A Modified Key Generation Algorithm to Rebalanced-RSA and RPower-RSA

Year 2024, Volume: 12 Issue: 2, 192 - 197, 27.12.2024

İsrafil Okumuş , Ercan Celık

https://doi.org/10.51354/mjen.1524490

https://izlik.org/JA26AZ68XB

Abstract

This paper presents a novel key generation algorithm for Rebalanced-RSA and RPower-RSA that accelerates encryption and decryption processes by utilizing smaller modular exponents. Subsequently, two of these variants are modified by altering the key generation process. A theoretical analysis of all variants, including the proposed modifications, demonstrates that these key generation algorithms improve the encryption process compared to the original variants, and since the encryption key size and one of the decryption key sizes are approximately equal in length, they achieve a more balanced computational effort between encryption and decryption.

Keywords

RSA , Variation of RSA , Rebalanced-RSA , RPower-RSA , Key Generation Algorithm

Ethical Statement

-

Supporting Institution

-

Project Number

-

Thanks

-

References

• [1] R. L. Rivest, A. Shamir and L. Adleman, "A method for obtaining digital signatures and public key cryptosystem," Communications of the ACM, vol. 21, no. 2, pp. 120-126, 1978.
• [2] D. Boneh and H. Shacham, "Fast Variants of RSA," CryptoBytes, vol. 5, no. 1, pp. 1-9, 2002.
• [3] J. J. Quisquater and C. Couvreur, "Fast decipherment algorithm for RSA public-key cryptosystem," Electronics Letters, vol. 18, no. 21, pp. 905-907, 1982.
• [4] A. Fiat, "Batch RSA," Journal of Cryptography, vol. 10, no. 2, pp. 175-195, 1995.
• [5] M. J. Wiener, "Cryptoanalysis of sort RSA secret exponents," IEEE Transactions on Information Theory, vol. 36, pp. 553-558, 1990.
• [6] T. Collins, D. Hopkins, S. Langford and M. Sabin, "Public Key Cryptographic Apparatus and Method". Us Patent #5,848,159, Jan. 1997.
• [7] T. Takagi, "Fast RSA-Type Cryptosystem modulo p^k.q," Advances in Cryptography - CRYPTO'98 Springer, vol. 1462, pp. 318-326, 1998.
• [8] C. A. M. Paixao and D. L. G. Filho, "An efficient variant of the RSA cryptosystem," 2005.
• [9] S. Verma and D. Garg, "Improvement in RSA Cryptosystem," Journal of Advences Information Technology, vol. 2, no. 3, 2011.
• [10] J. Gordon, "Strong RSA keys," Electronics Letters, vol. 20, no. 12, pp. 514-516, 1984.
• [11] D. M. Gordon, "A Survey of Fast Exponentiation Methods," Journal of algorithms, vol. 27, no. 1, pp. 129-146, 1998.
• [12] Ç. K. Koç, "High-Speed RSA Implementation," RSA Laboraties, Redwood City, CA 94065-1031, 1994.
• [13] P. L. Montgomery, "Modular multiplication without trial division," Mathematics of Computation, vol. 44, no. 170, pp. 519-521, 1985.
• [14] D. Coppersmith, "Small Solutions to Polynomial Equations and Low Exponent RSA Vulnerabilities," Journal of Cryptology, vol. 10, pp. 233-260, 1997.
• [15] D. Boneh and G. Durfee, "Cryptoanalysis of RSA with Private Key d less than N0.292," IEEE Transactions on Information Theory, vol. 46, no. 4, pp. 1339-1349, 2000.
• [16] İ. Okumuş and E. Çelik, "Classification of factors that affect the speed of the RSA cryptosystem," in Georgian Mathematical Union Third International Conference, Batumi, GEORGIA, 2012, September 2-9.
• [17] T. Takagi, "A Fast RSA_Type Public-Key Primitive Modulo pkq Using Hensel Lifting," IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences, Vols. E87-A, no. 1, pp. 94-101, 2004.
• [18] D. Garg and S. Verma, "Improvement over Public Key Cryptographic Algorithm," in 2009 IEEE International Advance Computing Conference (IACC 2009), Patiala, 2009.
• [19] İ. Okumuş, The Factors Affecting of RSA Cryptosystem, Ataturk University: Ph. D. Thesis, 2012.
• [20] A. Shamir, "RSA for paranoids," CryptoBytes (The technical Newsletter of RSA Laboratories), vol. 1, pp. 1-4, 1995.
• [21] G. Horng, "Identification Scheme Based on Shamir's 'RSA for Paranoids," Electronic Letters, vol. 35, no. 22, pp. 1941-1942, 1999.
• [22] Kenneth H. Rosen, "Discrete Mathematics Applications", Eighth Edition, New York, NY : McGraw-Hill, 2019.