Quantum Information, Game Theory, and the Future of Rationality
The Legacy Of Al-Kindi's Frequency Analysis: Patterns, Codes, And True Randomness
How secure is encrypted data? The answer often depends on the persistence and ingenuity of the codebreaker. In recent decades, however, the speed at which cryptanalysis can be performed has also become a crucial factor, with faster processing capabilities increasing the vulnerability of encrypted data. This risk is set to grow even more with the emergence of quantum computing. While encryption and hacking may seem like phenomena of the digital age, their roots stretch much further back in history—likely to the dawn of civilization itself. A prime example is Al-Kindi, whose groundbreaking work in frequency analysis was one of the earliest recorded methods for breaking cryptographic codes. His contributions, made over a thousand years ago, mark a significant milestone in the history of cryptography. But with the rise of quantum technology, this milestone may soon be surpassed.
Faisal Shah Khan, PhD
10/7/20243 min read
Around 850 CE, Abu Yusuf Al-Kindi, the director of the House of Wisdom in Baghdad, introduced the first known statistical technique for breaking substitution ciphers. These ciphers encrypt messages by replacing the letters of the alphabet with symbols or other letters, and the key for this transformation is shared only with trusted parties. One famous example is the Caesar cipher, used by Julius Caesar, which shifts letters by a fixed number of positions in the alphabet. For example, in a Caesar cipher where the letters are shifted by five places, the word "ATTACK" would be encrypted as "FYYFHP." Substitution ciphers, including Caesar's, exemplified the "simple but effective" approach to securing communications sent over insecure channels.
However, before Al-Kindi's breakthrough, no systematic method for analyzing and breaking these letter-shift ciphers is known to have existed. This means that the probability of correctly guessing the true letter value in a Caesar cipher was roughly 1 in 400 trillion trillion! In his work On Deciphering Cryptographic Messages, Al-Kindi outlined a method based on frequency analysis. This technique involves analyzing how frequently letters or symbols appear in the ciphertext, under the assumption that the language of the original message is known. For example, if the original message is in English, Al-Kindi's method would suggest that the most frequently occurring symbol in the cipher likely represents the letter "E," since "E" is the most common letter in English, appearing about 13% of the time. On the other hand, the letter "D" appears far less frequently, at around 4%.
Al-Kindi's analysis extends further by proposing the identification of frequently occurring letter pairs (bigrams) in the target language. In English, for instance, the pair "TH" occurs in approximately 15% of texts, "HE" in 12%, and "ER" in 11%. This approach can be extended to triples of letters, helping to identify commonly used words like "THE," "OFF," and "OUT" in encrypted text. However, it's important to note that the context of the original message (whether a scientific text, war manual, technical specification, or poetry) can influence these frequencies.
While Al-Kindi’s frequency analysis is less effective against more advanced modern encryption techniques—such as those involving variable shifts—his foundational concept of detecting patterns in data remains central to modern cryptanalysis. During World War II, for instance, the Allies famously broke the German Enigma machine encryption. Alan Turing, a pioneer in computer science, exploited patterns found in intercepted German communications. German soldiers repeatedly sent weather reports using a consistent format and terminology, along with predictable salutations and signatures. These recurring patterns, combined with operational lapses by the Germans in following best practices, enabled Turing and his team to crack the Enigma encryption.
The "curse of the pattern" continues to haunt modern cybersecurity as well. Despite the sophistication of today’s encryption algorithms, elements of modern encryption suites still remain vulnerable to frequency analysis and pattern recognition. With the rise of machine learning and neural networks, identifying patterns in data has become even faster and more accurate. One of the key challenges in modern encryption is the lack of true randomness in the data. True randomness is characterized by a sequence of events (or data) that exhibits unpredictability, lack of bias, and high entropy—qualities that are difficult to achieve in practice.
As discussed in the earlier post "Quantum Entanglement and the Art of Hotel Breakfast Management," even sequences that seem random at first glance may, upon further analysis, reveal biases or patterns. For example, a pair of anti-correlated digital coins may show no discernible bias in individual flips, but over the course of several days, a 70%-30% bias can become apparent, indicating lower entropy and allowing for pattern detection. Modern encryption methods, such as public-key cryptography, rely on the exchange of random numbers during the initialization process. However, if these numbers are not truly random (which they typically aren’t), an adversary could potentially collect a large enough sample, analyze it for patterns, and predict future numbers—compromising the encryption scheme and the security of transactions.
So, is the internet secure? The simple answer is: it’s not. Despite widespread use of encryption, numerous data breaches have already exposed the private information of hundreds of millions of people worldwide. As cryptography continues to evolve, ensuring true randomness and eliminating patterns remain critical challenges for the future of cybersecurity. This is a problem that quantum technology, specifically quantum random number generators, may be able to solve. Al-Kindi's legacy, over a millennium old, is beginning to face new challenges. I will explore this in more detail in the next post where we will see that a quantum solution exists to blunt the dramatic power of quantum computers.
