Beyond Al-Kindi: True Randomness From Quantum Sources

In my previous post, I introduced Abu Yusuf Al-Kindi, the director of the House of Wisdom, a leading institution for higher education and research in Baghdad around 850 CE. Al-Kindi is widely regarded as the father of modern cryptanalysis due to his innovative use of statistical frequency analysis to detect patterns in data encrypted with substitution ciphers. This foundational approach remains a cornerstone of cryptanalysis today.

Patterns in encrypted data can arise either from the design of the encryption scheme or from flaws in its implementation. As discussed earlier, older ciphers like the Caesar cipher—commonly used during Al-Kindi's era—were especially vulnerable to frequency analysis attacks due to their simplicity. In such ciphers, each letter in the plaintext is shifted by a fixed amount or replaced by a symbol corresponding to that shift, making them easy to decode by analyzing letter frequency patterns. To counter frequency analysis, encryption schemes have evolved to incorporate greater complexity. However, this complexity often comes with trade-offs, such as slower processing speeds and higher implementation costs. Modern encryption standards aim to strike a balance between security, efficiency, and cost, but even these can be compromised by a determined, well-funded adversary. For example, the breaking of German codes by the Allies during World War II demonstrated how pattern analysis, combined with sufficient resources, can overcome even advanced encryption systems of the time.

Looking ahead, emerging technologies like quantum computing pose an even more significant threat. Quantum computers, with their immense processing power, can break public-key encryption methods that rely on integer factorization and elliptic curve cryptography—both of which are foundational to today’s security protocols. Beyond these, quantum computers could potentially discern patterns in encrypted data better than conventional computers and compromise many other modern encryption algorithms, making current standards obsolete. This looming challenge underscores the urgent need for a new generation of cryptographic techniques to safeguard future communications.

There are, however, quantum solutions that can blunt the threat posed by quantum computers, and some of these have already been commercialized and are being successfully implemented in consumer electronics. One such solution is the quantum random number generator (QRNG), which harnesses true randomness derived from quantum phenomena. The randomness of data can be quantified in terms of how much pattern one can identify in the data. This is called entropy. The lower the entropy—or uncertainty—the more bias or pattern the data exhibits. For example, recall the anti-correlated coins used for managing tea and coffee inventory, mentioned in the post "Quantum Entanglement and the Art of Hotel Breakfast Management: 50%-50%?" These coins were biased, and therefore a pattern could be detected by looking at their tosses over a period of 10 days.

While various ingenious methods can help eliminate bias, only quantum physically generated data can be said to be truly unbiased. This is because of two reasons:

1. The Born rule: In quantum mechanics, measurement outcomes are inherently probabilistic. Unlike classical objects, which have well-defined properties that can be determined with certainty, quantum objects exist in a state of uncertainty until measured. For example, if one observes a beach ball, one can confidently assert that it is blue. However, with a "quantum beach ball," one can only describe its color in terms of probabilities—it might be blue with a certain likelihood, but there is always a non-zero chance it could be red.

2. The Heisenberg uncertainty principle: It is fundamentally impossible—not merely due to technological limitations—to know certain properties of quantum objects simultaneously and with complete certainty. For instance, one cannot know both the color of a quantum beach ball and whether it is wet. This is just a fun analogy of what Heisenberg's principle says in more technical terms: there exist pairs of observable properties of quantum objects, such that the more certain one is about one property, the more uncertain one is about the other. A helpful way to visualize this concept is by imagining the challenge of putting on a bed cover with elastic corners. As one attempts to tuck one side under the mattress, the opposite side frequently pops loose, illustrating the delicate balance of the elements at play. The big difference is that one can eventually get the bed cover laid out properly.

The Born rule tells us how we can build a quantum random number generator (QRNG) using a device that produces colored quantum beach balls—which, in reality, are particles like photons or electrons, or qubits (quantum bits) in the language of quantum information science. These particles can be in a "uniform quantum superposition," giving them an equal chance of being measured as one of two possible colors—blue and red. When one measures the color of these qubits, one gets a perfectly random outcome, with a true 50-50 chance of seeing either blue or red.

Can one not guarantee this kind of perfect randomness with a classical physical mechanism, like a coin flip? No. Studies have shown that even a simple coin toss can easily be biased. Factors like how the coin is held, the force applied during the flip, and even atmospheric conditions can influence the outcome. While these biases may seem trivial when flipping a coin to decide who makes the first move in a game or what to order at a restaurant, they become problematic when dealing with large datasets, where even tiny biases can introduce noticeable patterns. Furthermore, unless deliberately correlated through quantum entanglement (which I will discuss more in later posts), the result of measuring one qubit for color is completely independent of, and hence uncorrelated with, the results of measuring others. Since creating entanglement is neither cheap nor easy to achieve with today’s technology, one can be confident that commercially available QRNGs will generate truly random, unbiased data. This makes them ideal for applications where eliminating patterns and ensuring randomness is crucial.

The Heisenberg uncertainty principle introduces an additional layer of unpredictability in quantum systems. Imagine that a qubit starts in a uniform quantum superposition of the colors blue and red. Now, let us say one wants to know not only its color but also whether it is dry or wet. This introduces a pair of complementary observable properties: (blue, red) for color and (dry, wet) for dampness (again, this is a fun analogy; a realistic complementary observable pair would be (left, right) for position and (low, high) for momentum). When one first measures the color, there is a 50-50 chance of observing either blue or red. Suppose one measures it to be red. At this point, the qubit is definitively red, and the quantum superposition for color collapses. However, when one then measures for dampness, even with perfectly calibrated equipment, one still gets a 50-50 chance of the qubit being dry or wet. Knowing the color has no impact on the dampness measurement.

Now, if one observes the qubit to be dry and then decides to measure its color again, one will once again find a 50-50 chance of it being blue or red! The earlier measurement that showed the qubit was red no longer holds—because the act of measuring dampness has effectively erased the previous certainty about color, returning the qubit to a quantum superposition of blue and red. This illustrates the core of the uncertainty principle: the more precisely one knows one property (such as color), the less certain one is about the other (such as dampness), and vice versa. The act of measuring one property disturbs the other, creating a constant interplay of uncertainty between complementary properties.

Depending on the problem at hand, quantum random number generators (QRNGs) come in varying levels of sophistication. For tasks that require simply generating truly random data, such as bit streams, a basic device implementing the Born rule will suffice. These devices are also ideal for applications like key exchange, authentication, or even initializing random processes, genetic algorithms and machine learning models, where truly random bit strings are needed for seeding or setup.

However, more complex scenarios, such as quantum encryption key exchanges using protocols like BB84, demand a more advanced QRNG setup that implements Heisenberg's uncertainty principle. While QRNGs today can support such protocols, more intricate quantum key exchange schemes that rely on quantum entanglement, such as the E91 protocol, remain beyond the capabilities of current QRNGs.

One thing is clear: we are standing at the edge of a technological shift that will soon transcend Al-Kindi's 1,200-year legacy of cryptanalysis techniques. A new socio-technological and economic transformation—a true quantum leap—is just around the corner.