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- Published on Amazon.com
When you look at some of the most expensive books on Amazon, they are usually proceedings of conferences on very narrow topics that contain state of the art information on that niche. Often they are also published by Springer!
This little gem is somewhat of an exception. It is NOT a conference piece, but does use individual, expert authors to write each article, and each article DOES have numerous pages of supporting research papers, albeit mostly from the late 1990s and early 2000's.
Since "quantum computing" (QC) (a theoretical field, since quantum computers probably won't be actually built for at least 10 years or more) is applied to the hardness of encryption schemes in this book, you've got to add another 15 to 20 years to actually "assume" that QC can break a block cipher or hash table that's presently (relatively) intractable to classical computing. This is because cryptanalysts can't "prove" a negative-- that this or that system can or can't be broken by QC-- except by watching the research results of penetration trial, error and research.
I mean, practically, DES, and even relatively high rounds of AES, have already been broken with classical computing! This has taken over 30 years in the case of DES, and speculation in this volume is that QC will greatly speed up this process. That's the bottom line: this is an outstanding book of speculation-- looking at where QC is and isn't effective via theoretical QC algorithms alone (given no quantum machines to try them on yet). Most of this speculation will be irrelevant when and if real superpositioning machines are built. The interesting thing about cryptography is that the non deterministic probability cloud results of QC become deterministic-- because we either break the cipher or don't!
The math in this volume is grad to post grad, and although most of the symbology is in cryptography diagrammatic and equation form, the underlying subjects (which are not shown mathematically, but referred to the underlying research articles) do include the most advanced math behind state of the art crypto such as lattices, HSP, Factoring and discrete logs, linear algebra, Pell's equation, Graph isomorphism, and advanced analytic geometry, including elliptical encryption algorithms.
So, who should buy this book? The marketing material says "students" but that would mean, in my estimate, an advanced grad student specializing in QC. If you're a researcher, the bibliographies themselves might be worth the steep price of this small volume, but realize that these are 2003, not 2013 articles.
On the "get it" side-- there are very few (like, none?) treatments of this topic in book form, so if you're into saving time and don't do a lot of article reading, the web sites mentioned in the bibs are being kept up to date, and for that reason alone, you won't go wrong investing in this collection of articles. Just go in realizing that most of what's being written here is highly speculative due to the nature of crypto itself, which relies on researchers and hackers to let us know what is and isn't hard, not "proofs." The "truth" behind the speculation in this book is 25 to 30 years out. If you can live with that, enjoy this little technical journey across many aspects of QC as applied to Cryptography, with theoretical QC algorithms that have no machines to run on today.
If you're relatively new to Crypto, don't forget the industry analogy that good crypto is like putting a vault door on a tent-- hackers look for the weakest link, and this holds with or without QC. The average script kiddie, or even professional perp (possibly NOT including terrorist nations, or Moscow University), won't have access to QC in most of our lifetimes, but that doesn't mean that other areas of the tent aren't fair game! The authors recommend that we start NOW to prepare for QC, since crypto systems take a long time to develop and can last a long time, but I'm not sure that "securing" with speculative systems like lattices, that don't yet have practical implementations, is any more possible than actually breaking a hard math construct with QC.
For a good overview of Quantum Computing, if you are up on your linear algebra, check out: Quantum Computing: A Gentle Introduction (Scientific and Engineering Computation). If you need a great review OF linear algebra prior to taking on QC, check out the high cost/value ratio of: Linear Algebra.