Quantum Cryptography and Side Channel Attacks Suppose we have two individuals who wish to establish secure communication, Alice and Bob. While Alice and Bob are physically separated, they are connected by a single optical fiber cable. They also have access to ordinary, unsecured classical communication channels (such as the Internet). 1. Alice creates randomly polarized photons and sends them to Bob As the first step, Alice creates a long sequence of qubits in the form of randomly polarized photons. When modeled as a two-state quantum system, photon polarization consists of two quantum states that form a complete orthogonal basis spanning the two-dimensional Hilbert space. A common pair of basis states is horizontal (|Hi = |0i) and vertical (|V i = |1i). Through superposition, two additional orthogonal states can be created (non-orthogonal to H and V ): the diagonal (|Di) and antidiagonal (|Ai). Those states are defined as: (1) (2) So, prior to creating each photon qubit, Alice chooses a random polarization basis (HV or AD). She records this information. Then, she creates the photon with a random polarization state within that basis. She also records this polarization state and its associated bit value. Note that upon measurement |Hi and |Di correspond to bit 0 and |V i and |Ai correspond to bit 1. Thus, each photon that Alice creates has a random polarization state with a 25% probability of being |Hi, |V i, |Ai, or |Di. She then transmits the qubit to Bob via their optical fiber cable. 2. Bob receives the qubits from Alice and measures them Upon receiving the photons from Alice, Bob measures their polarization states to begin the process of creating a secret key. As follows from the basic principles of quantum mechanics, the basis that Bob uses for his measurements will affect their outcome. For each photon that Bob receives, he randomly chooses either the HV or AD basis, and performs the measurement. He records his basis choices and measurement results in the form of random bits. 3. Alice and Bob compare results As the final step in the BB84 protocol, Alice and Bob indirectly compare their random bits to obtain a sifted key. Alice announces to Bob over an insecure classical channel her random basis choices while keeping secret her state choices. Bob looks at his basis choices, and tells Alice which photons had Alice and Bob choosing the same basis, and which had a basis mismatch. Bob communicates this information to Alice over the insecure classical channel, keeping secret his measurement outcomes. Alice and Bob then agree to keeping measurements when their measurement basis matched, and discarding all other measurements. This step is significant because in keeping only the photons for which Bob knows he used the same basis as Alice, he can be certain that the random bit resulting from his measurement is exactly the same random bit that Alice obtained when randomly choosing a polarization state prior to photon transmission, due to the nature of quantum measurement. So the BB84 protocol allows Alice and Bob to create two sets of sifted keys of random bits that they know are identical just by comparing basis choices so that their actual random bits remain secret. As a result, Alice and Bob now share a string of random bits that they can use as their secret key for the proved-secure one-time pad procedure as discussed earlier. Note that the one-time pad also works with strings of random bits [9, 12]. Suppose Alice uses an encoding system to convert her secret alphanumerical message to the binary string "10111001." The secret key that she shares with Bob might be "11001101." She performs bitwise modulo-2 sum (XOR) with her message and the HKN.ORG 21http://www.HKN.ORG

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