Grading takes a lot of time… sorry, but I'm hoping to wrap up tonight
Assignment 3
Coming up
Midterm
Tuesday October 17, 2023
In class, with notes (no electronic notes)
Covering Homework 1 & 2
Office hours on Friday October 13, 2023 11am
Office hours on Monday October 16, 2023 11am
Last time
A cool new result: Privacy amplification
Today
More Privacy amplification
Glimpse of information theory and security
Applications to random number generation
Ultrafast random number generation
(c) Nature Publishing Group
Ido Kanter et al., An optical ultrafast random bit generator, Nature Photonics, (2010)
The generation of random bit sequences based on non-deterministic physical mechanisms is of paramount importance for cryptography and secure communications.
We present a physical random bit generator, based on a chaotic semiconductor laser, having time-delayed self-feedback, which operates reliably at rates up to 300 Gbit/s.
The randomness of long bit strings is verified by standard statistical tests.
Chaotic laser intensity fluctuations digitized at a 20 GHz sampling rate with an 8-bit resolution
How much true randomness can we generate?
Privacy amplification
Privacy amplification model
A code for privacy amplification coding a discrete memoryless source against side information consists of an encoding function .
The performance of an code is measured in terms of
The rate of the code (bits/source symbol)
The secrecy and uniformity of measured as
where is the uniform distribution on
Privacy amplification
Define again
For a discrete memoryless source ,
Achievability
Consider a generic source and a generic channel with .
For , let
For each , let be a bin index drawn independently with uniform distribution on .