1. INTRODUCTION OF LAGRANGE POLYNOMIAL ITERPOLATION
1.1 Interpolation:
• First of all, we will understand that what the interpolation is.
• Interpolation is important concept in numerical analysis. Quite often functions may not be available explicitly but only the values of the function at a set of points, called nodes, tabular points or pivotal points. Then finding the value of the function at any non-tabular point, is called interpolation.
Definition:
• Suppose that the function f (x) is known at (N+1) points (x0, f0), (x1, f1), . . . , (xN, fN) where the pivotal points xi spread out over the interval [a,b] satisfy a = x0 < x1 < . . . < xN = b and fi = f(xi) then finding the value of the function
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APPLICATIONS OF LAGRANGE POLYNOMIAL INTERPOLATION
Lagrange polynomials basis are used in the Newton–Cotes method of numerical integration
One of its application is in Cryptography such as “ Shamir's secret sharing scheme”.
It is appropriate for back-of-the-envelope calculations.
It is uses in Improving the Low Resolution Images Accuracy in Human Face Recognition.
It is uses in Contrast Based Color Watermarking In Wavelet Domain.
It is uses in Learning of Neural Network.
It is uses in Data Compression.
5.APPLICATION OF LAGRANGE POLYNOMIAL INTERPOLATION
Application: Secure Message Transmission using
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As any nth degree polynomial is uniquely determined by n+1 points, n +1 points are communicated to the other side, where the polynomial and hence the message is reconstructed.
Padding of length m is added to the message to overcome the message length issue.
Huffman coding is used for converting the plaintext into binary form.
5.2.CRYPTO SYSTEM BASED ON LAGRANGE INTERPOLATION
A random number N is assumed by the sender and the respective N value securely communicated to receiver through the concept of digital enveloping. Security of message is mainly depends on this randomly generated N.
Encryption: The sender is converting the actual message into points like (xi,yi) by passing the original message using the algorithm given in Fig 1. In Step 4, M is constructed by using the formula.
Decryption: Receiver collects all the interpolation points, retrieves the original message using the algorithm in fig2. Step 2 is used for constructing polynomial function is achieved by using following formula.
5.3.SYSTEM MODEL FOR MESSAGE
The sender would type the message in plaintext (not encrypted) and the letters would be illuminated on a glass screen. With the press of each typewriter key the rotor would shift 1/26 of a revolution giving each letter a different encryption each time, which made the code so difficult to crack. Due to the complexity of the code the enigma became very useful for the Germans for radioing messages to u-boats. The cipher was finally broken when the British were able to capture some key documents from a German warship.
This program uses mainly on the concept of cryptology. Cryptology is the study about secret communication between two parties, where there is a presence of a third party known as adversaries, and that party knows nothing about the content of the communication (Rivest, 1990).
The RSA encryption is related to the cipher of Julius Caesar (1300s) that shifts three letters to encode messages. The cipher of Julius Caesar was used in war to send messages securely. Here is how Caesar encodes his message using the cipher. First Caesar assigned A through Z to 0 through 25. For instance A is zero. Second, add three to each numbers.
..., Nicholas G. 2010. “Past, Present, and Future Methods of Cryptography and Data Encryption.” Department of Electrical and Computer Engineering
R. Rivest, A. Shamir, and L. Adleman. A method for obtaining digital signatures and public key cryptosystems. Communications of the ACM, 21(2):120-126, 1978. Computer Science, pages 223-238. Springer, 1999.
Message Decoded- The person who you are conversing with has to analyse your message, this is not always an easy job as the other person can make assumptions about your words and body language, so it is common for messages to be taken in a different way to how it has been intended.
Answer: A random number generator is a computational device which is able to generate a sequence of numbers or symbols that lack any pattern and appear to be random [3]. Ideally, a good random number generator should b...
Q1). How would you approach the creation of a generalized program to decipher /break any encrypted message, independent of the technique used to create the cipher? What is your algorithm?
Data encryption refers to the process of transforming electronic information into a scrambled form that can only be read by someone who knows how to translate the code. In nowadays business world, it’s the easiest and most practical way to secure the information that we stored and processed, and it’s significant for our sensitive information. For example, as electronic commerce is popular now, the vendors and retailers must protect the customers’ personal information from hackers or competitors. They also have many business files or contracts that need to be strictly protected. Without data encryption, these important information may fall into wrong hands and be misused by others. Besides, data encryption may be used to secure sensitive information that exists on company networks, or create digital signatures, and help to authorize in business. No one should underestimate the importance of encryption. A little mistake in encryption may make sensitive information revealing, or even result in illegal and criminal accuse.
Encryption has a very long history,1 which can be traced back to about 1900 B.C. Cryptography was first used in the form of hieroglyphic inscription by an ...
Alice sends the 1st 1 using the + scheme, the 2nd one using the X scheme, 1st 0 using the X scheme and so on.
with the public key, send it to the recipient, who will then decipher it again
The protection of data being transferred between ATMs and the bank, and the use of cell phones is the most common everyday encounter with encryption. To encrypt and decrypt information a cipher is used. In a cipher there is a set of well-defined steps that can be followed to encrypt and decrypt messages. The use of a cipher relies greatly on the use of an encryption key. The key may contain any auxiliary information added to the cipher to produce certain
In this era when the Internet provides essential communication between tens of millions of people and is being increasingly used as a tool for security becomes a tremendously important issue to deal with, So it is important to deal with it. There are many aspects to security and many applications, ranging from secure commerce and payments to private communications and protecting passwords. One essential aspect for secure communications is that of cryptography. But it is important to note that while cryptography is necessary for secure communications, it is not by itself sufficient. Cryptography is the science of writing in secret code and is an ancient art; In the old age people use to send encoded message which can be understand by the receiver only who know the symbolic and relative meaning of that encoded message .The first documented use of cryptography in writing dates back to circa 1900 B.C. Egyptian scribe used non-standard hieroglyphs in an inscription. After writing was invented cryptography appeared spontaneously with applications ranging from diplomatic missives to war-time battle plans. It is no surprise, then, that new forms of cryptography came soon after the widespread development of computer communications. In telecommunications and data cryptography is necessary when communicating in any untrusted medium, which includes any network, particularly the Internet [1].Within the context of any application-to-application communication, there are some security requirements, including: