15-853Page 1 COMPSCI 290.2: Computer Security “Quantum Cryptography” Including Quantum Communication Quantum Computing

Quantum Communication NOT used to encrypt data! (so not really cryptography) Goal, instead, is to detect eavesdroppers Could be used to distribute a private key (could also add extra security for transmitting encrypted data) Page 2

15-853Page 3 Uncertainty Principle In quantum mechanics, certain pairs of properties of particles cannot both be known simultaneously, e.g., –Position and momentum of an electron (Heisenberg) If a measurement determines (with precision) the value of one of the properties, then the value of the other cannot be known

Photon Spin (Polarization) Photons can be given either “rectilinear’’ or “diagonal’’ spin as they travel down a fiber. Rectilinear: or Diagonal: or Measuring rectilinear spin with a rectilinear filter yields polarization of photon Page 4 blocked

15-853Page 5 What if the wrong filter is used? (equal probability) or measure diagonal measure rectilinear destroys state

15-853Page 6 Quantum Key Exchange 1.Alice sends Bob photon stream randomly polarized in one of 4 polarizations: 2.Bob measures photons in random orientations e.g.: x + + x x x + x (orientations used) \ | - \ / / - \ (measured polarizations) and tells Alice in the open what orientations he used, but not what he measured. 3.Alice tells Bob in the open which are correct 4.Bob and Alice keep the correct values Susceptible to a man-in-the-middle attack

Detecting an Eavesdropper Alice and Bob now confirm that they have received the same private key. How could they do this? Page 7

15-853Page 8 In the “real world” In April 2014 China began installing a kilometer quantum communications link between Beijing and Shanghai

Quantum Computers The state of a computer consists of the contents of its memory and storage, including values of registers (including the program counter), memory, disk contents, etc. In a conventional computer each memory “unit” holds one value at a time. Computation consists of a sequence of state transitions. But in a quantum computer, a memory unit holds “superposituion” of possible values Page 9

Qubit A single quantum “bit” which is 1 with probability p and 0 with probability 1-p. Multiple qubits exhibit “quantum entanglement”. Suppose two bits have value 00 with probability ½ and 11 with probability ½. If the bits are separated and measured at different locations, the measurements must yield the same values. A qubit could be implemented using a photon to carry a horizontal or vertical polarization Page 10

Factoring Large Primes In 1994 Peter Shor showed that a quantum computer can factor a number n in O(log 3 n) time. A similar result holds for solving the discrete logarithm problem. If a large-enough quantum computer can be built, then RSA and Diffie-Hellman key-exchange will no longer be secure Page 11

Controversial Quantum Computer D-Wave Systems, Inc., purports to build a quantum computer based on a 128-qubit chipset. No convincing demonstration of speed-up over conventional computer yet. Unresolved debate about whether there is actually quantum entanglement among the qubits. (Evidence seems to be leaning towards yes?) Page 12