Ewing, the Admiralty's director of naval education, began gathering mathematicians, linguists and classicists to read German naval signals. The group, known as Room 40 after its office in the Admiralty Old Building, worked closely with Captain William Reginald "Blinker" Hall, who became Director of Naval Intelligence that autumn; Ewing ran it until 1917, when it passed fully to Hall's division.

Luck gave it a start. In the first months of the war the Allies captured all three main German naval code books: the SKM from the cruiser Magdeburg, which ran aground in the Baltic and whose book the Russians passed to Britain; the HVB from a German merchant ship seized in Australia; and the VB, dragged up in a fishing trawl from a chest thrown off a sunken German destroyer. With them Room 40 could follow the German fleet, and it warned of the sorties that led to the battles of Dogger Bank (1915) and Jutland (1916).

The Zimmermann telegram¶

On 16 January 1917, the German foreign secretary Arthur Zimmermann sent a coded telegram to his ambassador in Mexico, Heinrich von Eckardt, by way of the German embassy in Washington. It said that Germany would resume unrestricted submarine warfare on 1 February, and that if this brought the United States into the war, Eckardt should offer Mexico an alliance: Germany would provide money, and Mexico would "reconquer the lost territory in Texas, New Mexico, and Arizona". Mexico should also invite Japan to join.

Germany sent it over the American State Department's own cable, which President Wilson had let Germany use for peace talks (by the usual account it went by other routes as well). The cable ran through Britain, and Room 40 copied everything on it. Two of its codebreakers, Nigel de Grey and the Reverend William Montgomery, read the message in German code 0075 within hours, at first with gaps.

Hall now had a problem. Publishing the telegram would tell Germany its code was broken and tell the Americans that Britain read their cables. He solved it by obtaining the copy the Washington embassy had forwarded to Mexico City by ordinary commercial telegraph, in an older code Room 40 could read fully. That copy could plausibly have been stolen in Mexico. Britain gave the text to the American ambassador on 23 February, and it was published in American newspapers on 1 March. Many Americans assumed it was a British forgery, until Zimmermann himself confirmed it was genuine on 3 March.

The United States declared war on Germany on 6 April 1917. The submarine campaign, which was sinking American ships, was the main cause, but the telegram turned much of the public, especially in the West and Southwest, toward war. Kahn judged that no other single cryptanalysis has had such enormous consequences. Historians since have argued about how much it changed, but it is the classic case of codebreaking shaping events.

ADFGVX and the radiogram of victory¶

In early March 1918 (sources give the 1st or the 5th), during its great spring offensive, the German army introduced a new field cipher designed by Fritz Nebel. It used only the letters A, D, F, G and X, chosen because they sound very different in Morse code. Each plaintext letter was replaced by its row and column in a \(5 \times 5\) grid (the Polybius square again), and the resulting letters were then shuffled by a keyed column transposition. Around the start of June a sixth letter, V, extended the grid to \(6 \times 6\) so that digits could be sent too.

The French cryptanalyst Georges Painvin, working himself into exhaustion, found a way in. On 2 June 1918 he read a message ordering ammunition to be hurried forward, which pointed to where the next German attack would fall. It became known in France as the radiogramme de la victoire. How much it changed the battle that followed is still debated, but the French were ready.

The Choctaw telephone squads, 1918¶

In October 1918, during the Meuse-Argonne offensive, American field telephone messages were being intercepted by the Germans. An officer of the 142nd Infantry, in the US 36th Division, overheard two Choctaw soldiers talking in their own language and saw the answer. The regiment put Choctaw speakers on the telephones, and their first messages, on 26 to 28 October 1918, went by in a language no German listener knew. The group grew to about twenty men. They were the first code talkers, and the idea came back on a larger scale in the Second World War.

The American Black Chamber¶

In 1917 the United States Army set up a cipher section, MI-8, under Herbert Yardley, a former State Department telegraph clerk. After the war it continued in New York as the Cipher Bureau, known as the American Black Chamber, funded jointly by the Army and the State Department. Its best moment came at the Washington Naval Conference of 1921–22, when it read Japan's instructions to its delegates and the American side knew how far Japan would give way. In 1929 the new Secretary of State, Henry Stimson, cut off its money. Years later he summed up his view as "gentlemen do not read each other's mail". Yardley, out of a job, published The American Black Chamber in 1931 and caused a scandal.

Vernam and the one-time pad¶

A cipher for machines¶

Telegraph and teleprinter networks sent letters as electrical codes. In the Baudot code a teleprinter used, every character is five on-or-off pulses, holes or no holes across a paper tape. In 1917 Gilbert Vernam, an engineer at AT&T, saw that a machine could encrypt such a tape by combining it, pulse by pulse, with a second key tape: where the two match, send "off"; where they differ, send "on". Today that rule is called exclusive or (XOR). Doing it again with the same key tape gives back the original. The machine encrypted as fast as the line could carry text, with no clerk involved. Vernam's patent, US 1,310,719, was granted on 22 July 1919.

The first version used a loop of key tape, which repeated, and a repeating key falls to the same tricks as a repeating keyword. A colleague, Lyman Morehouse, combined two loops of slightly different lengths, 999 and 1,000 characters, to make a key nearly a million characters long before it repeated. But it was still a pattern.

Never use the key twice¶

The decisive idea was that the key tape should be random and as long as the message, and should never be used again. Kahn credits Major Joseph Mauborgne of the Army Signal Corps (later its chief) with insisting on the never-reuse rule; Steven Bellovin argued in 2016 that Vernam saw the need for a non-repeating key himself. Either way, the result was the one-time tape, and its paper form, the one-time pad: a pad of random letters or numbers, each sheet used once and destroyed.

Even this had a forerunner. In 2011 Bellovin found an 1882 telegraph code book by Frank Miller, a Sacramento banker, which describes adding random numbers from a list to the code numbers and crossing each one out once used. That is a one-time pad, 35 years before Vernam. Bellovin found no proof that Vernam or Mauborgne knew of it, though he suggested Mauborgne might have heard of it through his colleague Parker Hitt.

Why it can't be broken¶

A one-time pad isn't just hard to break; it is impossible, because the ciphertext contains no information about the message. For any ciphertext, every message of the same length is equally possible: for each candidate there is some pad that turns it into that ciphertext, and a truly random pad is as likely to be one as another. Claude Shannon proved this formally in the 1940s and showed that no cipher with a shorter key can do as well.

The rules are strict. The pad must be truly random, at least as long as all the messages it protects, kept secret, and never reused. If it is reused, two messages encrypted with the same pad can be combined so that the pad cancels out, leaving the two plaintexts mixed together, and a guessed word in one reveals the other. That is exactly how the Soviet one-time pads were broken in the Venona project, on the next page.

This program uses letters and addition modulo 26, the paper-pad version.

A = "ABCDEFGHIJKLMNOPQRSTUVWXYZ"

def add(text, pad, sign=1):
    return "".join(A[(A.index(t) + sign * A.index(p)) % 26] for t, p in zip(text, pad))

pad = "XQJRMWZBKTUE"                      # truly random, used once, then burned
secret = add("ATTACKATDAWN", pad)
print(secret, add(secret, pad, -1))

# Without the pad, every 12-letter message is equally possible:
for guess in ("HOLDPOSITION", "RETREATTONOW"):
    fake_pad = add(secret, guess, -1)    # the pad that would turn guess into secret
    print(guess, "needs pad", fake_pad, "->", add(guess, fake_pad))

# Reuse the pad once and the two messages leak into each other
other = add("SENDMOREMENX", pad)
diff = add(secret, other, -1)            # the pad cancels out
print(diff, add("ATTACK", diff[:6], -1)) # a guessed word reveals the other message

Output:

XJCROGZUNTQR ATTACKATDAWN
HOLDPOSITION needs pad QVROZSHMULCE -> XJCROGZUNTQR
RETREATTONOW needs pad GFJAKGGBZGCV -> XJCROGZUNTQR
IPGXQWJPRWJQ SENDMO

The catch is the key. Every message needs fresh key material as long as itself, delivered in advance by a trusted route. That is fine for a spy with a pad hidden in a cigarette lighter, or for the Washington–Moscow hotline, which ran on one-time tapes after 1963, but impossible for a whole army, let alone the internet. In the early 1920s the German Foreign Office adopted one-time pads for its diplomatic code, which made its traffic far harder to read, although its pads came from a machine rather than true chance, and American codebreakers attacked them in the Second World War. Most of the rest of cryptographic history is about getting close to one-time-pad security with a short key. The modern answer is a stream cipher such as ChaCha20, which stretches a 256-bit key into a long pseudo-random pad, and a key exchange such as Diffie–Hellman to agree on that key.

Can these be broken today?¶

Every cipher on this page except one falls to a computer in seconds. The exception is the one-time pad, used correctly.

Cipher	Broken today?	The attack in plain words
Commercial codebooks	at once, with the book	Codes were sold openly. Without the book, the same code word for the same phrase repeats, and context fills it in, as Room 40 did with the Zimmermann telegram.
Keyword ("Vigenère") cipher	in a fraction of a second	Kasiski's repeats give the key length; then each column is a Caesar shift. The program above does it.
Playfair	in seconds	The same pair always gives the same pair. A computer climbs: change the \(5 \times 5\) square a little, keep the change if the text looks more like English. A few hundred letters are enough.
Wheel cipher (Jefferson, Bazeries, M-94)	easily, with a guessed word	The disk order is the key, and the disks themselves are often captured. Guess a likely word: each plain letter and its cipher letter must sit the same distance apart on their disk, which rules out almost every order. The Marquis de Viaris broke Bazeries's cylinder this way in 1893.
The Chinese telegraph code with an added key	easily, with enough traffic	The book is public, so only the added digits are secret. If the key is reused, subtracting two messages cancels it, and the common characters' numbers show through.
Meiji code charts and the cipher wheel	instantly	One substitution per setting, and only five settings.
Choctaw on the telephone	not by codebreaking	A language, not a cipher. Only a speaker could follow it.
Route transposition (Union army)	easily	Letters and words are only moved, so they are all still there. Try the likely grids and paths until sentences appear; the code words for names need context.
ADFGVX	easily, by computer	Painvin needed weeks of work and messages with matching beginnings. Today a program tries column orders and checks whether the resulting pairs behave like letters of a substitution.
One-time pad, used once with a truly random pad	never	No attack exists: every message of that length fits. Shannon proved it.
One-time pad, reused	easily	Subtract two messages and the pad drops out, as the program above shows. Guess a word in one, read the other. That is how Venona worked.

The rule that came out of this age, Kerckhoffs's, is the one these attacks prove: assume the enemy knows the method, because sooner or later the enemy will.

What the telegraph age left behind¶

The keyword cipher was dead. After Kasiski, no repeating-key cipher could be trusted.
Kerckhoffs's principle: assume the enemy knows the method.
Codebreaking as an institution, from Room 40 to Yardley's Black Chamber, built on the flood of intercepted radio.
The one-time pad: perfect secrecy, at the price of a key as long as the message.
Encryption by machine. Vernam's teleprinter showed that a machine could encrypt faster and more reliably than any clerk. The next step was machines that generated their own key.

References¶

David Kahn, The Codebreakers (rev. ed., Scribner, 1996): Smith's code, Poe, Babbage, Kasiski, the Civil War, Kerckhoffs, Tannenberg, Room 40, Zimmermann, ADFGVX, Yardley, Vernam and Mauborgne
Friedrich W. Kasiski, Die Geheimschriften und die Dechiffrir-Kunst (Berlin, 1863)
Auguste Kerckhoffs, "La cryptographie militaire", Journal des sciences militaires 9 (January and February 1883), pp. 5–38 and 161–191
Ole I. Franksen, Mr. Babbage's Secret: The Tale of a Cypher and APL (Prentice Hall, 1985)
David Homer Bates, Lincoln in the Telegraph Office (Century, 1907)
Barbara Tuchman, The Zimmermann Telegram (Viking, 1958) / Thomas Boghardt, The Zimmermann Telegram: Intelligence, Diplomacy, and America's Entry into World War I (Naval Institute Press, 2012)
Patrick Beesly, Room 40: British Naval Intelligence 1914–1918 (Hamish Hamilton, 1982)
Herbert O. Yardley, The American Black Chamber (Bobbs-Merrill, 1931) / Henry L. Stimson and McGeorge Bundy, On Active Service in Peace and War (Harper, 1948)
Gilbert S. Vernam, "Secret Signaling System", US Patent 1,310,719 (1919) / Vernam, "Cipher Printing Telegraph Systems for Secret Wire and Radio Telegraphic Communications", Journal of the AIEE 45 (1926), pp. 109–115
Steven M. Bellovin, "Frank Miller: Inventor of the One-Time Pad", Cryptologia 35, no. 3 (2011), pp. 203–222 / Bellovin, "Vernam, Mauborgne, and Friedman: The One-Time Pad and the Index of Coincidence", in The New Codebreakers (Springer LNCS 9100, 2016)
William F. Friedman, The Index of Coincidence and Its Applications in Cryptography (Riverbank Publication 22, 1922)
Ruth Finnegan, Oral Literature in Africa (Open Book Publishers, 2012), chapter 17, "Drum Language and Literature" / John F. Carrington, The Talking Drums of Africa (Carey Kingsgate Press, 1949)
Septime Auguste Viguier, Dianbao xinshu (電報新書) (Shanghai, 1872) / Thomas S. Mullaney, The Chinese Computer: A Global History of the Information Age (MIT Press, 2024), on the 1871–1872 code
National Diet Library (Japan), "Cipher Wheel of the Meiji Era", Modern Japan in Archives, column 2, with Ōkuma Shigenobu's notice of 12 November 1879 (Papers of Mishima Michitsune, #474-10)
Victor Serge, What Everyone Should Know About State Repression (1926), on Zybin / Ivan Manasevich-Manuilov's notes in the Okhrana files, Hoover Institution, as described in a CIA Studies in Intelligence review of works on the Okhrana
William C. Meadows, The First Code Talkers: Native American Communicators in World War I (University of Oklahoma Press, 2021), as summarized by RealClearDefense

Weaker sources: a search summary of the NSA's "History Today" article on the Chinese telegraph code (15 February 2018), for the 4149 and 5555 example; the Wikipedia articles on the Chinese telegraph code and on Wabun code; a search summary of the NSA-hosted Cryptologic Quarterly article "Before Bourbon", for the Okhrana's black chambers in post offices; the National Cryptologic Foundation's "World War I: The Original Code Talkers" (2014), for the overheard conversation; search summaries of the Wikipedia articles on the Vigenère cipher (Thwaites, The Tempest, the keys "two" and "combined", the 1854 date) and Simon Singh's The Code Book (1999) for the Tennyson and EMILY story, Georges Painvin and the ADFGVX cipher (1 March and 2 June 1918, the V added around the start of June); Wemyss Reid's Memoirs of Lyon Playfair (1899) for the Foreign Office anecdote, known to me through retellings; the "BAFUZ" code word, a made-up example of the style rather than a quotation from a real code book.

The telegraph age¶

Wires change everything¶

Codes for a price per word¶

Ciphers as entertainment¶

The keyword cipher falls¶

Babbage, 1854¶

Kasiski, 1863¶

Trying it¶

New hand ciphers¶

Playfair, 1854¶

The wheel cipher: Jefferson, Bazeries and the M-94¶

The US Civil War: the first telegraph war¶

China: a number for every character, 1871–1872¶

Japan: ciphers for the new telegraph¶

Russia: the Okhrana's black chambers¶

Africa: drums that talk¶

Kerckhoffs's rules¶

Radio and the First World War¶

Everyone is listening¶

Room 40¶

The Zimmermann telegram¶

ADFGVX and the radiogram of victory¶

The Choctaw telephone squads, 1918¶

The American Black Chamber¶

Vernam and the one-time pad¶

A cipher for machines¶

Never use the key twice¶

Why it can't be broken¶

Can these be broken today?¶

What the telegraph age left behind¶

See also¶

References¶