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Review of Session 2007-2008 PRIZE LECTURES Security, Insecurity, Paranoia and Quantum Mechanics .................................. 46 New Antibiotics from the Sea Bed to the Hospital Bed .................................. 64 100 Years of Radio Astronomy: Past, Present and Future ............................... 69 Fuelling the Fire: On How Obesity Fuels D isease.............................................................................................................. 74 Mind, Matter and Mathematics ..................................................................... 79 45 Review of the Session 2007-2008 James Scott Prize Lecture Security, Insecurity, Paranoia and Quantum Mechanics Stephen M. Barnett SUPA, Department of Physics, University of Strathclyde 4 February 2008 The James Scott Prize Lectureship was established in 1918 in memory of James Scott, a farmer at East Pittendreich, near Brechin, by the Trustees of his Bequest. This prize is awarded quadrennially for a lecture on the fundamental concepts of Natural Philosophy. This year’s award goes to Professor Stephen Barnett FRS FRSE, who is based in the Department of Physics at the University of Strathclyde. Professor Barnett is one of the world’s most eminent scientists in the field of Quantum Optics. A previous winner of the Institute of Physics’ Maxwell Medal, he is perhaps best known for his co-discovery of the Barnett-Pegg phase operator. This established the first formally correct approach for handling both angles and phase as descriptions within quantum systems. Still within quantum physics, Professor Barnett holds a number of patents relating to techniques for writing unbreakable codes. For a subject that is potentially beyond most people’s understanding, Professor Barnett is well known for presenting the counter-commonsense implications of quantum mechanics in an accessible and entertaining way, stripping the subject of its supporting mathematics and leaving only the essence of pure ideas. 46 Prize and Bequest Lectures 1. Preamble Nearly all of you will carry an ATM card and use it to access your money via a bank autoteller machine. To get at your money you require the card and a “secret” PIN (personal identification number) which is usually four digits long. This PIN protects the machine, in that it establishes your identity. The machine, of course, only gives you money. It is sobering to realise that ATM fraud netts thieves in excess of £100 million each year in the UK alone. Some of you attending this lecture will have been victims of this. We are all familiar with the concept of computer hacking, whereby individuals use the internet to obtain unauthorised access to computers. It may be some comfort to discover that even the greatest are not immune. The following excerpts are from an article by Damian Whitforth in The Times, February 16th 2000: President Clinton had an astonishing confession to make. “Personally” he said, “I would like to see more porn on the internet”. … … Mr Clinton had given his first live online interview to CNN, which was confident that it had the technology to stop interference with its website for the duration. Instead, pranksters had a field day, posting ribald remarks that were attributed to Mr Clinton and asking impertinent questions. 2. Secure communications At the heart of information security is the communications problem. If we can live without communications then we can greatly increase security by physical isolation. On the other hand, if we can communicate securely then we can spend our (electronic) money and exchange information safely. The simplest and oldest method of secure communication is single key cryptography. The concept is to lock away our message in a strong box (too strong to break) and to send the box to our intended recipient. If they have a copy of the key used to lock the box then they can open it and retrieve the message. This is a good moment to introduce our cast of characters: the person transmitting a message is universally called “Alice” and her intended recipient is called “Bob”. The third character, whom we’ll meet shortly, is “Eve” the eavesdropper. The secrecy of single 47 Review of the Session 2007-2008 key cryptography relies crucially on the secrecy of the key, the only copies of which must be held by Alice and Bob and, of course, these two keys need to be identical. In practice there is no box but rather the message is enciphered using a secret key in the form of a piece of information. In the digital world, all messages are just a string of zeros and ones (… 00010010100100010001011 …) and so can be thought of simply as a (large) number. The key will be another number and the cipher text is produced by a mathematical operation on these two numbers. The vital question, of course: “is it secure?”. Perfect security can be achieved using the Vernam cipher, or one-time pad. For this to work we require Alice and Bob to share a secret key in the form of a random number that is the same length (has the same number of binary digits or bits) as the message they wish to share. The cryptogram, or ciphertext, is generated by bit- wise addition modulo 2, which we denote ⊕. This means that for each digit if the message and key bits are the same (both 0 or both 1) then the ciphertext is 0, but if they are different then it is 1. A simple example may clarify the point: message 011010001 … key 101001001 … ⊕ ciphertext 110011000 … All that Bob needs to do is to repeat the operation with his copy of the key: ciphertext 110011000 … key 101001001 … ⊕ message 011010001 … The method is completely secure if the key is truly secret and, crucially, is used only once. This secrecy is a consequence of the fact that the key is a random number and it necessarily follows, therefore, that the ciphertext is also a random number. There are two difficulties with the one-time pad: first we need to establish a secret key with our (distant) correspondent and second that we need to use large numbers of very long keys for even the most straightforward secure communications. Maybe there is a simpler way? Let us return to the locked-box concept and suppose 48 Prize and Bequest Lectures that the box has not one lock but two, one of which fits a key held only by Alice and the other that fits a key held only by Bob. Alice can put the message in the box, secure her lock and send the box to Bob who secures his lock and returns the box (now double-locked). Alice can undo her lock and return the box to Bob who can unlock it and retrieve the message (M). The box makes three journeys and is always closed, so surely it is secure? Let us see what happens if Alice and Bob each used their own key (KA and KB ) in an arrangement similar to the one-time pad. Alice locks the case M ⊕ KA = C1 Bob locks the case C1 ⊕ KB = M ⊕ KA ⊕ KB = C2 Alice unlocks the case C2 ⊕ KA = M ⊕ K/ A ⊕ KB ⊕ K/ A = C3 Bob unlocks the case C3 ⊕ KB = M At first sight these seems to be secure, as Eve has access only to the three random ciphertexts C1, C2 and C3. The modulo 2 sum of these three ciphertexts, however, reveals the original message without difficulty: C1 ⊕ C2 ⊕ C3 = M and so Eve, who has access to the transmitted ciphertexts, can retrieve the message. The underlying problem with this scheme is the simplicity of the operation corresponding to modulo addition. A protocol, due to Diffie and Hellman, does indeed work with multiple exchanges in the way suggested but relies, for its security, on the subtleties of modulo arithmetic. We shall not discuss it here, but note that it is closely related to the RSA public key cryptosystem, which we shall discuss shortly. The second difficulty associated with the one-time pad was the large number of very long keys needed to achieve perfect security. What we need is a method for achieving practical security; something that is good enough. A published and officially approved method is the data encryption standard or DES (or better, the advanced encryption standard – AES). This combines our message and a very much shorter key, usually 56 or 128 bits, in a sequence of mathematical operations to produce a ciphertext. Bob can easily convert the ciphertext back into the original message by Bob, using his copy of the key. The DES scheme is not perfectly secure 49 Review of the Session 2007-2008 and can be broken by a determined Eve with access to lots of computer power. The question then is “how long will this take?”. We might try to break it using an exhaustive key search; try every possible key until we find a meaningful message. If we had a 40 bit key then the number of possible keys is 240 ≈1012. If we had a machine capable of a million decryption operations a second then this would take about 6 days. Better algorithms exist, however, and security agencies have admitted to being able to crack 40 bit DES in under one hour. If we increase the length of the key then we greatly increase the number of possible keys. If we use a 128 bit key then the number of possible keys jumps to 2128 =1038. An exhaustive search on the machine described above would then take about 1024 years. But better algorithms do exist so … A radically different idea is public-key cryptography, in which no pre- arranged secret key is required. We can understand the principle by considering again the analogy of a locked box. In public key cryptography the box has only one lock but the keys required to lock and unlock it are different.
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