Abstract
We present a comparative analysis of the processes of factorization of Gaussian integers and rational integers, with the objective of demonstrating the advantages of using the former instead of the latter in RSA public key cryptosystems. We show that the level of security of a cryptosystem based on the use of the product of two Gaussian primes is much higher than that of one based on the use of the product of two rational primes occupying the same storage space. Consequently, to achieve a certain specific degree of security, the use of complex Gaussian primes would require much less storage space than the use of rational primes, leading to substantial saving of expenditure. We also set forth a scheme in which rings of algebraic integers of progressively higher and higher degrees and class numbers can be used to build cryptosystems that remain secure by forever staying ahead of advances in computing power.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Adleman, L.M., Rivest, R.L., Shamir, A.: A method for obtaining digital signatures and public-key cryptosystems. Commun. ACM 21, 12–126 (1978)
Rivest, R.L.: RSA chips (past/present/future). In: Advances in Cryptography, Proceedings of Eurocrypt, vol. 84, pp. 159–165. Springer, New York (1985)
Diffie, W., Hellman, M.E.: New directions in cryptography. IEEE Trans. Inf. Theory IT 22, 644–654 (1976)
Hardy, G.H., Wright, E.M. (Revised by Heath-Brown, D.R., Silverman, J.H.): An Introduction to the Theory of Numbers, 6th edn. Oxford University Press, Oxford (2008)
Ireland, K., Rosen, M.: A Classical Introduction to Modern Number Theory, 2nd edn. Springer, New York (1990)
Davenport, H.: The Higher Arithmetic, 7th edn. Cambridge University Press, Cambridge (1999)
Apostol, T.M.: Introduction to Analytic Number Theory. Springer, New York (2010)
Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to Algorithms, 3rd edn. PHI Learning Pvt. Ltd., New York (2011)
Knuth, D.E.: The Art of Computer Programming, vols. I and II. Addison-Wesley, Reading (1973)
Koblitz, N.: A Course in Number Theory and Cryptography, 2nd edn. Springer, Berlin (1994)
Niven, I., Zuckerman, H.S., Montgomery, H.L.: An Introduction to the Theory of Numbers, 5th edn. Wiley, New York (2006)
Rosen, K.H.: Discrete Mathematics and Its Application, 4th edn. Tata McGraw-Hill Publishing Company Limited, New Delhi (1999)
Silverman, J.H.: A Friendly Introduction to Number Theory, 3rd edn. Prentice Hall, Upper Saddle River (2011)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer India
About this paper
Cite this paper
Paul, A., Datta, S., Sharma, S., Majumder, S. (2016). On the Use of Gaussian Integers in Public Key Cryptosystems. In: Nagar, A., Mohapatra, D., Chaki, N. (eds) Proceedings of 3rd International Conference on Advanced Computing, Networking and Informatics. Smart Innovation, Systems and Technologies, vol 44. Springer, New Delhi. https://doi.org/10.1007/978-81-322-2529-4_30
Download citation
DOI: https://doi.org/10.1007/978-81-322-2529-4_30
Published:
Publisher Name: Springer, New Delhi
Print ISBN: 978-81-322-2528-7
Online ISBN: 978-81-322-2529-4
eBook Packages: EngineeringEngineering (R0)