Maciej Obremski

Divesh Aggarwal, Eldon Chung, Maciej Obremski

The known constructions of negligible error (non-malleable) two-source extractors can be broadly classified in three categories: (1) Constructions where one source has min-entropy rate about $1/2$, the other source can have small min-entropy rate, but the extractor doesn't guarantee non-malleability. (2) Constructions where one source is uniform, and the other can have small min-entropy rate, and the extractor guarantees non-malleability when the uniform source is tampered. (3) Constructions where both sources have entropy rate very close to $1$ and the extractor guarantees non-malleability against the tampering of both sources. We introduce a new notion of collision resistant extractors and in using it we obtain a strong two source non-malleable extractor where we require the first source to have $0.8$ entropy rate and the other source can have min-entropy polylogarithmic in the length of the source. We show how the above extractor can be applied to obtain a non-malleable extractor with output rate $\frac 1 2$, which is optimal. We also show how, by using our extractor and extending the known protocol, one can obtain a privacy amplification secure against memory tampering where the size of the secret output is almost optimal.

Divesh Aggarwal, Naresh Goud Boddu, Rahul Jain et al.

Multi-source-extractors are functions that extract uniform randomness from multiple (weak) sources of randomness. Quantum multi-source-extractors were considered by Kasher and Kempe (for the quantum-independent-adversary and the quantum-bounded-storage-adversary), Chung, Li and Wu (for the general-entangled-adversary) and Arnon-Friedman, Portmann and Scholz (for the quantum-Markov-adversary). One of the main objectives of this work is to unify all the existing quantum multi-source adversary models. We propose two new models of adversaries: 1) the quantum-measurement-adversary (qm-adv), which generates side-information using entanglement and on post-measurement and 2) the quantum-communication-adversary (qc-adv), which generates side-information using entanglement and communication between multiple sources. We show that, 1. qm-adv is the strongest adversary among all the known adversaries, in the sense that the side-information of all other adversaries can be generated by qm-adv. 2. The (generalized) inner-product function (in fact a general class of two-wise independent functions) continues to work as a good extractor against qm-adv with matching parameters as that of Chor and Goldreich. 3. A non-malleable-extractor proposed by Li (against classical-adversaries) continues to be secure against quantum side-information. This result implies a non-malleable-extractor result of Aggarwal, Chung, Lin and Vidick with uniform seed. We strengthen their result via a completely different proof to make the non-malleable-extractor of Li secure against quantum side-information even when the seed is not uniform. 4. A modification (working with weak sources instead of uniform sources) of the Dodis and Wichs protocol for privacy-amplification is secure against active quantum adversaries. This strengthens on a recent result due to Aggarwal, Chung, Lin and Vidick which uses uniform sources.