Category Archives: Math

The secrets of RSA encryption

When clicking on the padlock in the address bar of an internet session, a window appears with the message: “Safari uses an encrypted connection with …”. [red. this message may look slightly different for other browsers]

After pressing the buttons ‘Show certificate’ and ‘detail’, a lot more is shown. The typically used security algorithm nowadays at most news sites etc. at the opening session is: public key with elliptic curve.

But for the sites where security really is an issue, e.g. a login session into your bank account or a large online store, RSA is the encryption algorithm. And RSA encryption is the subject of my contribution this time. Continue reading →

P vs NP – A promise fulfilled

P versus NP – An early encounter

My first programming experience was in the early 80’s. I had bought myself a Texas instruments 58-c programmable calculator, and I was curious what could be done with such a device. That turned out to be very modest.
The calculator was capable of 480 program steps but held then zero memories for data storage. Each memory used for data consumed 8 program steps, so with the storage of e.g. 10 integers, the programming space was diminished with 80 steps.
The 58-c’s memory was retained even after switching off the calculator, but before creating another program, memory first had to be erased. Continue reading →

Graham’s number

In the 2nd or 3rd grade of my catholic primary school our teacher spoke of stuff like ‘God’
and ‘Heaven’.
“People live in Heaven after their death,” she told us. “All eternity.”
Nobody knew what eternity was, so she had to explain.
“Eternity,” she said, “never ends. “The years go on forever.”
Apparently she saw her pupils struggling with this concept and that made her tell us a
story. Continue reading →

Mathematical issues

Some remarkable mathematical issues

Although the Dutch newspapers Volkskrant and NRC can be blamed for being too political (D66) biased to be independent as journals ought to be, it must be said that both have excellent science sections.
On an irregular base even topics of mathematical nature have been published.

Of course for a layman’s audience, mathematics lacks the ability of other science disciplines of being easily visualized.
So the topics in these sections were about trivial stuff like the latest calculated decimals of π or some large regions on the number line without any prime number called prime deserts, a newly found Mersenne number, etc.
But that hardly scratches the surface. Continue reading →

Cantor’s Continuum Hypothesis

One of the most important mathematical objects is the set with its many useful properties. We can look at the size of the set by wondering how many members it embraces. The answer obviously can be found by counting them.
Then we can take another set and compare its size with the first one, again by counting the members. We call this size the cardinality of the set. Continue reading →