Hoffstein, Pipher, and Silverman provide a thorough treatment of the topics while keeping the material accessible. The book uses examples throughout the. Jeffrey Hoffstein (Author), Jill Pipher (Contributor), . Mathematical Cryptography (Undergraduate Texts in Mathematics) by Jeffrey Hoffstein Paperback $ An Introduction to Mathematical Cryptography. Jeffrey Hoffstein, Jill Pipher, Joseph H. Silverman. Springer-Verlag – Undergraduate Texts in Mathematics.
Taking the nth power of the Frobenius map and adding to it the endomorphism which simply multiplies elements by -1, one can show that the number of points of the elliptic curve is equal to the degree of this endomorphism. It arises when studying endomorphisms of elliptic curves of fields of non-zero characteristic, and involves defining rational functions.
Get to Know Us. It could have been included in the last chapter or possibly as a long exercise. One good example would be cryptography based on the mathematical theory of piphwr and braids the braid group is non-Abelianeven though this approach is in its infancy at the hoftstein time, and in almost all cases shown to be highly vulnerable to attacks.
Cryptography and Network Security: There was a problem filtering reviews right now. Suffice it to say that the strategy of Weil descent involves finding a cover of the elliptic curve by a hyperelliptic curve that is defined over the extension of the ground field.
Discover Prime Book Box for Kids. Get fast, free shipping with Amazon Prime. It really interferes with the reading process.
An Introduction to Mathematical Cryptography
The only hiccup was that I tried to work plpher the text example myself and came up with different answers. Customers who viewed this item also viewed.
The authors correctly don’t want to elaborate on Weil descent in any more detail, since it requires a solid knowledge of field extensions and theory of algebraic varieties at a level that one obtains in a graduate course in algebraic geometry. To me, this book is still the first-choice introduction to public-key cryptography. Showing of 18 reviews.
The book includes an extensive bibliography and index; supplementary materials are available online. Amazon Renewed Refurbished products with a warranty. The field of cryptography is vast of course, and a book of this size could not capture it effectively. Topics are well-motivated, and there are a good number of examples and nicely chosen exercises.
The students have expressed how much they get from the book. One of these items ships sooner than the other. The Frobenius map is not separable, and this fact allows one to show that its degree is strictly greater than the number of points in its kernel.
The book focuses on these key topics while developing the mathematical tools needed for the construction and security analysis of diverse cryptosystems. Only basic linear algebra is required of the reader; techniques from algebra, number theory, and probability are introduced and developed as required.
Add both to Cart Add both to List. Share your thoughts with other customers. AmazonGlobal Ship Orders Internationally. For more purely math books, this isn’t as large of an issue bec there are so many propositions and islverman that it’s easy to silvegman the back reference — but for this text, it is quite difficult. The distortion maps are used to define a modified Weyl pairing, which is proved to be non-degenerate.
Buy the selected items together This item: Undergraduate Texts in Mathematics Paperback: This is discussed very briefly in the last chapter, but the subject is mature enough to be presented at the undergraduate level. Amazon Restaurants Food delivery from local restaurants.
I highly recommend it. I hope that a revised version is issued that corrects these errata. The case where the characteristic is equal to 2 is delegated to its own section. Page 1 of 1 Start over Page 1 of 1. Please try again later. There’s a problem loading this menu right now. May sure you get it before starting to work through text examples and end-of-chapter exercises.
Some more of the highlights of this part of the book: Withoutabox Submit to Film Festivals. There is an extensive errata file that you can get online. Herstein LC to fully grasp all the related Math fundamentals. Read reviews that mention elliptic curves cryptography text math mathematical level class theory examples mathematics background introduction solid topics. Would you like to tell us about a lower price?
This self-contained introduction to modern cryptography emphasizes the mathematics behind the theory of public key cryptosystems and digital signature schemes.
Amazon Second Chance Pass it on, trade it in, give it a second life. This review is based on a reading of chapters pjpher and 8 of the book.
The proofs were no doubt omitted due to their dependence on techniques from algebraic geometry. The systems are described and important attacks on the mathematical underpinnings are given in detail. Just a few more arithmetical calculations establishes Hasse’s estimate. Topics are well motivated, and there are a good number of examples and nicely chosen exercises. The authors give an elementary overview of elliptic curves over the complex numbers, and most importantly over finite fields whose characteristic is greater than 3.