STEPS FORWARD: Math geniuses strive to make a pivotal advance — by obfuscating software code

By Byron V. Acohido

Most of time we take for granted the degree to which fundamental components of civilization are steeped in mathematics.

Everything from science and engineering to poetry and music rely on numeric calculations. Albert Einstein once observed that “pure mathematics is, in its way, the poetry of logical ideas.”

Related: How Multi Party Computation is disrupting encryption

An accomplished violinist, Einstein, no doubt, appreciated the symmetry of his metaphor. He was keenly aware of how an expressive Haydn symphony applied math principles in a musical context in much the same way has he did in deriving breakthrough physics theorems.

Math once more is being conjured to help civilization make a great leap forward. Digital technology, like music, is all about math. We’ve come a long way leveraging algorithms to deliver an amazing array of digital services over the past 30 years; yet so much more is possible.

Math is the linchpin to innovations that can dramatically improve the lives of billions of people, perhaps even save the planet. However, a quintessential math conundrum, is, for the moment, holding these anticipated advancements in check. The math community refers to this bottleneck as “indistinguishability obfuscation,” or iO.

Our top math geniuses point to iO as a cornerstone needed to unleash the full potential of artificially intelligent (AI) programs running across highly complex and dynamic cloud platforms, soon to be powered by quantum computers. Simply put, iO must be achieved in order to preserve privacy and security while tapping into the next generation of IT infrastructure.

I recently had the chance to discuss iO with Dr. Tatsuaki Okamoto, director of NTT Research’s Cryptography and Information Security (CIS) Lab, and Dr. Amit Sahai, professor of computer science at UCLA Samueli School of Engineering and director of UCLA Center for Encrypted Functionalities (CEF). NTT Research sponsored research led by Sahai that recently resulted in a achieving an important iO milestone.

For a full drill down on my discussion with Okamoto and Sahai, please give the accompanying podcast a listen. Here are a few key takeaways:

The security bottleneck

The next great leap forward in digital technologies will give us driverless ground transportation, green cities that continually optimize energy usage and self-improving medical treatments. It will, of course, be vital to have these next-gen, AI-infused systems run securely, in ways that preserve individual privacy.

Math can do this – and iO is the consensus solution, though at the moment it is a missing piece. To explain why this is so, Sahai drew an analogy to the human brain. Consider, he says, what would happen if a mind reader could, at any time, not only see everything stored in your brain but also had the power to tinker with your synapses and meddle with your critical thinking.

Now consider the software programs running digital services – they are the equivalent of human critical thinking. While it’s impossible to remotely access and tinker with a human brain, it’s currently trivial for a proficient hacker to remotely access and alter just about any piece of software coding.

This, in fact, is the core security challenge companies face defending their business networks. And the risk factors will only rise exponentially as reliance on cloud infrastructure and Internet of Things (IoT) systems accelerates. An intolerable security bottleneck, in fact, is taking shape. “Sending your program out to an untrusted cloud to be executed raises the stakes even more,” Sahai observes.

The math conundrum

This is where iO comes in — the notion of rendering software coding unintelligible while at the same time preserving its functionality. The scientific community first began theorizing about achieving iO in the 1970s. In the rarefied world of math geniuses, iO is viewed as an unsolved problem, something that typically takes decades to resolve.

The milestone achieved by Sahai’s team — which included Aayush Jain, a UCLA graduate student, and Huijia Rachel Lin, an associate professor at the University of Washington’s Paul G. Allen School of Computer Science & Engineering — puts us one step closer to a working iO prototype.

Sahai recently gave this presentation outlining the technical aspects.

My layman’s understanding is that Sahai’s team arrived at a construct that makes it not so trivial – in fact, virtually impossible – for a malicious party to remotely access and alter any piece of software coding.


“We are still at a very early stage here,” Sahai emphasized. “For the first time, we can prove that reverse engineering the software is as hard as solving certain standing conjectures in mathematics.”

This reminds me about a similar unsolvable problem that I’ve written about called homomorphic encryption. This a math construct for adapting a leading-edge form of cryptography that’s in a very early phase of commercial deployment.

Homomorphic encryption is the next step beyond encrypting data kept in storage (data at rest) as well as encrypting data as it is being transported from one server to another (data in transit.) It negates the need to ever have to decrypt data, thus enabling encrypted data to be accessed and utilized even while it’s at rest or in transit.

It wasn’t until 2008, after decades of theorizing, that an IBM researcher name Craig Gentry came up with a viable mathematical solution to do this. But it took massive processing power to make Gentry’s crude prototype work. And it would be another decade before the initial commercial prototypes of homomorphic encryption solutions emerged.

I asked Sahai if iO was now on a similar trajectory. “It could be that in just a couple of years maybe there’ll be an avalanche of breakthroughs following this one, or it could be another decade or two,” he replied. “We don’t know because that’s just the nature of basic research.”

While mathematicians shy away from speculation, the urgency to commercially deliver new tools that can deepen cybersecurity and reinforce privacy is palpable. Cloud and mobile computing continue to accelerate, fueled by our rising reliance on IoT systems and 5G networks. And the race is on to extend our dependence on automated AI-enabled services, soon to be souped up by quantum computers.

It is in this heady environment that Tokyo-based telecom giant NTT Corp chose to open the doors of NTT Research in Silicon Valley in July 2019 and immediately begin recruiting top scientists and researchers, like Sahai and his collaborators.  NTT endowed its new U.S. think tank with a portion of its $3.6 billion R&D budget and gave it wide leeway.


“Our labs only conduct basic research,” Okamoto told me. “We do not require any contributions to any of NTT’s business. We focus on basic research.”

Prior to this research breakthrough in collaboration with NTT Research, Sahai had been hammering away at iO for more than 20 years. “Finally, we were able to make this amazing progress with a project that was two years in the making,” he says.

The future benefits

NTT Research has other irons in the fire. In short order it has landed a passel of top scientists and has underwritten a wide range of studies on quantum computing, neuro-science, photonics, cryptographic, blockchain, information security and healthcare informatics.

For instance, basic research led by Dr. Robert L. Byer, the former Dean of Research at Stanford University, could support the eventual deployment of a specialized quantum computer, called a Coherent Ising Machine, designed to efficiently solve ultra-complex operational problems.

 “Every day last year, three thousand aircraft took off and landed along the Eastern seaboard of the United States,” Byer noted at a recent panel discussion. “Suppose a hurricane rolls in and you have to now cancel a large fraction of those flights. One of the problems you’d love to solve would be, ‘What is the optimum way to restart the system and get it back online with . . . best use of your aircraft. That’s the type of problem that these specialty quantum computers can solve.”

 Another exciting NTT Research project is headed by Dr. Joe Alexander the former medical director at pharmaceutical giant Pfizer. Alexander now heads up studies to advance “digital twin” technology, focusing on eventual deployment of a virtual human heart. The idea is that the digital twin heart could receive and process bio data, in real time, to optimize healthcare.

“What we aim to do is to create a digital replica, a kind of electronic version of everything that’s known about an individual physiology, pathophysiology, genomics, poly-omics and lifestyle behaviors so that we have an actual electronic copy of that person,” Alexander said at the panel discussion. “Now as that person lives and grows and experiences some illnesses, we want to bring in all of that information into the digital twin, making use of physiologically-based models, as well as a data-driven models . . . to have a copy of that person so that we can actually do predictive health maintenance.”

Basic research like this is so vital. It both contributes to — and provides a preview glimpse of — an exciting future in which the full potential of digital transformation becomes realized. Math is the tool that will enable this all to unfold in ways that are as secure and private as they need to be. iO’s traction over the next few of years will tell us a lot.  I’ll keep watch – and keep reporting.


Pulitzer Prize-winning business journalist Byron V. Acohido is dedicated to fostering public awareness about how to make the Internet as private and secure as it ought to be.

(LW provides consulting services to the vendors we cover.)

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