Watch “BONUS LATTICE VIDEO 2” and “…3” (these appear at the end of the default listing order on canvas) which is about lattice-based cryptography, which we didn’t have time to cover in class. No need to hand in anything on canvas.
Click back through the daily posts for some important stuff:
Yesterday’s has announcements for FCQs and feedback form (please do these!)
This old one has info on last minute activities to improve your final grade. Email me with any questions.
Watch “BONUS LATTICE VIDEO 1” (these appear at the end of the default listing order on canvas) which is about lattice-based cryptography, which we didn’t have time to cover in class. No need to hand in anything on canvas.
Click back through the daily posts for some important stuff:
Yesterday’s has announcements for FCQs and feedback form (please do these!)
This old one has info on last minute activities to improve your final grade. Email me with any questions.
Please think about the following (also listed in the form above): “Ask me anything” What questions are you left with about cryptography? This is very broad: you can ask about current events, research, related topics, my experience, anything. I may have a little time left in class to use, and one option would be to answer these questions. If you tell me some questions now, I could research them a little. Feel free to email/DM these to me, or put them in the form above. (Don’t hand them in on canvas, I’ll notice them less immediately there.)
On Friday there will be a presentation by one of our expert graduate students on cryptography in real life (as it pertains to their research). Attendance is expected — please support our student presenters, in person if possible!
For the Hamming code example we used in the notes, i.e. with generating matrix $\begin{pmatrix} 1& 0 & 0 &0&1&1&0 \\ 0&1&0&0&1&0&1 \\ 0&0&1&0&0&1&1 \\ 0&0&0&1&1&1&1 \end{pmatrix}:
Write out the parity check matrix and check that the first row of the generating matrix is a codeword.
Suppose you receive the transmission 1000101. Determine the syndrome.
Determine the most likely codeword that was sent.
In class, I listed out 8 elements of the example cyclic code given, which lives in the ring $R = \mathbb{F}_2[x]/(x^7-1)$.
Write out all the 8 codewords we found in class, i.e. $g(x)x^k$ for various $k$.
I then pointed out that $g(x)(x^3 + x^2+1) = x^7-1$. Explain why this means that $g(x)f(x) = g(x)f_1(x)$ for some $f_1(x)$ of degree $2$ or lower.
How many elements of the ring $R$ of degree $\le 2$ are there?
Explain why the above means the elements we already found are all the elements of this code.
Consider the cyclic code generated by $g(x) = x^3 + 3x^2 + x + 6$ in the ring $R = \mathbb{F}_7[x]/(x^6-1)$.
Find a generating matrix.
What is the length of this code?
What dimension is this code?
What is the minimum distance of this code?
Divide $x^6-1$ by $g(x)$ (polynomial long division!)
Watch the video “AT HOME VIDEO: Linear codes (for Dec 4th, 2023)” on canvas (look toward bottom of gallery default listing order). The lecture notes are here. This video sums up what happened on the worksheet, and goes a little further, into syndrome decoding.
Here’s the worksheet and solutions. If you didn’t finish it, please work on it and compare to solutions.
I’ve placed a copy of Chapter 18 of Trappe and Washington’s book up on the main page of the canvas site as a PDF. It’s the chapter about Coding Theory that we will be following, so it’s a good accompaniment to our material.
In the dropbox please just hand in a copy of your self-eval sheet so I can see how we are doing.
Watch the video entitled “AT HOME VIDEO: Error correcting codes (for Dec 1, 2023)” in Canvas (it is at the bottom of the list of videos, not the top, in the default sort). The corresponding lecture notes are here. The video is around 45 minutes.
The above is preparation for an in-class worksheet we will do in class on Friday, so please prepare the material carefully. I will post the worksheet under the Archive tab at the time of class – there will be no zoom option.
Be aware that the quantum unit test will be on Wednesday, November 29th! We still have a little bit of material to cover on Monday. There are review problems and info on the test under Tests tab above.
There’s a bonus work for grade opportunity available due the last day of class. Information is on the Grading tab above.
I promised some written retakes for the first 3 modules. They are here, due by the final examination begin time. You are only eligible for one retake per test, which is in-person if you scored 6 or below or written if you scored 7 or above. If you did an in-person retake, you can’t do a written one, and vice versa. If you have missed your chance for an in-person retake, I’ll keep adding some slots to my appointment calendar (link on the main page in canvas) — contact me if you have questions.
Please fill in this poll (one question about your preferences for the rest of the course).
There are test review problems on the overleaf, Section 6.18. Do some of these to hand in.
We have almost made it to break, and almost made it to factoring with a quantum computer! Take heart! Friday’s class will cover Shor’s Algorithm and finish up the topic. If you are travelling, I’ll make sure it is available on zoom/canvas (but I do hope to have a few of you in class! 🙂
Daily exercises are given in Section 6.15 of the Overleaf notes.
Study the first three example problems in the Course Notes, “Quantum Gates Exercises” (currently Section 6.11). That means attempt the problems and compare to the solutions.
Do the rest of the problems that are posted there (that don’t have solutions) for handing in online.