The Role of Shannon Information and Cryptography

Introduction

Secure communication is an important subject of concern owing to the increase in electronic communication media. Cryptography studies the ability of two parties to achieve safe communication in the presence of another party. Communication security is an interesting topic because it has always been implemented, for example, Julio Caesar used encrypted messages when computers were not available.

From a scientific perspective, an interesting feature of cryptography is the development of protocols or systems whose security can be validated thoroughly. Previous research studies highlight various methods of certifying secure communication but most of these methods are not actually acceptable. To test the validity of a cryptographic structure, a parameter must be developed to define security and the expectations of the third party’s accessible information and the third party’s computing ability must be specified.

In theory and practice, three variables validate a system’s security. The generalizability and applicability of the description of security, the rationality of the assumptions, and the system’s reality contribute to validating the security of a communication system. In the trending electrical communication pulse, Claude Shannon appears to be the pioneer of mathematical cryptography. This paper presents a summary of Shannon’s experiment and its influence on the interpretation of how information theory is related to cryptography. Shannon’s investigation of the relationship between information theory and cryptography has been reviewed by various researchers. This paper summarizes and analyzes the findings and conclusions of three research studies that investigate the relationship between information theory and cryptography. The three papers analyzed in the current paper include “The Role of Information Theory in Cryptography” by Ueli M. Maurer, “Quantum-cryptography network via continuous-variable graph states” by Yujing Qian, Zhean Shen, Guangqiang He, and Guihua Zeng, and “Experimental Quantum Cryptography” by Charles H. Bennett.

Research Review

Maurer’s Research

Maurer’s paper titled “The Role of Information Theory in Cryptography” presents a historical analysis of the relationship between information theory and cryptography using the premises of information theory presented by Shannon and other researchers. The paper emphasizes the extent information theory has been applied in cryptography to demonstrate lower levels on the extent of the secret key necessary to accomplish a specific amount of security in confidentiality and verification systems. Analysis of information theory models, different from Shannon’s model suggests that flawless secrecy is essentially accomplished with a small secret key, which seemingly opposes Shannon’s lower bound on the key dimension of a flawless encryption.

Maurer’s article presents theoretical computation and explain that information theory has been applied for information encryption principally to get negative outcomes, which refers to the lower boundaries on the secret key magnitude required to derive a particular amount of security. One of the sections in the Maurer’s article presents what he calls the most significant aspects for which such boundaries have been achieved, which include authentication, secrecy, and secret sharing. The article also considers the exciting aspect of information theory in information encryption by proofing that flawless secrecy described by Shannon may be gained in a practical situation. Maurer considers it spontaneously when Shannon’s information theory assumes that in all systems, wherein the third party can witness the whole communication between two interacting parties, ideal confidentiality can only be attained if the secret key’s entropy is the same as the shared information (Maurer 14). Nevertheless, the verification of this instinctive outcome is not totally inconsequential (Maurer 4).

Maurer’s article investigated various connections between Shannon’s information model and information encryption. Although the results of the computations Maurer presents in one of the article’s sections were doubtful since they merely indicated what was unachievable, a simple alteration of the traditional Shannon prototype of an encryption structure yield positive outcomes on ideal confidentiality, further described in the latter parts of the article. Maurer’s article do not provide concrete conclusion about the relationship between Shannon’s information theory and information encryption systems, but it influenced investigations in the absolutely safe and secret, key synchronization procedures.

Bennett’s Research

The paper was written to investigate the earliest experimental quantum key sharing channel ever modeled and assembled (Bennett 8). The article applied a scenario involving three people (two people interacting and one eavesdropper). The article explains that traditional information encryption and information theory does not consider the possibility that digital communications may be inertly monitored, which allows the listener understands the whole content, without the communication participants understanding that any form of prying occurred.

On the contrary, encrypting electronic data is encrypted in basic quantum structures, such as single photons, makes it possible to create a route for information exchange whose communication cannot in theory be dependably accessed or recorded by a third party unaware of some information applied in performing the communication. The third party cannot achieve partial messages about such communication without upsetting it in a haphazard and uncontainable manner, which may be sensed by the legal users of the communication path.

The article presents a detailed report on the outcomes from a device and procedure created to perform quantum key sharing, whereby two people who exchange no confidential messages previously, share an arbitrary quantum exchange, comprising of indistinct spark of opposing lights. People can approximate the level of communication breach by considering the transmitted and accepted forms of communication and, if the approximations are negligible, extract from the transmitted and accepted forms fewer exchanged random messages. Extracted messages are verifiable and confidential because any eavesdropper’s anticipated message is an exponentially negligible segment of one fragment. The fact that the model is based on the uncertainty theory of quantum physics, and not the conventional mathematical calculations such as the complexity of verification, it is safe against an eavesdropper with unrestricted computing control.

Yujing’s Research

Yujing’s article is developed to investigate the possibility of expanding the quantum cryptography system. The operability of quantum cryptography network systems is described and analyzed using graphs (Yujing et al. 13). The reliability of a specific model depends on the experimental reliability of the identified graphs. Yujing’s article suggests a quantum-cryptography system that is developed using a continuous-factor graph model with the conforming quantum key distribution (QKD) procedure. The authors use the article to predict whether their planned graph permits two random people to exchange a confidential Gaussian key. Using a mathematical prototype, the authors investigate the properties of a random graph, which include the probability of related principles. This article analyzes the general entangling cloner emergency approach using Shannon’s theory of information. The outcome of the study indicates that the suggested system is safe against the attacks provided the graph satisfied specific standards (Yujing et al. 15).

The authors offer a QKD system and the matching procedure based on chart conditions and homodyne detection. In the QKD system, each dual model is capable of launching a message transmission system whether they are directly or indirectly connected. The article also suggests a universal and effective approach that is related to linear algebra and can be used to create an applicable QKD system using all graph conditions. By analyzing the adjacency of one matrix with another, there may be various QKD systems used for computing provisional variances and the communal messages.

The suggested procedures can be safe and confidential against the potential attack method provided an equation is met (Shannon 631). The factors determined to influence the QKD supportive chart include protocol description, confidentiality, and able to squeeze through limits, integration effeteness, and transmission. The authors emphasize the validity of their research, and this validity is obvious as research studies have begun to create four-mode graph conditions.

Summary and Open Questions

The aim of this paper was to review the role Shannon’s information theory plays in cryptography. The paper reviewed various research articles and paid specific attention on using information encryption to prevent eavesdropping. The prevalence of electronic communication systems makes it necessary for data security analysts and information scientists to understand the basis of the research on cryptography. A review of the articles shows that there is need for further research to investigate the potential for modern cryptography models. Over the past decade, there has been a tremendous change in communication transmission. Future research should investigate the efficiency of applying cryptography for information security in trending communication systems.

The three articles reviewed in this paper discuss the relationship between information theory and cryptography and their findings leave open questions. The following are examples of some open questions observed during the review of three articles:

• Does cryptography eliminate communication insecurity?
• How easy is it for both parties to decipher encrypted messages?
• What are the disadvantages of using encrypted messages?

The first question is developed because the three articles focus more on analyzing the effects of cryptography on communication security than on the possibility of applying cryptography to eliminate communication insecurity. The primary objective of cryptography is to create a transmission line that prevents third parties from eavesdropping on people’s communication, and this makes is necessary for articles investigating the relationship between information theory and cryptography to focus on the possibility of eliminating communication insecurity through cryptography.

Information encryption increases communication security but may deter the communicating parties’ understanding of the shared information. Communication is achieved when there is an understanding between all participants in the communication network. If the message is encrypted and transmits a different meaning to the receiver, the aim of communication is defeated. The second question investigates the role of information encryption on ideal interpretation of the messages contained and transmitted in the communication network.

The use of message encryption may eliminate or reduce the problems of communication security but may negatively affect some qualities of effective communication. Ideal communication involves the transmission of comprehensible messages between two or more people within the least possible time. None of the articles reviewed in this paper investigates the relationship between cryptography and communication lag time. The third open question considers the possible effect of encryption procedures on message delivery periods because of the significance of delivery time in message transmission. Communication may be delayed during the encryption process.

Works Cited

Bennett, Charles. “Experimental Quantum Cryptography IBM.” J. Cryptology 5.2 (1992): 3-28. Print.

Maurer, Ueli “The Role of Information Theory in Cryptography.” Proc. of 4th IMA Conference on Cryptography and Coding 1.1 (1992): 1-20. Print.

Shannon, Claude. “Bell System.” Tech. J 27.339 (1948): 623-633. Print.

Yujing Qian, Shen Zhean, He Guangqiang, and Zeng Guihua. “Quantum-Cryptography Network via Continuous-Variable Graph States.” Physical Review, 86.52 (2012): 1-7. Print.