By Luther Martin
Identity-based encryption (IBE) is a brand new expertise that enables the id of clients for use as cryptographic keys rather than the lengthy, random strings of bits that previous applied sciences required. this permits for the production of cryptographic platforms which are as safe as conventional structures, yet are a lot less complicated and more uncomplicated to take advantage of. in the past, info on IBE have in basic terms been present in bulky, hard-to-follow magazine articles and convention complaints. this is often the 1st e-book to supply entire, obtainable counsel at the topic. It offers execs and scholars with an in-depth figuring out of IBE, and gives practitioners a wealth of sensible thoughts, algorithms and various labored examples to assist them successfully enforce this know-how within the box.
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Extra info for Introduction to identity-based encryption
Abstract Algebra, New York: Wiley, 2001. , G. Seroussi, and N. : Cambridge University Press, 1999. 3 Properties of Elliptic Curves Many IBE algorithms rely on the properties of certain functions on elliptic curves called pairings. This chapter describes the basic properties of elliptic curves that will be used in following chapters to understand properties of pairings and how to calculate them. Further detail on the connection between elliptic curves and elliptic functions can be found in ; additional detail on the algebraic structure of groups of points on elliptic curves can be found in ; further details on the efficient implementation of algorithms involving points on elliptic curves can be found in .
Ii) Polynomials with real coefficients are an extension field of infinite degree of the real numbers. (iii) Let v ∈ ކq and ␣ be a solution to the equation x d − v = 0 with ␣ n ≠ v for n < d. So if ␣ is a sixth root of v, for example, then it is not a cube root or square root. Then the smallest extension to ކq in which x d − v = 0 has a solution is ކq d . (iv) Suppose that F 3 is a finite field that is an extension of degree k 2 of the finite field F 2 and that F 2 is a finite field that is an extension of degree k 1 of the finite field F 1 .
B n − 1 ), then a + b = (a 0 + b 0 , . . , a n − 1 + b n − 1 ). We can also define −a in the obvious way, where −a = (−a 0 , . . , −a n − 1 ). Such operations supply the 34 Introduction to Identity-Based Encryption group structure under the operation of addition that the definition of a field requires. Because ކq is a vector space of dimension n over ކp , we can talk about elements of ކq being linearly independent, which has the same meaning as in linear algebra. 32 Elements of ކq k x and y are linearly independent if for all a, b ∈ ކq we have that a и x + b и y = 0 implies that a = 0 and b = 0.