Friday , June 22, 2018

Refining Asymmetric Encryption

A handful of arcane mathematicians way back in the 18th and 19th centuries aspired to invent a useless mathematical theory that would shine for its beauty alone, unstained by practical applications. It was called number theory, and it stood useless and shining until late in the 20th Century, when this very same math became the foundation of modern e-commerce.

Today, this “useless math” is churning in millions of computational sessions an hour, every day, year after year. To understand why, consider the problem of privacy between complete strangers. Two parties in cyberspace require mutual encryption to communicate confidentially. Alas, encryption requires a shared secret key. That means that when a stranger surfs into a cyberstore, she cannot use encryption because she and the store never met and exchanged a secret key. If you exchange the key online, you allow cyber thieves to listen in.

It was an intellectual feat to achieve privacy between two strangers. You can learn in the Crypto Academy ( how the RSA team, Diffie Hellman and Ralph Merkle, devised a creative means to establish privacy and confidentiality online. These means are based on that old and “useless” number theory, and without these intellectual achievements there would have been no open and free trade in cyberspace.

Unfortunately, even many security professionals do not realize that these methods to achieve confidentiality between strangers, while indeed establishing private communication channels, do so without identifying who is connected  (confidentially) to whom.

Alice may think she has established privacy with Bob because he has called himself Bob, but in fact he is Jerry, and Alice doesn’t know—and this fancy math will not tell her. In fact, Alice will turn down the real Bob, should he show up later, because she regards Jerry as Bob.

This subtle point is how hackers practice their trade. Some hackers convince our bank they are us, and other hackers convince us that they are our bank. The lock icon on our screen snaps to “secure” mode, and it is hard to remember that it comes with no guarantee against identity theft.

Overnight almost, this so called asymmetric encryption has mushroomed into countless protocols. They are the foundation of all those “certificates of authority.” The new exciting form of money, bitcoin, owes its existence to this very same esoteric math.

Another cardinal fact that virtually no one suspects is that we are not at all sure that this arcane math is as secure as we hope it is. Imagine that one day “combination locks” show up on the market. One expert lockpick checks them out, finds no keyhole, and pronounces the locks unbreakable. Along comes a street-smart thief, who quickly figures out the right combination by sound and picks the lock. It’s the same for these asymmetric locks. Several cryptographers tried to crack them, and when they failed they pronounced them safe. Are they? Would you deposit your family fortunes in bitcoin?

Many of the myriad chips in our computers are manufactured by Intel and benefit from Intel reliability. By contrast, ciphers are described in books, and every shop, every programmer, programs in assumed obedience. Alas, every programmer can introduce changes, sneak out a copy of the secret data, or otherwise enable a compromise. Implementation vulnerability is different from mathematical vulnerability. The latter is global, the former is local.

What’s to come? As asymmetric cryptography plays an increasing role in our cyberlife, its reliability and simplicity will have to increase, too. Cyber identification will also improve dramatically and become based on more and more randomized dialogues.

The battle between identity verifiers and identity thieves will continue with mixed results into the foreseeable future. For that reason, society should pursue its inevitable progress towards digital money, disengaging payment from payor identification, except in circumstances where money-laundering considerations prevail.

For now, however, our blind trust in asymmetric cryptography blunts our drive to prepare for ugly and costly surprises. Few security manuals, for example, properly address the tedium of recovery. I well recall how one client listened patiently to my “day after” presentation, then waved me off while saying, “I’ll take the chance this won’t happen on my watch!”

—Gideon Samid •

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