By Luther Martin
If you are seeking to absolutely comprehend and successfully enforce identity-based encryption (IBE) expertise, this authoritative source is a great selection. formerly, info on IBE have merely been present in bulky, hard-to-follow magazine articles and convention lawsuits. this is often the 1st publication to provide you whole, easy-to-understand information at the topic. evaluating and contrasting IBE with conventional public-key applied sciences, the publication essentially explains how and why IBE structures are safe. you discover a wealth of sensible ideas, algorithms and various labored examples that provide help to create a safe IBE method.
From simple mathematical techniques and homes, homes of elliptic curves, divisors and the Tate pairing, and cryptography and computational complexity, to similar cryptographic algorithms, a variety of IBE schemes, hierarchical IBE and grasp mystery making plans, and calculating pairings, this entire quantity serves as a transparent consultant to this more and more vital safeguard expertise. This hands-on quantity contains specific pseudocode for identity-based encryption algorithms and aiding algorithms that aid prevent time and simplify your tough initiatives within the box.
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Extra info for Introduction to Identity-Based Encryption (Information Security and Privacy Series)
The multiplicative inverse of 3 is not an integer, for example. (iii) The natural numbers ގunder addition are not a group because the natural numbers lack an additive identity, that is, 0 ∈ ގ. (iv) The nonzero real numbers under multiplication form a group. In this case, the real number 1 acts as the identity element. (v) ޚn is a group under addition but may not be a group under multiplication; ޚn is a group under multiplication if and only if n is prime. 2 is a group. In this group, every element is its own inverse.
We have that G = 〈2〉, and that the discrete (ii) In the group G = (ޚ11 9 logarithm of 6 ≡ 2 (mod 11) to the base 2 is 9. In some cases, we will have two groups that behave exactly the same way, but are labeled differently in some way. In a trivial case, we could write one version of the integers in an italic font and another version in bold font and notice that these two versions behave exactly the same way if we ignore this slight difference. So while we could not add an italic 2 to a bold font 2, for example, we can easily map the two sets to each other by making the necessary font change.
15 A group (G, *) with the additional property that a * b = b * a for all a and b in G is called an Abelian group. 15 (i) The integers under addition are an Abelian group. (ii) The set of all 2 × 2 invertible matrices with real entries is a group under matrix multiplication, but not an Abelian group because matrix multiplication is not commutative. If a group is Abelian we often write the group operation as + instead of and using + to denote a group operation is usually reserved for Abelian groups.