@article {1982, title = {Randomness in nonlocal games between mistrustful players}, journal = {Quantum Information and Computation}, volume = {17}, year = {2017}, month = {2017/06/15}, pages = {0595-0610}, abstract = {

If two quantum players at a nonlocal game G achieve a superclassical score, then their measurement outcomes must be at least partially random from the perspective of any third player. This is the basis for device-independent quantum cryptography. In this paper we address a related question: does a superclassical score at G guarantee that one player has created randomness from the perspective of the other player? We show that for complete-support games, the answer is yes: even if the second player is given the first player\&$\#$39;s input at the conclusion of the game, he cannot perfectly recover her output. Thus some amount of local randomness (i.e., randomness possessed by only one player) is always obtained when randomness is certified from nonlocal games with quantum strategies. This is in contrast to non-signaling game strategies, which may produce global randomness without any local randomness. We discuss potential implications for cryptographic protocols between mistrustful parties.

}, url = {https://arxiv.org/abs/1706.04984}, author = {Carl Miller and Yaoyun Shi} } @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} }