@article {1883, title = {Robust Protocols for Securely Expanding Randomness and Distributing Keys Using Untrusted Quantum Devices}, journal = {Journal of the ACM}, volume = {63}, year = {2016}, month = {2016/10/26}, pages = {33:1{\textendash}33:63}, abstract = {

Randomness is a vital resource for modern-day information processing, especially for cryptography. A wide range of applications critically rely on abundant, high-quality random numbers generated securely. Here, we show how to expand a random seed at an exponential rate without trusting the underlying quantum devices. Our approach is secure against the most general adversaries, and has the following new features: cryptographic level of security, tolerating a constant level of imprecision in devices, requiring only unit size quantum memory (for each device component) in an honest implementation, and allowing a large natural class of constructions for the protocol. In conjunction with a recent work by Chung et al. [2014], it also leads to robust unbounded expansion using just 2 multipart devices. When adapted for distributing cryptographic keys, our method achieves, for the first time, exponential expansion combined with cryptographic security and noise tolerance. The proof proceeds by showing that the R{\'e}nyi divergence of the outputs of the protocol (for a specific bounding operator) decreases linearly as the protocol iterates. At the heart of the proof are a new uncertainty principle on quantum measurements and a method for simulating trusted measurements with untrusted devices.

}, keywords = {key distribution, nonlocal games, privacy, quantum cryptography, random-number generation, untrusted device}, issn = {0004-5411}, doi = {10.1145/2885493}, url = {http://doi.acm.org/10.1145/2885493}, author = {Carl Miller and Yaoyun Shi} } @inbook {1863, title = {Optimal robust self-testing by binary nonlocal XOR games}, booktitle = {8th Conference on the Theory of Quantum Computation, Communication and Cryptography, TQC 2013}, volume = {22}, year = {2013}, pages = {254{\textendash}262}, publisher = {Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing}, organization = {Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing}, abstract = {

Self-testing a quantum apparatus means verifying the existence of a certain quantum state as well as the effect of the associated measuring devices based only on the statistics of the measurement outcomes. Robust (i.e., error-tolerant) self-testing quantum apparatuses are critical building blocks for quantum cryptographic protocols that rely on imperfect or untrusted devices. We devise a general scheme for proving optimal robust self-testing properties for tests based on nonlocal binary XOR games. We offer some simplified proofs of known results on self-testing, and also prove some new results.

}, keywords = {nonlocal games, quantum cryptography, Random number generation, Self-testing}, doi = {10.4230/LIPIcs.TQC.2013.254}, author = {Carl Miller and Yaoyun Shi} }