The Biggest Milestone in the History of Cryptography is Quietly Upon Us

Mathematical Insight is No Longer an Advantage

Abstract: Throughout its stormy history and remarkable track record, cryptography was always a battle of wits. Mathematical insight was the power to be matched.  This unchallenged premise is now in question, as a new class of ciphers has been patented, recognized and stealthy applied: pattern-devoid. The asymptotic version of pattern-devoid ciphers is the famous 1917 Vernam cipher. Alas Vernam is an "Over kill".  The emerging ciphers in this class allow the transmitter to adjust the measure of injected unilateral randomness to apply the Vernam principle over the plausible plaintext candidates only, thereby rendering pattern-devoid ciphers into a practical alternative to the prevailing class which is universally vulnerable to a smarter mathematician.  The greater the role of randomness, the smaller the role of cryptanalytical insight, moving towards a day when mathematical insight will become irrelevant. This will be the biggest milestone in the history of cryptography.

1.0 Introduction

Cryptography from its very beginning was a mathematical game, the best mathematician took home the trophy, whether he or she were a cryptographer or a cryptanalyst. In fact, the attraction of the profession was based on the challenge to prove your mathematical superiority over your adversary. Math was the name of the game before computers and ever since. The profession went through serious revolutions, the biggest are (i) use of computers, and (ii) asymmetric cryptography, but through them all, the premise of mathematical advantage was an enduring constant.

And this is about to change. Alas, the profession behaves as it the new cryptography that renders mathematical talent irrelevant does not exist.

Dethroning mathematics from the practice of cryptography is such a showstopper, such a paradigm change that cryptographers instinctively embrace denial, look the other way, pretend it is not happening. Academic cryptographers spend their best years building up mathematical complexity to frustrate the opposing mathematician, or to crack the mathematical complexity presented as a challenge by an adversarial mathematician. If mathematical insight is no longer the name of the game then lifetime of efforts are no longer a credit. One should not expect academia to let go without a fight.

It is worse for national defense. From its inception the National Security Agency used a simple modus operandi: get the adversary to use ciphers that appear to serious cryptographers as hard and secure, while secretly cracking them and reading the enemy's mail. This strategy was based on building a pool of unmatched hidden mathematical talent that used its advantage to distinguish itself over its adversaries. The glorious (mostly still stealth) history of the NSA proves the efficacy of this smarter mathematician strategy. If math insight becomes irrelevant then the National Security Agency will have to recalibrate its operation, and find a replacement to its current winning strategy.

2.0 How did math lose its grip on cryptography?

What happened? All along mathematics worked with a partner: randomness: pattern-devoid data. It was a junior partner. Randomness was expressed through a known-size key drawn from a large but finite key space, subject to brute force cryptanalysis. Everything beside this key was pattern-bearing mathematical complexity. To generate an effective ciphertext from a given plaintext two ingredients were deployed: a pattern-devoid element (the randomized key), and a pattern-bearing element: the algorithmic construction, the non-randomized parameters.

[Ciphertext] = f[ Plaintext, Pattern-Devoid Ingredient, Pattern-Bearing ingredient ]

Historically the field evolved towards minimizing the pattern-devoid element (smaller keys), and boosting the pattern-bearing element (smart math). The smart math became the battlefield favoring the superior mathematician. Until recently it was difficult to secure a rich supply of high-quality randomness, but now with the migration to cyberspace maturing, it is getting very easy to use large quantities of high-quality randomness. (Advanced algorithms, complex physical contraptions, and quantum randomness).    Randomness is considered cyber oil, powering up cryptographic engines.   This new "oil" called for matching ciphers.  A new class of ciphers was steadily developed, aiming to minimize the pattern-bearing ingredient (the math), and maximize the pattern-devoid ingredient (the randomness). Math is vulnerable to a smarter mathematician; high-quality randomness voids the advantage of mathematical talent. By tipping the scales to generate ciphertext from pattern-devoid ingredient versus pattern-bearing ingredient, one decreases their cipher's vulnerability to an attacker smarter than they are.

The emerging new class is properly dubbed: pattern-devoid cryptography (PDC): ciphers designed to minimize pattern-bearing elements and maximize pattern-devoid elements. Typical PDC ciphers replace arbitrary specifics with random choices. They deploy randomized-size key.  Rather than using the full key for every instant of encryption, PDC ciphers select a random portion of the key, every time the key is used.  Rather than replace a given plaintext letter with a specified ciphertext letter, PDC ciphers use a randomized choice among ciphertext replacement options. Pattern devoid ciphers tend to be decoy-tolerant. A decoy tolerant cipher, DTC, allows the content-bearing bits of a ciphertext, to be mixed with noise -- contents-devoid bits, and generate a decoy ciphertext of randomized size. The recipient of the decoy ciphertext will readily discard the noise, and process only the contents-bearing bits, while an attacker will have to treat the entire decoy ciphertext as potentially content bearing. Decoy tolerant ciphers allow the transmitter to inject unilateral randomness, and do so to the degree deemed necessary, without pre-coordination with the recipient.

3.0 Innovating the Use of Randomness in Cryptography

The prevailing approach to randomness is to use a small key as shared randomness. In fact ciphers are being prioritized according to how small a key they can use for a given measure of security.  This approach ignores the inherent power of randomness to resist pattern-detection effort, since it offers no pattern to be detected.  One would then explore means to increase the role of randomness in the cryptographic operation, and decrease the cipher's vulnerability to a smarter mathematician. This leads to a new approach to the shared key. Today the key is kept small, and is used by its entirety each time the encryption algorithm is invoked. A vulnerable pattern.  Instead, one could keep the size of the key as a randomized selection without a preset limit, and further, each instant of encryption a randomized part of the key will be used.  Such open size key right away denies the attacker the option of brute force success because the open-size key may include parts that were not subject to the brute force attack, and only will show up later on. 

When weighing the role of randomness in cryptography it is incumbent on the analyst to cite the famous Vernam cipher where randomness is of the size of the message, but its efficacy is mathematically solid.  As Claude Shannon has famously proved, the Vernam ciphertext is mathematically invulnerable because any possible plaintext of the size of the ciphertext could have been the plaintext hidden by that ciphertext.  Come to think about it, Vernam is an overkill.  In every practical situation a ciphertext could represent a limited number n of plausible plaintexts. All that is needed is to inject a measure of randomness to cover these n plausible messages.  The transmitter is naturally aware of the field of plausible messages, and can therefore adjust the amount of randomness to keep every plausible message alive -- denying the cryptanalyst any advantage from capturing the ciphertext.

For this strategy of randomness-adjustment to work in full flexibility, it is necessary for the transmitter to be able to inject unilateral randomness, which was not pre-coordinated with the intended recipient.  Pattern devoid cryptography provides for such unilateral randomness to be readily applied.

The following figure highlights the innovative view of cryptographic randomness.

4.0  Fully Credentialed Pattern-Devoid Ciphers.

We discussed above some of the means used by pattern-devoid ciphers to void the advantage of mathematical insight. The specifics are readily available in a new peer-reviewed book, in the public record of some three dozen patents, and in other references, see below. The emphasis in this writing is on the fact that cryptography is reaching its biggest milestone ever, and the cryptographic establishment is not yet preparing itself to the new  era where math talent and advanced computing power is no longer the determining factor.

We see the signs of stealth use of pattern-devoid cryptography, mostly in China, Russia, Iran, Hamas. The horrifying strategic surprise pulled by Hamas against Israel on October 7, 2023 was so successful, as recently reported, because Hamas used the 'recommended' pattern-bearing ciphers to feed Israel with false misleading information, (assuming Israel's venerable cryptanalysis cracks them) while using unbreakable pattern-devoid cryptography to communicate war plans.

5.0 A Tale of One Die versus two Dice

The following tale sharpens the message. Alice and Bob are playing a game where each in turn is tossing two dice, and the other guesses the outcome between 2 and 12. Alice being mathematically smart she guesses 7 each time, Bob being not so smart, is guessing differently each time. They play several rounds each evening, and lo and behold Alice trounces Bob using her mathematical advantage. She knows that the chance for 7 is six times the chance for 12. Frustrated Bob introduces a small change to the game: tossing one die only. This tiny change voids the pattern-bearing element of the game, and constitutes it on pure randomness (pattern devoid ingredient). Immediately Alice loses her advantage, no matter what a great mathematician Alice, no matter how math-stupid Bob, Alice is no longer the predominant winner.

This level-playing field, this defanging of the NSA, is what is coming upon us, and we don't even talk about it. How will these days look to us in hindsight??

Reference

For the raw, detailed data regarding pattern-devoid cryptography please search for about 40 US patents, available online (Inventor: Gideon Samid).  For a thorough overview of pattern-devoid cryptography (PDC) please read the new peer-reviewed book,  chapter:

 

"Pattern Devoid Cryptography" https://www.intechopen.com/online-first/pattern-devoid-cryptography

   For later publications please peruse the least below:

Lifeboats on the Titanic Cryptography  https://eprint.iacr.org/2025/587

Transmitting Secrets by Transmitting only Plaintext. https://eprint.iacr.org/2025/438

"Tesla Cryptography:" Powering Up Security with Other Than Mathematical Complexity. https://eprint.iacr.org/2023/803

AI Resistant (AIR) Cryptography. https://eprint.iacr.org/2023/524

The Prospect of a New Cryptography: Extensive use of non-algorithmic randomness competes with mathematical complexity. https://eprint.iacr.org/2023/383

FAMILY KEY CRYPTOGRAPHY: Interchangeable Symmetric Keys; a Different Cryptographic Paradigm https://eprint.iacr.org/2021/458

Finite Key OTP Functionality: Ciphers That Hold Off Attackers Smarter Than Their Designers. https://eprint.iacr.org/2024/129

Polar Lattice Cryptography. https://eprint.iacr.org/2025/452

Cryptographic Key Exchange: An Innovation Outlook https://eprint.iacr.org/2023/1372

Randomness as Absence of Symmetry THE 17TH INTERNATIONAL CONFERENCE ON INFORMATION & KNOWLEDGE ENGINEERING (IKE'18: JULY 30 - AUGUST 2, 2018, LAS VEGAS, USA)

 NEPSAR: Secure Key Exchange https://www.bitmintalk.com/nepsar

Military and political implications of pattern-devoid cryptography are handled through a newly published fictional account "The Cipher Who Came in from the Cold". https://www.bitmintalk.com/thriller