A New Cryptosystem Based on Factoring and Discrete Logarithm Problems

Abstract

Problem statement:A cryptosystem allows a sender to send any confidential or private message using a receiver's public key and later the receiver confirms the integrity of the received message using his secret key. Currently the existing cryptosystems were developed based on a single hard problem like factoring, discrete logarithm, residuosity, knapsack or elliptic curve discrete logarithm. Although these schemes appear secure, one day in a near future they may be broken if one finds a solution of a single hard problem. Approach: To solve this problem, we developed a new cryptosystem based on two hard problems; factoring and discrete logarithm. We integrated the two problems in our encrypting and decrypting equations so that the former depends on two public keys whereas the latter depends on two corresponding secret keys. Results: The new cryptosystem is shown secure against the most three considering attacks. The efficiency performance of our scheme only requires 3T exp +T mul + T hash time complexity for encryption and 2T exp + T mul time complexity for decryption and this magnitude of complexity is considered minimal for multiple hard problems-like cryptosystems. Conclusion: The new cryptosystem based on multiple hard problems provides longer and higher security level than that schemes based on a single hard problem. The adversary has to solve the two problems simultaneously in order to recover a corresponding plaintext (message) from the received ciphertext (encrypted message).

Synchronization and an application of a novel fractional order King Cobra chaotic system

“…Thus, the security of the proposed cryptosystem is very stronger than an existing cryptosystems 15,17 since ADV has extra trouble to find out the solutions of CCP and synchronized fractional order chaotic systems.…”

“…29 A new fast public key cryptosystem based on two cryptographic assumptions, namely, Diophantine approximation and IFP expected the high level of security of the system. 4 The authors 16,17 have been shown that the multiple cryptographic assumptions offer a greater security level than those schemes based on a single assumption. Therefore, the hybrid mode based cryptosystem provides greater security level while comparing with a single hard problem.…”

The Beta Cryptosystem

“…This is due to unlikely solving two hard problems simultaneously. Many public key cryptosystem have been designed based on both IFP and DLP [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23] but to design such schemes is not an easy task since many of them have been shown insecure.…”

New Cryptosystem Using Multiple Cryptographic Assumptions

“…Many cryptographers realize it and start to develop a more secure cryptosystem. One of the methods to design such scheme is by using multiple cryptographic assumptions (Ismail et al, 2008a;Elkamchouchi et al, 2004;Harn, 1994;Baocang and Yupu, 2005;Ismail et al, 2008b;Ismail and Hijazi, 2011). The reason behind this is an adversary needs a longer period of time in order to break the multiple cryptographic assumptionsbased cryptosystem since it is very unlikely for the adversary to obtain the solutions of these cryptographic assumptions simultaneously.…”