Joshua Holden: Quantum cryptography is unbreakable. So is human ingenuity

Two basic types of encryption schemes are used on the internet today. One, known as symmetric-key cryptography, follows the same pattern that people have been using to send secret messages for thousands of years. If Alice wants to send Bob a secret message, they start by getting together somewhere they can’t be overheard and agree on a secret key; later, when they are separated, they can use this key to send messages that Eve the eavesdropper can’t understand even if she overhears them. This is the sort of encryption used when you set up an online account with your neighbourhood bank; you and your bank already know private information about each other, and use that information to set up a secret password to protect your messages.

The second scheme is called public-key cryptography, and it was invented only in the 1970s. As the name suggests, these are systems where Alice and Bob agree on their key, or part of it, by exchanging only public information. This is incredibly useful in modern electronic commerce: if you want to send your credit card number safely over the internet to Amazon, for instance, you don’t want to have to drive to their headquarters to have a secret meeting first. Public-key systems rely on the fact that some mathematical processes seem to be easy to do, but difficult to undo. For example, for Alice to take two large whole numbers and multiply them is relatively easy; for Eve to take the result and recover the original numbers seems much harder.

Public-key cryptography was invented by researchers at the Government Communications Headquarters (GCHQ) – the British equivalent (more or less) of the US National Security Agency (NSA) – who wanted to protect communications between a large number of people in a security organisation. Their work was classified, and the British government neither used it nor allowed it to be released to the public. The idea of electronic commerce apparently never occurred to them. A few years later, academic researchers at Stanford and MIT rediscovered public-key systems. This time they were thinking about the benefits that widespread cryptography could bring to everyday people, not least the ability to do business over computers.

Now cryptographers think that a new kind of computer based on quantum physics could make public-key cryptography insecure. Bits in a normal computer are either 0 or 1. Quantum physics allows bits to be in a superposition of 0 and 1, in the same way that Schrödinger’s cat can be in a superposition of alive and dead states. This sometimes lets quantum computers explore possibilities more quickly than normal computers. While no one has yet built a quantum computer capable of solving problems of nontrivial size (unless they kept it secret), over the past 20 years, researchers have started figuring out how to write programs for such computers and predict that, once built, quantum computers will quickly solve ‘hidden subgroup problems’. Since all public-key systems currently rely on variations of these problems, they could, in theory, be broken by a quantum computer.

Cryptographers aren’t just giving up, however. They’re exploring replacements for the current systems, in two principal ways. One deploys quantum-resistant ciphers, which are ways to encrypt messages using current computers but without involving hidden subgroup problems. Thus they seem to be safe against code-breakers using quantum computers. The other idea is to make truly quantum ciphers. These would ‘fight quantum with quantum’, using the same quantum physics that could allow us to build quantum computers to protect against quantum-computational attacks. Progress is being made in both areas, but both require more research, which is currently being done at universities and other institutions around the world.

Yet some government agencies still want to restrict or control research into cryptographic security. They argue that if everyone in the world has strong cryptography, then terrorists, kidnappers and child pornographers will be able to make plans that law enforcement and national security personnel can’t penetrate.

But that’s not really true. What is true is that pretty much anyone can get hold of software that, when used properly, is secure against any publicly known attacks. The key here is ‘when used properly’. In reality, hardly any system is always used properly. And when terrorists or criminals use a system incorrectly even once, that can allow an experienced codebreaker working for the government to read all the messages sent with that system. Law enforcement and national security personnel can put those messages together with information gathered in other ways – surveillance, confidential informants, analysis of metadata and transmission characteristics, etc – and still have a potent tool against wrongdoers.

In his essay ‘A Few Words on Secret Writing’ (1841), Edgar Allan Poe wrote: ‘[I]t may be roundly asserted that human ingenuity cannot concoct a cipher which human ingenuity cannot resolve.’ In theory, he has been proven wrong: when executed properly under the proper conditions, techniques such as quantum cryptography are secure against any possible attack by Eve. In real-life situations, however, Poe was undoubtedly right. Every time an ‘unbreakable’ system has been put into actual use, some sort of unexpected mischance eventually has given Eve an opportunity to break it. Conversely, whenever it has seemed that Eve has irretrievably gained the upper hand, Alice and Bob have found a clever way to get back in the game. I am convinced of one thing: if society does not give ‘human ingenuity’ as much room to flourish as we can manage, we will all be poorer for it.Aeon counter – do not remove

Joshua Holden is professor of mathematics at the Rose-Hulman Institute of Technology and the author of The Mathematics of Secrets.

This article was originally published at Aeon and has been republished under Creative Commons.

David Alan Grier: The Light of Computation

by David Alan Grier

When one figure steps into the light, others can be seen in the reflected glow. The movie Hidden Figures has brought a little light to the contributions of NASA’s human computers. Women such as Katherine Goble Johnson and her colleagues of the West Area Computers supported the manned space program by doing hours of repetitive, detailed orbital calculations. These women were not the first mathematical workers to toil in the obscurity of organized scientific calculation. The history of organized computing groups can be traced back to the 17th century, when a French astronomer convinced three friends to help him calculate the date that Halley’s comet would return to view. Like Johnson, few human computers have received any recognition for their labors. For many, only their families appreciated the work that they did. For some, not even their closest relatives knew of their role in the scientific community.

GrierMy grandmother confessed her training as a human computer only at the very end of her life. At one dinner, she laid her fork on the table and expressed regret that she had never used calculus. Since none of us believed that she had gone to college, we dismissed the remark and moved the conversation in a different direction. Only after her passing did I find the college records that confirmed she had taken a degree in mathematics from the University of Michigan in 1921. The illumination from those records showed that she was not alone. Half of the twelve mathematics majors in her class were women. Five of those six had been employed as human computers or statistical clerks.

By 1921, organized human computing was fairly common in industrialized countries. The governments of the United States, Germany, France, Great Britain, Japan, and Russia supported groups that did calculations for nautical almanacs, national surveys, agricultural statistics, weapons testing, and weather prediction. The British Association for the Advancement of Science operated a computing group. So did the Harvard Observatory, Iowa State University, and the University of Indiana. One school, University College London, published a periodical for these groups, Tracts for Computers.

While many of these human computers were women, most were not. Computation was considered to be a form of clerical work, which was still a career dominated by men. However, human computers tended to be individuals who faced economic or social barriers to their careers. These barriers prevented them from becoming a scientist or engineer in spite of their talents. In the book When Computers Were Human, I characterized them as “Blacks, women, Irish, Jews and the merely poor.” One of the most prominent computing groups of the 20th century, the Mathematical Tables Project, hired only the impoverished. It operated during the Great Depression and recruited its 450 computers from New York City’s unemployment rolls.

During its 10 years of operations, the Math Tables Project toiled in obscurity. Only a few members of the scientific community recognized its contributions. Hans Bethe asked the group to do the calculations for a paper that he was writing in the physics of the sun. The engineer Philip Morse brought problems from his colleagues at MIT. The pioneering computer scientist John von Neumann asked the group to test a new mathematical optimization technique after he was unable to test it on the new ENIAC computer. However, most scientists maintained a distance between themselves and the Mathematical Tables Project. One member of the Academy of Science explained his reservations about the Project with an argument that came to be known as the Computational Syllogism. Scientists, he argued, are successful people. The poor, he asserted, are not successful. Therefore, he concluded, the poor cannot be scientists and hence should not be employed in computation.

Like the human computers of NASA, the Mathematical Tables Project had a brief moment in the spotlight. In 1964, the leader of the Project, Gertrude Blanch, received a Federal Woman’s Award from President Lyndon Johnson for her contributions to the United States Government. Yet, her light did not shine far enough to bring recognition to the 20 members of the Math Tables Project who published a book, later that year, on the methods of scientific computing. The volume became one of the most highly sold scientific books in history. Nonetheless, few people knew that it was written by former human computers.

The attention to Katherine Goble Johnson is welcome because it reminds us that science is a community endeavor. When we recognize the authors of scientific articles, or applaud the distinguished men and women who receive Nobel Prizes (or in the case of computer science, Turing Medals) we often fail to see the community members that were essential to the scientific work. At least in Hidden Figures, they receive a little of the reflected light.

David Alan Grier is the author of When Computers Were Human. He writes “Global Code” for Computer magazine and products the podcast “How We Manage Stuff.” He can be reached at