GEOMETRY IN CRYPTOGRAPHY: A REVIEW
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paper_title: A New Symmetric Key Encryption Algorithm Based on 2-d Geometry

paper_content:

Symmetric Key Cryptography is one of the prominent means of secure data transfer through unreliable channel. It requires less overhead than Public Key Cryptosystem. We present here, a new algorithm based on 2-d geometry using property of circle, and circle-centered angle. It is a block cipher technique but has the advantage of producing fixed size encrypted messages in all cases. It incorporates low computational complexity with fairly high confidentiality
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paper_title: Chakra: A new approach for symmetric key encryption

paper_content:

Encryption is an art of protecting data that win wars, protect properties and personal information if performed properly. It ensures that the appropriate data is exchanged between the intended persons only; even if the eavesdroppers get the content of the data they should not be able to understand it. Chakra Algorithm is a symmetric key encryption technique. It is a process of encrypting the data with the concepts of Cartesian Co-ordinate Geometry andcircle generation. The process considers the translation and rotation of axis when the data is grouped into circles each circle holds the portion of data. The Cartesian axis will be migrated to the respective centerscircles and rotated by certain angle. The collection of angle with which each individual circle is rotated; the co-ordinates to which it is swapped, the size of the square grid the radius of the circle hold the symmetric key. Unlike the other current algorithms, in Chakra Algorithm we will not directly change the data instead location of data.
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paper_title: Symmetric key cryptosystem using combined cryptographic algorithms - Generalized modified Vernam Cipher method, MSA method and NJJSAA method: TTJSA algorithm

paper_content:

In the present paper the authors have introduced a new combined cryptographic method called TTJSA. Nath et al. have already developed some symmetric key methods. In the present work the authors have used two methods MSA and NJJSAA which were developed by Nath et al. and have developed a new algorithm, generalized modified Vernam Cipher Method. The above three methods are applied in random order on any given plain text for a number of times to get the ultimate cipher text file. In the present work, authors modified the standard Vernam Cipher Method for all characters (ASCII code 0–255) with randomized keypad, and have also introduced a feedback mechanism. The method has been closely monitored on different known plain text and it was found that this method is almost unbreakable. The present method allows multiple encryption/decryption. The present method is an extremely secure block cipher method and it can be applied to encrypt data in Defense system, Banking sector, mobile network etc. The advantage of the present method is that one can apply this method on top of any other standard algorithm such as DES, AES or RSA. The method is suitable to encrypt any type of file.
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paper_title: A Modified Approach for Symmetric KeyCryptography Using Circles

paper_content:

Cryptography is the science or art of transforming an intelligible message(plaintext) into one that is unintelligible(cipher text) and then transforming the message back to its original form. . Symmetric key Cryptography is a cryptographic approach where the sender and receiver of a message share a single, common key that is used to encrypt and decrypt the message Geometry based cryptography is a new and emerging approach in the field of cryptography. It uses geometric shapes such as circles, ellipses etc and perform geometric transformations on these figures to produce cipher text. The presented work focuses on the Symmetric key Cryptography technique, using the concepts of Cartesian coordinate geometry and circle generation. Chakra algorithm, for symmetric key cryptography, is used as the basis for this work with some modifications in it for better results. Chakra is a Sanskrit term which means a circle or a disc. It plays a key role in encryption of data. Data is grouped into circles and each circle holds a portion of data. An improved geometric cryptographic algorithm is developed, that considers data into a 2- dimensional data grid, generate circles on the grid and apply some geometric transformations over data. This encryption technique adapts hybrid geometric transformations,(i.e., translation followed by scaling ) of the circumference points of every circle by some scaling factors(S,Sy) and translation factors(Tx,Ty). The proposed algorithm is an improvement in the basic Chakra algorithm in terms of accuracy.
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paper_title: A New Symmetric Key Encryption Algorithm Based on 2-d Geometry

paper_content:

Symmetric Key Cryptography is one of the prominent means of secure data transfer through unreliable channel. It requires less overhead than Public Key Cryptosystem. We present here, a new algorithm based on 2-d geometry using property of circle, and circle-centered angle. It is a block cipher technique but has the advantage of producing fixed size encrypted messages in all cases. It incorporates low computational complexity with fairly high confidentiality
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paper_title: A Hybrid Crypto System based on a new Circle- Symmetric key Algorithm and RSA with CRT Asymmetric key Algorithm for E-commerce Applications

paper_content:

It is widely recognized and accepted that data security will play a crucial and critical role in modern times for businesses will be transacted over the Internet through e-commerce and m-commerce channels. To address these security concerns, various security protocols that are of symmetric-key and asymmetric-key type have been developed. In this paper, we present a hybrid cryptographic system that combines both the symmetric key algorithm, which uses the properties of a circle and asymmetric-key algorithm of RSA with CRT. The circle symmetric key algorithm is based on 2-d geometry using property of circle, and circle-centered angle. It is a block cipher technique but has the advantage of producing fixed size encrypted messages all cases. The asymmetric algorithm is RSA with CRT which improves the performance of the basic RSA algorithm by four.
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Title: GEOMETRY IN CRYPTOGRAPHY: A REVIEW

Section 1: INTRODUCTION
Description 1: Provide a general overview of the history and importance of cryptography, describe the basic processes of encryption and decryption, and outline the types of cryptography (symmetric and asymmetric). Discuss why new ciphers are needed and mention the role of geometry in creating these ciphers.

Section 2: RELATED WORK
Description 2: Review recent literature and research related to the application of geometry in cryptography. Include a discussion on Elliptic Curve Cryptography (ECC) and mention other cryptographic techniques based on geometrical concepts such as circles, Cartesian coordinate geometry, and ellipses. Provide examples from various research papers, explaining each method briefly.

Section 3: CONCLUSION
Description 3: Summarize the key points discussed in the paper, emphasizing the potential of geometry in cryptography. Reflect on the convergence of geometry and cryptography and highlight the opportunities for future research in this field.
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