Customer Reviews

BigNum Math: Implementing Cryptographic Multiple Precision Arithmetic

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As the author of this book is correct when he says that multiple-precision arithmetic is essential for cryptography, and of course this book would not have been written if this were not the case. The languages of usual choice for cryptography, namely Java and C, support only single precision arithmetic and integer values too small for effective encryption. To obtain larger values that are necessary for cryptography, one must use special data structures, and the author has developed these and put them in the public domain. The trick to using his approach, along with those developed by other researchers is to design the algorithms and data structures so as to optimize memory, as the latter can be very restricted, especially in embedded systems.

The C data structure that the author constructs and uses throughout the book is called `mp_int' and consists of a dynamically allocated array of digits representing the multiple-precision integer. This data structure also elements that denote how many digits of the array contain the digits used to represent the integer at hand. The author gives the pseudocode and the explicit algorithm for initializing and deallocating mp_int. In fact, throughout the book the author writes down the explicit C code for every algorithm he discusses. This reviewer did not attempt to run any of the code and so cannot speak to its efficacy in real applications or devices. The book was therefore read attentively but not with the intent of using any of the algorithms in the book.

The book however has much more than just C code, as the author discusses many of the details behind each algorithm, many of these taken for granted even by professional cryptographers and professional applied mathematicians, who sometimes forget about some of the difficulties in actual implementation. The standard operations of mathematics, and also modular arithmetic are discussed in detail, with the author putting particular emphasis on the features of his approach that depart from some familiar algorithms, such as the algorithm for adding two multiple-precision integers. Of particular interest, and of enormous practical interest, is the discussion on fast multiplication, such as the Comba method, and Karatsuba multiplication.

I am a coder and to be honest I am somewhat afraid of crypto becasue of the heavy math needed. I have used LibTomCrypt so I thought a book by the same guy could no be bad. The book progressed at a perfect pace for following along if you are not a math genius and even provide code sample tests that allow you to apply what you have learned. I would suggest this book to anyone who wants to know more but doesn't have time for college classes.