The book commences by introducing the fundamental concept of a bit, examining its essence both from an algebraic perspective and a practical standpoint. It proceeds to expound upon various structures derived from bits, including polynomials, vectors, and multivariate polynomials. In the subsequent chapter, bytes are introduced, emphasizing the contrast between their formal algebraic definition and their practical utilization in computer science. The discussion delves into the elucidation of (vectorial) Boolean functions, which formally describe algorithms generating bits. Essentially, whenever an algorithm operates on bits as input and output, it fundamentally computes a Boolean function.
Moving to the third chapter, the book delves into algebraic concepts closely intertwined with bytes, hence referred to as ‘friends’. This section focuses on the fundamental properties of numbers and primes pertinent to public-key cryptography. Secure cryptosystems rely on underlying mathematical problems that are intrinsically hard to solve, and number theory offers numerous such examples, such as integer factorization. Concluding with the final chapter, the book outlines several cryptosystems, providing a link to the preceding chapters. While the primary focus isn’t cryptography, these cryptographic systems can captivate and motivate curious readers. Targeted at students unacquainted with abstract mathematics, the book employs an elementary expository style, replete with examples, straightforward applications, and a plethora of exercises designed to facilitate the reader’s progress assessment.
