Category: Books

Book: Flat and Curved Space Times

The first time I read this book was during my special relativity course at university. I couldn’t understand a thing the teacher was saying (probably because his explanations were always: “you won’t be able to understand that”) and I needed to replace a 35% grade I got in the first exam to complete the course.

Well, hopeless as I was, headed to the library in search of a magical book (other classmates were helpless as well) and found this one. The magic in it is that, instead of trying to force the Lorentz transformations down the throat first and then explain the basic principles of relativity, it does it by simply showing the topology of the space and assuming that the speed of light is constant (pretty much the same path Einstein took in the first place).

So, the first chapter has no equations whatsoever, only graphics with light waves going back and forth and he derives the light-cones automagically from it, what happens to the “world” at high speeds and how does it affect our senses of reality. It goes on for all kinematic principles only using Newton equations and gamma. Lorentz transformations only appear in the fourth chapter.

After that, not only I could understand relativity as a whole, but I also got 90% grade on the final exam! It’s an old (88) book but time has no meaning for a very good book, especially for a subject that hasn’t changed that much in the last decades.

I recommend it to physics-wannabe as well as lay people with little background in math, and if your teacher is as hopeless as mine was, ignore him and read this book.

Click here for the US version.

Book: Elementary Cryptanalysis: A Mathematical Approach

It’s quite difficult to write a book in cryptography today and not talk about RSA, DSA, keys and the internet. Some make the effort to write about a bit of history, information theory and the arcane cryptosystems, but so far I’ve only found small references just for the sake of having it.

If you don’t understand the basics, the advanced may sound right, but faint. If you don’t have a hands-on experience with the basic technics, you’ll never get quite right the more advanced stuff, that’s why I strongly recommend this book. It was written in the sixties with the intent to describe basic cryptanalysis that was already obsolete at that time, specially after the WWII when cryptanalysis was boosted to a new level.

The book always explain the concepts by examples. Every chapter have a encrypted text that needs decryption and then the author goes on through the theory and practice of solving it. As the theory is worked out together with the practice you won’t loose any important concept, what always happens in mathematical texts (minimal theory, one useless example and lots of exercises).

It’s organized in five parts, one for each basic cryptosystem: direct standard alphabet (caesar cipher, rot13), generic monoalphabetic substitution (linear transformations), polyalphabetic substitution, polygraphic systems (matrices) and transpositions. All of which are, somehow still used in advanced cryptography, so the knowledge of how it used to work in plain text will definitely give you important clues on how to understand even the Rijndael (a.k.a. AES) algorithm.

I’m also building a tool kit to help me checkpoint my work throughout the book.

You can find the book at Amazon UK following clicking in the picture:

For Amazon US and International, follow this link: Elementary Cryptanalysis: A Mathematical Approach