Secure Numerical and Logical Multi Party Operations

We derive algorithms for efficient secure numerical and logical operations using a recently introduced scheme for secure multi-party computation~\cite{sch15} in the semi-honest model ensuring statistical or perfect security. To derive our algorithms for trigonometric functions, we use basic mathematical laws in combination with properties of the additive encryption scheme in a novel way. For division and logarithm we use a new approach to compute a Taylor series at a fixed point for all numbers. All our logical operations such as comparisons and large fan-in AND gates are perfectly secure. Our empirical evaluation yields speed-ups of more than a factor of 100 for the evaluated operations compared to the state-of-the-art

On Oblivious Amplification of Coin-Tossing Protocols

We consider the problem of amplifying two-party coin-tossing protocols: given a protocol where it is possible to bias the common output by at most ?, we aim to obtain a new protocol where the output can be biased by at most ?* < ?. We rule out the existence of a natural type of amplifiers called oblivious amplifiers for every ?* < ?. Such amplifiers ignore the way that the underlying ?-bias protocol works and can only invoke an oracle that provides ?-bias bits. We provide two proofs of this impossibility. The first is by a reduction to the impossibility of deterministic randomness extraction from Santha-Vazirani sources. The second is a direct proof that is more general and also rules outs certain types of asymmetric amplification. In addition, it gives yet another proof for the Santha-Vazirani impossibility

Privacy-Preserving Quantum Two-Party Geometric Intersection

Privacy-preserving computational geometry is the research area on the intersection of the domains of secure multi-party computation (SMC) and computational geometry. As an important field, the privacy-preserving geometric intersection (PGI) problem is when each of the multiple parties has a private geometric graph and seeks to determine whether their graphs intersect or not without revealing their private information. In this study, through representing Alice's (Bob's) private geometric graph G_A (G_B) as the set of numbered grids S_A (S_B), an efficient privacy-preserving quantum two-party geometric intersection (PQGI) protocol is proposed. In the protocol, the oracle operation O_A (O_B) is firstly utilized to encode the private elements of S_A=(a_0, a_1, ..., a_(M-1)) (S_B=(b_0, b_1, ..., b_(N-1))) into the quantum states, and then the oracle operation O_f is applied to obtain a new quantum state which includes the XOR results between each element of S_A and S_B. Finally, the quantum counting is introduced to get the amount (t) of the states |a_i+b_j> equaling to |0>, and the intersection result can be obtained by judging t>0 or not. Compared with classical PGI protocols, our proposed protocol not only has higher security, but also holds lower communication complexity

Authentication of Quantum Messages

Authentication is a well-studied area of classical cryptography: a sender S and a receiver R sharing a classical private key want to exchange a classical message with the guarantee that the message has not been modified by any third party with control of the communication line. In this paper we define and investigate the authentication of messages composed of quantum states. Assuming S and R have access to an insecure quantum channel and share a private, classical random key, we provide a non-interactive scheme that enables S both to encrypt and to authenticate (with unconditional security) an m qubit message by encoding it into m+s qubits, where the failure probability decreases exponentially in the security parameter s. The classical private key is 2m+O(s) bits. To achieve this, we give a highly efficient protocol for testing the purity of shared EPR pairs. We also show that any scheme to authenticate quantum messages must also encrypt them. (In contrast, one can authenticate a classical message while leaving it publicly readable.) This has two important consequences: On one hand, it allows us to give a lower bound of 2m key bits for authenticating m qubits, which makes our protocol asymptotically optimal. On the other hand, we use it to show that digitally signing quantum states is impossible, even with only computational security.Comment: 22 pages, LaTeX, uses amssymb, latexsym, time