We have seen the problems in the US elections, and where if one partner (eg Donald Trump) doesn’t think the election is fair, they could declare the election as null and void. This is not good for trust. And so, in our elections, we rely on witnesses to prove that votes have been cast correctly, and where it is unlikely that someone who is defrauding the system will be able to do so in front of witnesses to their votes. We also do this when we are signing a document, and where we must gather witnesses to our signature. The more witnesses we can gain, the likely less chance our signature will be fake. …
We live in a digitally flaw world. Very little of what we see can be truly trusted. But there are some people who have strived to make our world more trusted, and Michael O. Rabin is one of the most predominant. He was born in 1931 in Germany. In the 1960s he worked in the University of California and MIT, and then moved onto a Professorship at Harvard University. Finally, in 1981, he became a professor at the Hebrew University, and has worked there ever since.
Miller-Rabin Test for Primes is one of the most popular methods for testing for prime numbers used in RSA. Given an odd number (n), we will have an odd number of (n−1), of which we can calculate the power of 2 with a value of s so…
As a reviewer for a journal, I receive many papers that go on for many pages and are full of references. But in the end, you often worry about whether the paper is just manufactured to look like a research paper, or whether it has some real contributions. Often you feel that the author could have just said what the wanted to in just a few pages. Merkle’s classic patent on Merkle trees was just a few pages long, for example, but it has since become the foundation of blockchain technology. I read many classic papers from the past, and they would probably struggle to get past the first review, as they don’t follow the current standard for research papers. …
Bitcoin was a 5pm to 3am job?
Next week I give one of my favourite lectures of the year, and where I outline how blockchains are created and in the application of cryptocurrencies. For me, it is just a way of showing a future which is based on trusted tokens, and where public-key encryption is used to make everything trustworthy. And, of course, I start the lecture with the story of Satoshi Nakamoto and the mystery about who he actually was. And it’s a story too about Hal Finney.
So this week new work shed more light on Satoshi with an analysis around the Wayback Machine on Bitcointalk posts, emails, code commits, and related data…
A Mersenne prime is in the form of 2^S−1. Known Mersenne prime numbers are 2³−1, 2⁵−1, 2⁷−1, 2¹³−1, 2¹⁷−1, 2¹⁹−1, 2³¹−1, 2⁶¹−1, 2⁸⁹−1, 2¹⁰⁷−1 and 2¹²⁷−1. Overall Mersenne primes are efficient in their implementation. This article outlines the the Lucas-Lehmer test to test for a Mersenne prime number. A fast elliptic curve name FourQ uses a prime of 2¹²⁷-1:
Lucas-Lehmer Test
The Lucas–Lehmer test (LLT) is used to test for the primality of Mersenne numbers. It was initally created Edouard Lucas and then enhanced by Derrick Hentry Lehmer. For this test, we initially define u_0=0 and we calculate:
u_{k+1}=(u_k²−2)(mod n)
If u_{s−2}=0 then it is a prime number. Here are some Mersenne…
I just loving analysing data, and finding trends. As a lad, I would continually draw league tables and calculate averages. I have never lost this love, and I still analyse trends and forecasts wherever I can.
So, after watching Scotland doing so well away from home, and in seeing Scottish teams winning away from home in European matches, it is becoming obvious that home advantage doesn’t have much of an affect in football. The main difference must be the crowd.
So, I wanted to prove this, and surprising the statistics show no real advantage to one team or another. I thus looked at the Scottish Premier League for 2019–2020, and the current league. For SPL home wins, in 2019–2020, I found that there were 44% home wins, against 30% away wins. …
Better Teaching Does
In government circles, there is a feeling that the more you invest in research at university level, the higher the quality of the teaching will be. Personally, I see no such link, in that high-quality researchers often buy themselves out of teaching, and where universities can put their resources into research rather than teaching. There is also no guarantee that what you invest in, in your research, will filter through into teaching.
From what I see too, there is good and not so good research that is undertaken, and, in some cases, the linkage between research topics and the topics that need to be taught to students is perhaps not always as strong as it could be. The UK, perhaps, his heading to a two-tier system of academics who are research-active or teaching-active, and the days of the great teacher who is highly research-active are perhaps receding. …
Well, if Bob sends out the same message to Alice, Carol, Dave and Trent
There’s a feeling that RSA is a 100% secure method, but it is in no way a perfect method, and it sometimes needs to be treating with care when implement with it. Dan Shumow, for example, recently found a major problem in the way that the keys are created [here]:
I love reading classic patents, and [here] is a classic that was submitted by Brickwell, Gordon, and McCurley. It was patent number 5,299,262 and was assigned to the United States of America:
For us, we need researchers who can code. The industry increasingly needs people who can code and script, so sometime soon we will have to create a workforce that does not run away from coding and sees it as natural as using a spread. Excel has been our friend for decades, but it is becoming cumbersome in a world of open-source dataset and machine learning. It is a package that has hardly changed over the years, and still basically remains the same as it did all those years ago.
So how are we going to do this? Setup kids at school with Linux virtual desktops and get then to use vi to edit their code? No. It’s much easier than this. Let’s them use Jupyter Notebooks for their key lessons, and they will start to code naturally. A few lessons on Python as a start, and then integrate it with Maths, Physical, Biology, and anywhere else there is the need to solve things, draw graphs, and, in fact, anything that has tutorial/lab work. …
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