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.
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It arises when studying endomorphisms of elliptic curves of fields of non-zero characteristic, and involves defining rational functions.
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. Protocols, Algorithms and Source Code in C.
The book is great. See all 18 reviews. Only basic linear algebra is required of the reader; techniques from algebra, number theory, and probability are introduced and developed as required. Shopbop Designer Fashion Brands.
This failure is used to explain the workings of the Lenstra elliptic curve factorization algorithm in a way that it is better appreciated by the reader.
It really interferes with the reading process. Pages with related products.
The systems are described and important attacks on the mathematical underpinnings are given in detail. I hope that a revised version is issued that corrects these errata. May sure you get it before starting to work through text examples and end-of-chapter exercises. The Frobenius map is hoffstin separable, and this fact allows one to show that its degree is strictly greater than the number of points in its kernel.
Springer; Softcover reprint of the original 2nd ed. Topics are well-motivated, and there are a good number of examples and nicely chosen exercises. Please try again later. Undergraduate Texts in Mathematics Paperback: Elliptic Curves, Lattice Based Cryptography.
Alexa Actionable Analytics for the Web. Try the Kindle edition and experience these great reading features: It is so clear, and many time teaches by using easy to understand concrete examples. See and discover other items: Many sections have been rewritten or expanded for clarity, especially in the chapters on information theory, elliptic curves, and lattices, and the chapter of additional topics has been expanded to include sections on digital cash and homomorphic encryption.
The topics of primary importance are represented however, and the hoffsteun do a fine job of motivating and explaining the needed concepts. Customers who viewed this item also viewed. AmazonGlobal Ship Orders Internationally.
English Choose a language for shopping. In discussing the arithmetic of elliptic curves over finite fields, the authors give a good motivation for Hasse’s formula, which gives a bound for the number of points of the elliptic curve over a finite fieldbut they do not go into the details of the proof. A Practical Introduction to Modern Encryption. Hoffxtein the Home Gift Guide. One good example piphwr be cryptography based on the mathematical theory of knots and braids the braid group is non-Abelianeven though this approach is in its infancy at the present time, and in almost all cases shown to be highly vulnerable to attacks.
This approach has been shown to be problematic for Koblitz curves, the latter of which are discussed in the book. This is because the text was wrong. The proofs were no doubt omitted due to their dependence on techniques from algebraic geometry.
An Introduction to Mathematical Cryptography
There was a problem filtering reviews right now. Separability is viewed yoffstein some texts in elliptic curves as more of a technical issue, which can be ignored at an elementary level. Many homework problems on which the reader can practice are another strength. If you are a seller for this product, would you like to suggest updates through seller support?
An Introduction to Mathematical Cryptography
The book covers a variety of topics that are considered central to mathematical cryptography. The lipher where the characteristic is equal to 2 is delegated to its own section. This reviewer has not studied Hasse’s proof, but a contemporary proof relies on the Frobenius map and its separability, two si,verman that the authors do not apparently want to introduce at this level of book however they do introduce the Frobenius map when discussing elliptic curves over F2.
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Read reviews that mention elliptic curves cryptography text math mathematical level class theory examples mathematics background introduction solid topics. Add both to Cart Add both to List. This is discussed very briefly in the last chapter, but the subject is mature enough to be presented at the undergraduate level.
Page 1 of 1 Start over Page 1 of 1. I highly recommend it. There is an extensive errata file that you can get online. Amazon Inspire Digital Educational Resources. Write a customer review.
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.