Nobody downloaded yet

Cryptosystems Based on Discrete Logarithm - Essay Example

Comments (0) Cite this document
Any data we input into the computer with the help of the key board is converted into numbers of the binary system in accordance with ASCII code. For instance the character 'A' is entered as 10100001 in the binary notation (Subramaniun, 140), which corresponds to the number 161 in the usual decimal notation…
Download full paperFile format: .doc, available for editing
GRAB THE BEST PAPER93.7% of users find it useful
Cryptosystems Based on Discrete Logarithm
Read TextPreview

Extract of sample
"Cryptosystems Based on Discrete Logarithm"

Download file to see previous pages Rather it will be sent as the binary string corresponding to another number which depends on the number 161 according to some fixed rule. For example we can subtract 161 from the largest 3-digit number 999 and send the result 838. Thus the rule for encryption is:
But there is a drawback of using this method of encryption. The receiver has also to be conveyed what rule has been used for the encryption, so that he can decrypt it. If some hacker in between cracks the information about this rule, then it is a trivial job for him to get the number 161 back from 838. For, he will easily deduce from this rule for encryption, the rule for decryption:
Therefore we make use of an ingenious technique. This technique makes the decryption of the encrypted message very difficult (if not impossible) for any third person (hacker). In order to know the technique, we need to learn some of the mathematical concepts. So first of all we take up these.
Given two natural numbers and an integer n, then by the modular exponentiation of b to the base a, which is symbolized as, we mean obtaining the remainder on dividing. Thus, for example,, on being evaluated yields 7. Observe that we can also write using the above concept of congruence modulo m.
Further given two natural numbers and an integer n, then the smallest (non-negative) integer x (if exists) such that, is known as the discrete logarithm of b to the base a. (, 1)
To find the modular exponentiation is an easy task even if the numbers a and b are large. For, we can make use of the 'square and multiply method' (Schneier, 244) as explained in what follows: We know that stands for the remainder obtained on dividing by n. For large values of a and b, it will be very difficult to evaluate the expression. But to evaluate is much easier. For we can find the remainder (say) on dividing, multiply and obtain the remainder (say) on dividing the product by n; and so on till the number a is taken b times for the multiplication and thus the last remainder is obtained. As an illustration let us compute. Let us find the remainder on dividing; we get 1. Then
find the remainder on dividing 1.3 (=3) by 8; we get 3. Now find the remainder on dividing 3.3 (=9) by 8; we get 1. Again find the remainder on dividing 1.3 (=3) by 8; we get 3. Finally find the remainder on dividing 3.3 (=9) by 8; we get 1, which is the result of the modular exponentiation. For the sake of verification we can compute. It comes out 729. On dividing 729 by 8 we get 1, the same result.

However, to find the discrete logarithm for large numbers is a very hard problem by any means. So if we base the cryptosystem on the discrete logarithm, it becomes extremely hard for a hacker to crack it. Now we will describe this system. The basic work for the development of the system was done by Diffie and Hellman in 1976, but the system was fully developed by ElGamal. ((, 2). First we take up the work done by

These two fellows invented an algorithm which can be used by two persons to generate a secret common key. The algorithm is explained below.

Let Alex and Bobby be the two persons who are going to exchange some information over the internet ...Download file to see next pagesRead More
Cite this document
  • APA
  • MLA
(“Cryptosystems Based on Discrete Logarithm Essay”, n.d.)
Cryptosystems Based on Discrete Logarithm Essay. Retrieved from
(Cryptosystems Based on Discrete Logarithm Essay)
Cryptosystems Based on Discrete Logarithm Essay.
“Cryptosystems Based on Discrete Logarithm Essay”, n.d.
  • Cited: 0 times
Comments (0)
Click to create a comment or rate a document
Industrial/Discrete Manufacturing
...Industrial/Discrete Manufacturing Section Analysis Demand is well-known to be the driving factor of any business. Fluctuations in demand patterns differ significantly between industries (Agarwal 2). The clothing industry, for instance, is subject to substantial demand adjustments driven by seasonality as well as business cycles, while the diaper market benefits from a relatively steady demand. One would be expecting players in various retail supply chains to habitually misjudge demand, creating shortages or inventory surpluses at diverse stages in the supply chain. Changes in demand patterns also affect the supply chain of different manufacturing environments. These environments are, for instance, Make-to-Stock...
6 Pages(1500 words)Research Paper
Discrete Population Growth
... _
2 Pages(500 words)Lab Report
Discrete Mathematics(Mathematical Algorithms)
...DISCRETE MATHEMATICS Mathematical Algorithms Table of Contents Introduction 3 Mathematical Algorithms Overview 3 Evolution 5 Relation of Computer Science and Mathematical Algorithms 6 Algorithm-Supported Mathematical Theory 7 Mathematical Algorithm Analysis 8 Impotence of Mathematical Algorithms 9 More Real-world Examples 10 Conclusion 10 Bibliography 11 Introduction Discrete mathematics is a section or element of mathematics that is concerned with the objects which are capable of assuming just divided, distinctive values. The concept of discrete mathematics is thus applied in distinction with continuous mathematics, that is the subdivision of mathematics concerned with the objects which...
9 Pages(2250 words)Research Paper
What is Discrete trial Training
...What is Discrete Trial Training? Discrete Trial Training A. ABA Guidelines: Response Cost This is one of the behavioral methods used to stop inappropriate behavior in children by parents. This method involves taking away something from the child, when he performs any undesired behavior. Various response cost plans do not work because the child was supposed to wait a week to obtain the reinforcement. Short time durations to wait for fortification are the best for children with ADHD (Moore, 2001). Below are the steps to expand the success of a response cost behavioral involvement. Step 1: Identify target behaviors Clearly describe what behavior you intend to stop. Note how frequently the behavior happens and when it happens. Step 2... :...
3 Pages(750 words)Research Paper
Introduction to Discrete Event Dynamic Systems
...Discrete event dynamic system (DEDS) The target behind the article is the extension of the finite automata. This will impact on the regular expression, which in different instances encompassed with the expression in relation to direct construct in reference with the corresponding finite automaton. Exploration and expression of automata is in respect with the minimization, determination, primeness, and the extension on output feedback, observability, stability, and invertibility regarding the framework. The approach resembles that used by Mon-talbano’s and Giammarresi in the illustration of generalized automata. It is evident that the deterministic expression in automata is just mere regular languages. From the article,...
2 Pages(500 words)Research Paper
Mathematical reasoning and discrete structures
...Number Mathematical Reasoning and Discrete Structures Question a) (A – B) – C = A – (B ᴗ C) Let 2, 3, a) ϵ A Let (2, a) ϵ B Let (3) ϵ C [(1, 2, 3, a) - (2, a)] - (3) = (1, 2, 3, a) – [(2, a) ᴗ (3)] (1, 3) – (3) = (1, 2, 3, a) – (2, 3, a) 1 = 1 Therefore this theoretic statement is true. b) p= x ϵ A, q = x ϵ B and r = x ϵ C p ¬q ¬r → p ¬ (q ˅ r) Question 2 Let P(x) be the propositional function “x is perfect” Let Q(x) be the propositional function “x is a friend” Let ﻻ be “for every” a) No one is perfect ­­­ ﻻx ­­­­­¬ P(x) b) Not everyone is perfect Ǝx ¬ P(x) c) All your friends are perfect ﻻx (Q(x) → P(x)) d) At least one of your friends is perfect Ǝx (Q(x) → P(x)) e) Not everyone is your friend or someone is not...
1 Pages(250 words)Speech or Presentation
Discrete and Combinatorial Mathematics (Week 4)
...that must be removed so that the resulting subgraph has an Euler trail but not an Euler circuit? Which bridge(s) should we remove? PLEASE PLACE ANSWER HERE (in red) One bridge. Bridge b should be removed for the resulting sub graph to have a Euler trail. Exercise 12.2 (page 604 in ebook.pdf) 6.) List the vertices in the tree shown in Fig. 12.31 when they are visited in a preorder traversal and in a post order traversal. PLEASE PLACE ANSWER HERE (in red) 2, 15, 17, 8 9.)LetG = (V , E) be an undirected graph with adjacency matrix A(G) as shown here.Use a breadth-first search based on A(G) to determine whether G is connected. PLEASE PLACE ANSWER HERE (in red) A (G) is connected since v8 v8 are connected within the provided...
2 Pages(500 words)Assignment
MATH203-1402B-04 : Applications of Discrete Mathematics - PHASE 3 IP
...APPLICATIONS OF DISCRETE MATHEMATICS-PHASE 3 IP Part We present a tree diagram based on the adjacency matrix provided. It is clear that the graph has five vertices based on the fact that the matrix given was a 5X5 matrix. Since the vertex is connected to the vertex having exactly number of edges, this is in regard to the definition of an adjacency matrix. Moreover, due to the fact that the diagonal of the matrix has zeroes only, the vertices do not contain any loop. If we could recall a simple path graph does not have recurring vertices. Now to obtain the number of simple paths that are connected to the vertices 1 and 5, we write the sequences of the vertices in simple paths of our...
3 Pages(750 words)Speech or Presentation
MATH203 - Applications of Discrete Mathematics -PHASE 4 DB
...Math Problem, Mathematics MATH203 – Applications Discrete Mathematics -PHASE 4 DB Q1: Transition Diagram Drawing of a transition diagram(digraph) Q 2: The 5 strings generated by the automation are as follows: String 1 = v = x + y String 2 = x = x + δ String 3 = w where (w = uv, the substring of w) String 4 = s4 = w + x String 5 = s5 = w + δ Q 3: 5 Strings that use similar inputs but not in same language String 1 = v = x + δ String 2 = x = x + δ String 3 = w = xδ String 4 = s4 = δx String 5 = δ + δ + x Question 4: Statement describing the conditions of a string When a string is part of the Language When a string is in the accept mode, the input string is generated. The automation is able to read in the string one symbol...
2 Pages(500 words)Speech or Presentation
Discrete Math Project
... Application of the Leslie Matrix Model in the Management of Wildlife Leslie matrix is a discrete and age-structured model used in representing the population by abundances vector of differing age classes represented in rows and columns ( The matrix has a number of applications in wildlife management, as it is useful in determining the dynamics of the animal’s population given that births and deaths are age-dependent. An important application of the matrix in wildlife management is projecting the population growth of specific animals or a certain species. Using the Leslie matrix model, which is based on the multiplication of the Leslie Matrix and the Population vector, institutions managing wildlife are able...
1 Pages(250 words)Essay
sponsored ads
We use cookies to create the best experience for you. Keep on browsing if you are OK with that, or find out how to manage cookies.
Let us find you another Essay on topic Cryptosystems Based on Discrete Logarithm for FREE!
logo footer
Contact us:
Contact Us Now
FREE Mobile Apps:
  • StudentShare App Store
  • StudentShare Google play
  • About StudentShare
  • Testimonials
  • FAQ
  • Blog
  • Free Essays
  • New Essays
  • Essays
  • Miscellaneous
  • The Newest Essay Topics
  • Index samples by all dates
Join us:
Contact Us