Cryptography after alien landing

The author of the article: Bruce Schneier is an American cryptographer, writer and computer security specialist. He is the author of several books on security, cryptography and information security. The founder of the cryptographic company Counterpane Internet Security, Inc., a member of the Board of Directors of the International Association of Cryptological Research and a member of the advisory board of the Electronic Privacy Information Center.

Quantum computing is a new way of making calculations that will allow humanity to perform calculations simply impossible with the use of modern computers. The quick search capability will break some of the modern encryption algorithms. A light factorization of large numbers will break the RSA cryptosystem with any key length.

That is why cryptographers are now intensively developing and analyzing "quantum-stable" algorithms with a public key. Currently, quantum computing is not yet ready for a normal assessment: what is safe and what is not. But if we assume that aliens have developed the technology in full, then quantum computing is not the end of the world for cryptography. For symmetric cryptography, quantum stability is elementary, and now we are looking for quantum-stable encryption algorithms with a public key. If public key cryptography turns out to be a temporary anomaly that exists due to gaps in our mathematical knowledge and computational abilities, we will still survive. And if some unthinkable alien technology breaks all cryptography, we will have secrecy based on the theory of information, albeit with significant loss of opportunities.

The Grover algorithm shows that a quantum computer accelerates attacks so much that the effective length of the key is halved. That is, a 256-bit key is also complex for a quantum computer, like a 128-bit key for a conventional computer: both are safe in the foreseeable future.

For cryptography with a public key, the results are worse. Shore's algorithm easily breaks all popular algorithms with a public key, based both on factorization and on discrete logarithm. Doubling the length of the key increases the hacking complexity by eight times. This is not enough for sustainable development.

There are a lot of reservations about the last two paragraphs, the main one being that quantum computers capable of doing something like that do not exist at the moment, and no one knows when we will be able to build such a one - and whether we can do it at all. We also do not know what practical difficulties will arise when we try to implement the Grover or Shore algorithms on anything other than toy-sized keys (the error correction mechanism on a quantum computer can easily become an insurmountable problem). On the other hand, we do not know what other methods will be discovered once people start working with real quantum computers. I put on the fact that we will overcome engineering problems, and that there will be many achievements and new methods, but it will take time to invent them. Just as it took us decades to design pocket supercomputers, it would take decades to work through all of the engineering problems needed to build powerful quantum computers.

In the short term, cryptographers make significant efforts to develop and analyze quantum-stable algorithms. Probably, they will remain safe for decades. The process will certainly go slowly, because good cryptanalysis takes time. Fortunately, we have time. Real quantum computations in practice seem to always be "ten years in the future." In other words, no one has the slightest idea.

But there is always the possibility that aliens with the best quantum technologies will crack the algorithms. I'm less worried about symmetric cryptography, where the Grover algorithm is in fact the maximum limit of the possibility of quantum computing. But public-key algorithms based on number theory seem more fragile. It is possible that quantum computers will sometime break them all - even those that are now considered quantum-stable.

If this happens, we will remain in a world without public key cryptography. This will be a huge security impact and will break many systems, but we will be able to adapt. In the 1980s, Kerberos was a completely symmetric authentication and encryption system. And now GSM cellular communication standard performs both authentication and key distribution - on a large scale - only with symmetric cryptography. Yes, these systems have centralized points of trust and denial, but other systems that use both secret sharing and secret sharing can be developed to minimize this risk. (Imagine a pair of communication participants receiving a portion of the session key from each of the five different key servers). The ubiquitous spread of communications makes the situation easier. We can use out-of-band protocols: for example, your phone will help generate a key for the computer. For added security, you can use personal registration: perhaps in a store where you buy a smartphone or register an Internet service. The development of hardware will also help protect the keys in this world. I do not try to invent anything, only I say that there are many possibilities. We know that cryptography is based on trust, and we have much more methods of managing trust than in the early years of the Internet. Some important technologies, such as direct privacy, will become much more complicated, but while symmetric cryptography works, we will continue to have protection.

This is a strange future. Perhaps the whole idea of cryptography on number theory, like modern systems with a public key, is a temporary phenomenon that exists due to gaps in the computation model. Now that the model has expanded and included quantum computation, we can end up where we were in the late 1970s and early 1980s: symmetric cryptography, code-based cryptography, and Merkle's signatures. It will be funny and ironic.

Yes, I know that the distribution of quantum keys is a potential substitute for public key cryptography. But let's be honest: does anyone even believe that a system that requires specialized communications equipment and cables will be used for anything other than niche applications? The future is for mobile, constantly enabled computing devices. All security systems for them will be only software.

There is one more scenario of the future, not to mention quantum computers. At the heart of one-way functions lie several mathematical theories, which have not yet been proved. This is one of the open problems in computer science. Just as a smart cryptographer can find a new trick that makes it easy to crack a particular algorithm, we can imagine aliens with sufficient mathematical theory to break all the encryption algorithms. For us today, it's just ridiculous. Public-key cryptography is number theory, potentially vulnerable to mathematically more intelligent aliens. Symmetric cryptography is so nonlinearly complex, and the length of the key is so easily increased that the future is difficult to imagine. Imagine an AES option with a 512-bit block and key size, and 128-round encryption. Unless we come up with a fundamentally new mathematics, such encryption will be safe until computers do something other than matter, in some other dimension.

But if unthinkable happens, then there will be cryptography based solely on information theory: one-time notebooks and their variants. It will be a huge blow for safety. Disposable notebooks can be theoretically safe, but in practice they are not suitable for anything other than specialized niche applications. Today, only psychics are trying to build common-use systems based on one-time notebooks - and cryptographers laugh at them because they replace the problems of developing algorithms (easy) with key management and physical security problems (which is much, much more difficult). Perhaps in our fantastic future, engulfed by aliens, we will have only such an exit.

Against these godlike aliens, cryptography will remain the only technology in which we can be sure. Nuclear bombs can not explode, and fighters can fall from the sky, but we can still communicate safely using one-time notepads. There is a certain optimism in this.

It may be interesting

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Author**22-09-2018, 08:28**

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#### Mathematics / Cryptography / Information Security

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