I just bought John D. Barrow’s „Ein Himmel voller Zahlen“ („Pi in the Sky“) because I thought it might be interesting to a mathematician. I don’t know yet, if it is, but the reference section is amazing.
However, I started reading chapter 4 about Intuitionism, which is something that fascinates me. For some reason yet undiscovered by me, the chapter has a section about trapdoor functions. To say it blankly, the mathematics in this section are so simplified that they become useless.
I hate simplifications like this! Some teachers like to fake that everything is easy. At first sight, students are very happy with this „approach“. But, once the students start thinking and taking a closer look, they find out that they have not understood anything. As Einstein said it: „Make things as simple as possible, but not simpler!“.
The section proposes the following public encryption method. The message M is encrypted with a large prime number, and the product MP is sent by A to B, where P is another prime number. Then MPQ is sent back from B to A with the third prime number. A divides that by P, and sends MQ to B, who divides by Q to get the message M.
Of course, this will not work at all. First any observer of this communication knows MP, MPQ, and MQ. Thus, he knows P and then M! Moreover, after sending MP and getting MPQ, A will know Q and thus the key of B. It would be better to send MQ right away next time. It just does not work in this simplified way.
Moreover, it would be easier to XOR instead of multiply, and work just the same way, without the mystification with „large prime numbers“.
I might continue reading this book. But I have lost my trust, definitely.