Read or Download A density lemma PDF
Similar information theory books
Cognitive informatics is a multidisciplinary box that acts because the bridge among normal technological know-how and data technology. in particular, it investigates the capability purposes of data processing and normal intelligence to technological know-how and engineering disciplines. Transdisciplinary developments in Cognitive Mechanisms and Human details Processing examines cutting edge learn within the rising, multidisciplinary box of cognitive informatics.
Quantum physics, which deals a proof of the realm at the smallest scale, has basic implications that pose a significant problem to dull common sense. relatively counterintuitive is the idea of entanglement, which has been explored for the earlier 30 years and posits an ubiquitous randomness in a position to manifesting itself concurrently in additional than one position.
- Does Measurement Measure Up? How Numbers Reveal and Conceal the Truth
- Extrapolation Methods: Theory and Practice
- Mathematical Analysis, Wavelets, and Signal Processing
- Information, mechanism and meaning
Extra resources for A density lemma
A cyclic group g of order p and an element h ∈ g . Task. Compute a ∈ ZZ p such that h = ga . We next define another well-known basic computationally hard problem for a cyclic group. Computational Diffie-Hellman (CDH). Instance. A cyclic group g of order p and a tuple (g, ga , gb ) where a and b are uniform random elements of ZZ p . Task. Compute gab . 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.
Just like in PKE, it is a formalisation of the adversary’s inability to distinguish between ciphertexts arising out of two equal length messages M0 and M1 . , the adversary’s goal is to compromise the security of the identity it chooses as the target identity. A random bit γ is chosen and the challenge ciphertext is produced by encrypting Mγ under the target identity. The adversary wins if it can predict γ with a probability significantly away from half. The main difference from PKE schemes is that a coalition of valid users of an IBE scheme can possibly launch an attack against another user of the scheme.
In the above sequence, the following points are to be noted 1. G0 is the game which defines the security of the protocol and so Adv(A ) = |Pr[γ = γ ′ ] − 1/2| = |Pr[X0 ] − 1/2|. 2. Gk is designed such that the bit γ is statistically hidden from the adversary. So, Pr[Xk ] = 1/2. 3. Games Gi−1 and Gi differ: a. the difference is not too much; b. the adversary should not be able to notice whether he is playing Game Gi−1 or Game Gi . 4. More precisely, Pr[Xi−1 ] − Pr[Xi ] is bounded above by a. either, the advantage of an adversary in breaking one of the smaller protocols; b.
A density lemma