Journal of Network and Information Security

Open Access Open Access  Restricted Access Subscription Access
Open Access Open Access Open Access  Restricted Access Restricted Access Subscription Access

Fully Homomorphic Encryption with Matrix Based Public Key Crypto Systems


Affiliations
1 CSE Department, Navodaya Institute of Tech. Raichur, Karnataka, India
2 Electrical Engineering, Madhya Pradesh, India
3 CSE Department, VITS, Hyderabad, Telangana, India
     

   Subscribe/Renew Journal


In this work, a novel mechanism is considered for asymmetric mode of encrypting data. A generator matrix is used to generate a field with a large prime number. The generator matrix, prime number and quaternary vector are used as global variables. Those global variables are used to calculate public key and also sub keys which in turn are used in the ElGamal mode of encryption. The decryption of data is done with Private Key. The proposed algorithm supports the features like authenticity of users, security&confidentiality of data transmitted. The mechanism can well be used in homomorphic encryption where computations are carried out on cipher text and generate an encrypted result which, when decrypted, matches the result of operations performed on the plaintext.

Going by the construction of the algorithm, encryption is being done on blocks of data for which it consumes less computing resources. Going by complexity of the algorithm, the key length needed is much less to provide sufficient strength against crypto analysis.


Keywords

Homomorphic Encryption, Public and Private Keys, Elgamal Mode, Crypto Analysis and Complexity.
Subscription Login to verify subscription
User
Notifications
Font Size


  • Chun-Sheng, G. (2012). Crypto analysis on Public key encryption scheme Using Ergodic matrices over GF(2). Advances in Technology and Management, Advances in Intelligent and Soft computing, 165, 129-135.

  • DSN Progress Report. (2007). A public key crypto system based on algebraic coding theory, 42-44,114.

  • Gentry, C. (2009). A Fully Homomorphic Encryption Scheme (Ph.D. thesis).

  • Gentry, C. (2009). Fully homomorphic encryption using ideal lattices. In 41st ACM Symposium on Theory of Computing (STOC).

  • Goswami, B. (2013). Enhancing security in cloud computing using public key cryptography with matrices. International Journal of Advanced Research in Computer Science and Software Engineering, 3(8).

  • Guo-Ping, J., & Chun-Sheng, G. (2012). A Novel Public Key Cryptosystem Based on Ergodic Matrices Over GF(2). International Conference Computer Science & Service System(CSSS).

  • Kahrobaei, D., Koupparis, C., & Shpilrain, V. (2013). Public Key Exchange using Matrices over Group rings. Lecture Notes, Groups Complexity Cryptology, 5(1), 97-115.

  • Krishna, A. V. N., & Pandit, S. N. N. (2004). A new algorithm in network security for data transmission. Acharya Nagarjuna International Journal of Mathematics and Information Technology, 1(2), 97-108.

  • Krishna, A. V. N. (2005). A simple algorithm for random number generation. Journal for Scientific & Industrial Research, October, 64, 794-796.

  • Krishna, A. V. N., Pandit, S. N. N., & Babu, A. V. (2007). A Generalized scheme for data encryption technique using a randomized matrix key. Journal of Discrete Mathematical Sciences and Cryptography, 10(1), 73-81.

  • Krishna, A. V. N., & Babu, A. V. (2009). Training of a new probabilistic encryption scheme using an optimal matrix key. Georgian Electronic & Scientific Journal, 2(19), 24-34.

  • Mahalanobis, A. (2013). Are matrices useful in Public key cryptography. International Mathematics Forum, 8(39), 1939-1953.

  • Stuntz, C. (2010). What is Homomorphic Encryption, and Why Should I Care?


Abstract Views: 352

PDF Views: 0




  • Fully Homomorphic Encryption with Matrix Based Public Key Crypto Systems

Abstract Views: 352  |  PDF Views: 0

Authors

Addepalli V. N. Krishna
CSE Department, Navodaya Institute of Tech. Raichur, Karnataka, India
Addepalli Hari Narayana
Electrical Engineering, Madhya Pradesh, India
Kokk Madhura Vani
CSE Department, VITS, Hyderabad, Telangana, India

Abstract


In this work, a novel mechanism is considered for asymmetric mode of encrypting data. A generator matrix is used to generate a field with a large prime number. The generator matrix, prime number and quaternary vector are used as global variables. Those global variables are used to calculate public key and also sub keys which in turn are used in the ElGamal mode of encryption. The decryption of data is done with Private Key. The proposed algorithm supports the features like authenticity of users, security&confidentiality of data transmitted. The mechanism can well be used in homomorphic encryption where computations are carried out on cipher text and generate an encrypted result which, when decrypted, matches the result of operations performed on the plaintext.

Going by the construction of the algorithm, encryption is being done on blocks of data for which it consumes less computing resources. Going by complexity of the algorithm, the key length needed is much less to provide sufficient strength against crypto analysis.


Keywords


Homomorphic Encryption, Public and Private Keys, Elgamal Mode, Crypto Analysis and Complexity.

References