New Cryptosystem Using Multiple Cryptographic Assumptions

Abstract

Problem statement:A cryptosystem is a way for a sender and a receiver to communicate digitally by which the sender can send receiver any confidential or private message by first encrypting it using the receiver's public key. Upon receiving the encrypted message, the receiver can confirm the originality of the message's contents using his own secret key. Up to now, most of the existing cryptosystems were developed based on a single cryptographic assumption like factoring, discrete logarithms, quadratic residue or elliptic curve discrete logarithm. Although these schemes remain secure today, one day in a near future they may be broken if one finds a polynomial algorithm that can efficiently solve the underlying cryptographic assumption. Approach: By this motivation, we designed a new cryptosystem based on two cryptographic assumptions; quadratic residue and discrete logarithms. We integrated these two assumptions in our encrypting and decrypting equations so that the former depends on one public key whereas the latter depends on one corresponding secret key and two secret numbers. Each of public and secret keys in our scheme determines the assumptions we use. Results: The newly developed cryptosystem is shown secure against the three common considering algebraic attacks using a heuristic security technique. The efficiency performance of our scheme requires 2T exp +2T mul +T hash time complexity for encryption and T exp +2T mul +T srt time complexity for decryption and this magnitude of complexity is considered minimal for multiple cryptographic assumptions-like cryptosystems. Conclusion: The new cryptosystem based on multiple cryptographic assumptions offers a greater security level than that schemes based on a single cryptographic assumption. The adversary has to solve the two assumptions simultaneously to recover the original message from the received corresponding encrypted message but this is very unlikely to happen.

FPGA Implementation of Cryptographic Algorithm Using ASCII Conversions for Secure Communications

“…The enemy or adversary has to solve the two problems simultaneously which is unlikely to happen in order to read any secret message [6]. Some researchers have developed a new cryptosystem using multiple cryptographic assumptions which offers a greater security level than that schemes based on a single cryptographic assumptions [8]. S. Kumar, Addgarla, and Y. Babji made a comparative security study on symmetric key crptosystem based algorithms such as DES, TDES, IDEA, and AES [9].…”

“…As the explanation in the encryption phase the characters of each packet are converted to their equivalent ASCII. Then using the 8-bit binary equivalent of the ASCII the first matrix P1 [8,8] is formed for the first packet as shown in Fig.4.1 with the subsequent calculations to encrypt the characters of the packet. In the decryption phase of the algorithm, at first the characters of the received unprintable ciphertext are converted to their equivalent ASCII.…”

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

“…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.…”

Development of a New Elliptic Curve Cryptosystem with Factoring Problem

“…If one day in a near future an attacker solves the hard problem, the underlying system will no longer be secure. Thus to overcome this disadvantage, many designers are proposing cryptosystems based on two hard problems (Baocang and Yupu, 2005;Elkamchouchi et al, 2004;Harn, 1994;Ismail and Hijazi, 2011). If the attacker find a solution to one of these hard problem the system stays secure as the another problem is still hard to solve.…”