By Sanjit Chatterjee
Identity dependent Encryption (IBE) is a kind of public key encryption and has been intensely researched long ago decade. Identity-Based Encryption summarizes the on hand learn for IBE and the most principles that may permit clients to pursue additional paintings during this sector. This booklet also will hide a short heritage on Elliptic Curves and Pairings, safeguard opposed to selected Cipher textual content assaults, criteria and extra. Advanced-level scholars in computing device technology and arithmetic who focus on cryptology, and the overall neighborhood of researchers within the quarter of cryptology and knowledge protection will locate Identity-Based Encryption an invaluable publication. Practitioners and engineers who paintings with real-world IBE schemes and want a formal realizing of the elemental IBE strategies, also will locate this e-book a invaluable asset.
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Extra info for Identity-Based Encryption
Note that since G1 and G2 are both cyclic groups of the same prime order, they are certainly isomorphic. In Type-2 such an isomorphism can be easily computed whereas in Type-3 no such isomorphism is known. In both Type 2 and Type 3 it is assumed that there is no efficiently computable isomorphism from G1 to G2 . , e(P, Q) = e(Q, P). In contrast, both Type 2 and Type 3 are asymmetric pairings. , Type 1) setting as this allows a relatively simpler description of the protocol and its security argument.
The general belief in the community is that such problems indeed cannot be solved in probabilistic polynomial time, but, currently, we are far from proving any such statement. Later in this chapter, we discuss some of the basic hard problems that have been proposed in the literature. 1 Finite Fields, Elliptic Curves and Tate Pairing In this section, we provide an overview of some facts regarding the algebraic structures required to construct and compute a bilinear map. We start with the basic idea of exponentiation in a general cyclic group, briefly discuss finite fields and elliptic curves and present a definition of Tate pairing and describe Miller’s algorithm for computing it.
In other words, an algorithm (or an adversary) A for solving the CDH problem takes as input a tuple (g, ga , gb ) and has to output gab . The advantage of A in solving the CDH problem is defined as follows. AdvCDH (A ) = Pr A (g, ga , gb ) ⇒ gab The CDH problem in g is said to be (ε ,t)-hard if for any adversary A running in time at most t, AdvCDH (A ) ≤ ε . This problem has a decision version. Decisional Diffie-Hellman (DDH). Instance. A cyclic group g of order p and a tuple (g, ga , gb , gc ) for independent and uniform random a and b from ZZ p .
Identity-Based Encryption by Sanjit Chatterjee