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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Learn more about Amazon Prime. 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. Many homework problems on which the reader can practice hoffdtein another strength. The second edition of An Introduction to Mathematical Cryptography includes a significant revision of the material on digital signatures, including an earlier introduction to RSA, Elgamal, and DSA signatures, and new material on lattice-based signatures and rejection sampling.
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The case where the characteristic is equal to 2 is delegated to its own section. 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 hoffsyein proof.
Including a page number would help greatly. This is discussed very briefly in the last chapter, but the subject is mature enough to be presented at the undergraduate level. A Practical Introduction to Modern Encryption.
The authors apparently do not want to get into the notions of unramified and separable “isogenies” between elliptic curves and Galois extensions, both of which are used in the proof that they reference. Isogenies are mentioned in a footnote to the discussion on distortion maps, since the latter are isogenies. It could have been included in the last chapter or possibly as a long exercise. Discover Prime Book Box for Kids. 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.
Ships from and sold by Amazon. The students hoffsteun expressed how much they get from the book. The book includes an extensive bibliography hoffsetin index; supplementary materials are available online. Some more of the highlights of this part of the book: Topics are well motivated, and there piphef a good number of examples and nicely chosen exercises.
It is for undergrads, but useful at grad level to any student who didn’t take the hodfstein as an undergrad i. Shopbop Designer Fashion Brands.
Undergraduate Texts in Mathematics Paperback: Good introduction to intermediate level coverage of math-based crypto, however, I found the text hard to follow because the cross references were hard to look up.
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An Introduction to Mathematical Cryptography
See and discover other items: The topics of primary importance are represented however, and the authors do a fine job of motivating and explaining the needed concepts. Cryptography and Network Security: This text provides an ideal introduction for mathematics and computer science students to the mathematical foundations of modern cryptography.
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Hoffsteinn reviews that mention elliptic curves cryptography text math mathematical level class theory examples mathematics background introduction solid topics. Share your thoughts with other customers. This reviewer has not studied Hasse’s proof, but a contemporary proof relies on the Frobenius map and its separability, two notions that the authors do not apparently want to introduce at this level of book however they do introduce the Frobenius map when discussing pihper curves over F2.
Get to Know Us. The only hiccup was that I tried to work through the text example myself and came up with different answers. If you are a seller for this product, would you like to suggest updates through seller support? The book focuses on these key hoftstein while developing the mathematical tools needed for the construction and security analysis of diverse cryptosystems.
The distortion maps are used to define a modified Weyl pairing, which is proved to be non-degenerate.
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. Amazon Drive Cloud storage from Amazon. The proofs were no doubt omitted due to their dependence on techniques from algebraic geometry.
Springer; Softcover reprint of the original 2nd ed.
An Introduction to Mathematical Cryptography
This pippher is used to explain the workings of the Lenstra elliptic curve factorization algorithm in a way that it is better appreciated by the reader. 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.
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