The Mathematician Who Invented Modern Cryptography

Introduction

For roughly three centuries, the Vigenère cipher was considered the gold standard of secret communication. First described in 1553 by Italian cryptographer Giovan Battista Bellaso and later misattributed to the French diplomat Blaise de Vigenère, the cipher used a repeating keyword to shift letters in a message, creating a polyalphabetic substitution that defeated the simple frequency analysis techniques available to most codebreakers of the era. Military commanders, diplomats, and revolutionaries trusted it with their most sensitive correspondence. During the American Civil War, Confederate forces used a variant of it to encode battlefield communications, relying on its complexity as a shield against Union intelligence. Its reputation was so formidable that nineteenth-century writers took to calling it le chiffre indéchiffrable — the indecipherable cipher.

That reputation turned out to be wrong, and the man who first proved it wrong never told anyone.

The story of how the Vigenère cipher fell is not simply a chapter in the history of codes and codebreaking. It is a story about how scientific knowledge can be discovered, suppressed, overlooked, and misattributed all at once — and how the consequences of a single unpublished result can ripple forward through generations of scholarship, military strategy, and technological development. It is also, in a way that becomes clearer the more closely one examines it, a story about Charles Babbage: a man already remarkable enough in the historical record, whose full significance has still not been entirely absorbed.

Charles Babbage’s Secret Breakthrough

Charles Babbage is remembered today primarily as the inventor of the Difference Engine and the Analytical Engine, mechanical precursors to the modern computer. Less known is that sometime around 1846, Babbage broke the Vigenère cipher — a cryptanalytic achievement that would not be publicly credited to him until historians examined his unpublished notebooks in the twentieth century.

Babbage’s method exploited a structural weakness in the cipher that its users had never seriously considered. If the same keyword is used repeatedly to encode a long message, identical sequences of plaintext encrypted under the same portion of the keyword will produce identical ciphertext sequences. By searching for repeated strings of letters in the ciphertext and carefully measuring the distances between them, an analyst can deduce the probable length of the keyword. The distances between repeated sequences will tend to be multiples of the keyword length, because those repetitions arise precisely when the same plaintext falls under the same part of the cycling key. Once the keyword length is known, the message can be divided into independent columns, each of which is effectively a simple Caesar cipher — a single-letter shift applied consistently throughout — and each of which is therefore solvable by ordinary frequency analysis, comparing letter distributions against the expected frequencies of the target language.

This technique is elegant, systematic, and entirely general. It does not require guessing the keyword, does not depend on the message's subject matter, and scales naturally with the length of the intercepted text. Babbage apparently developed it in response to a challenge from John Hall Brock Thwaites, an amateur cryptographer who had written to him, claiming that the Vigenère cipher was unbreakable and that his own variant was even more secure. Babbage demonstrated otherwise in his correspondence but, characteristically, never published his findings. His letters and working notes on the subject sat in the archives of the British Museum largely unexamined for decades, waiting for someone to ask the right question.

The reasons for this silence remain genuinely unclear. Babbage was a prolific correspondent and an enthusiastic self-promoter in many areas of his intellectual life. That he would develop a solution to one of the most celebrated unsolved problems in cryptography and then simply not mention it publicly is, on its face, strange. But Babbage was also a man perpetually overwhelmed by the scale of his own ambitions, and the cryptographic work may simply have seemed like a diversion from the larger mechanical projects that consumed his attention and his finances.

Friedrich Kasiski and the Stolen Credit

In 1863, a retired Prussian infantry officer named Friedrich Wilhelm Kasiski published a short book titled Die Geheimschriften und die Dechiffrir-Kunst, which translates roughly as Secret Writing and the Art of Deciphering. In it, he described precisely the same technique Babbage had developed seventeen years earlier: the search for repeated ciphertext sequences, the measurement of distances between them, the factorization of those distances to identify probable keyword lengths, and the subsequent reduction of the problem to simple frequency analysis. Because Kasiski published and Babbage did not, the method became known as the Kasiski examination and remained attributed to the Prussian officer throughout the nineteenth century and most of the twentieth.

It was not until researcher Cipher A. Deavours and historian David Kahn examined Babbage’s original notebooks more closely in the latter decades of the twentieth century that the timeline was reconstructed with reasonable confidence. Kahn’s landmark 1967 work The Codebreakers had already hinted at Babbage’s role, but the full picture required archival verification that took additional years to complete. Historians conclude that Kasiski was not a fraud. He appears to have arrived at the same solution independently, without knowledge of Babbage’s earlier work. But chronological priority clearly belongs to Babbage, and the misattribution persisted long enough to distort the intellectual history of cryptanalysis for well over a century.

One theory that has attracted some attention among historians, though it remains unproven, is that British military or intelligence interests may have quietly discouraged Babbage from publishing in order to preserve a tactical advantage. If British codebreakers could read Vigenère-encrypted messages while the cipher’s users remained confident in its security, that asymmetry would have had obvious strategic value. The theory is plausible in principle — governments have suppressed cryptographic breakthroughs for strategic reasons at other points in history, most famously in the case of wartime work at Bletchley Park — but no documentary evidence has emerged to confirm it in Babbage’s case. It remains speculation, which is itself a measure of how incompletely the episode has been resolved.

Why This Matters Beyond the History of Codes

The story of Babbage and the Vigenère cipher sits at an intersection that modern readers may find surprisingly familiar. The core insight he developed — that patterns in structured repetition betray hidden keys — is not merely a historical curiosity. It is conceptually related to attacks used against poorly implemented modern encryption systems. Early implementations of the RC4 stream cipher, which was widely used in WEP wireless security protocols in the early 2000s, were vulnerable to related-key attacks that share a structural kinship with the Kasiski examination. The fundamental warning embedded in Babbage’s work, that key reuse creates exploitable regularities in ciphertext, did not become obsolete with the invention of computers. It became a foundational principle of cryptographic design, one that engineers continue to violate at their peril.

Babbage’s broader legacy in computation is also being reexamined with increasing seriousness. The Science Museum in London completed a working Difference Engine No. 2 in 1991, built entirely from Babbage’s original plans using manufacturing techniques consistent with what would have been available in the nineteenth century. The machine worked. A second complete Difference Engine was assembled in 2008 and is now on permanent display at the Computer History Museum in Mountain View, California. These machines, constructed from plans drawn up before the American Civil War, perform their calculations exactly as Babbage intended. The question of why they were never built in his lifetime says more about the economics and institutional structures of Victorian England than it does about the soundness of his engineering.

What remains underappreciated is the degree to which Babbage thought about information itself — not merely calculation. His unpublished notebooks contain passages on encoding, pattern recognition, and the manipulation of symbolic sequences that anticipate concerns central to twentieth-century information theory. Claude Shannon, whose 1949 paper "Communication Theory of Secrecy Systems" mathematically formalized the concept of cryptographic security, worked in a tradition that Babbage approached from the opposite direction: not from axioms downward, but from puzzles upward. Shannon asked what security meant in the abstract. Babbage asked what weakness looked like in practice. Both questions proved essential, and the fact that they converge on similar structural insights across a century of separation is no coincidence.

The Lesson of the Unpublished Breakthrough

The Babbage cryptography episode is a case study in how scientific priority and historical memory diverge, and in how the consequences of that divergence can be surprisingly durable. Credit in science and mathematics has always depended heavily on publication, and the consequences of silence — whether chosen, forced, or simply deferred — can persist for generations. Rosalind Franklin’s X-ray diffraction work on DNA, Lise Meitner’s contributions to nuclear fission theory, and Jocelyn Bell Burnell’s discovery of pulsars all illustrate the same structural problem: the person who does the work is not always the person who receives the recognition, and the archive does not always correct the record in time to matter professionally or personally to those involved.

In Babbage’s case, the correction came eventually, though it arrived long after it could have made any difference to him. His priority over Kasiski in breaking the Vigenère cipher is now accepted by historians of cryptography. But the delay meant that for nearly a century, the intellectual genealogy of modern cryptanalysis was miscounted by one important name — a name that already belonged to one of the most consequential thinkers of the nineteenth century, whose published work had already been undervalued in his own lifetime. Babbage died in 1871, widely regarded as a brilliant but frustrated eccentric whose greatest projects had come to nothing. The Analytical Engine was never completed. The Difference Engine sat unbuilt. His contributions to statistical analysis, operational research, and cryptography were scattered across notebooks and letters that most of his contemporaries never read.

The fuller picture that has emerged over the past several decades is of a thinker whose reach consistently exceeded what his era could accommodate or recognize. The Vigenère breakthrough is perhaps the sharpest example of this pattern, precisely because it is so concrete. He solved a problem that the entire cryptographic community believed was unsolvable. He solved it cleanly, using a method that remained valid and in active use for generations afterward. And then he said nothing, for reasons that history has not yet fully explained. That silence, and the long effort required to undo it, is worth remembering the next time a cipher is called indecipherable.