Mathematics Department

Over the last few years, among various alternatives to the Einstein theory of gravity, especially theories of gravity have received more importance due to number of interesting results in cosmology and astrophysics. Pandey [10] gave an theory of gravity to obtain conformally invariant gravitational waves in which field equations have the form given by (3). In this paper we have investigated Lyttleton Bondi Cosmological model in view of field equations of theory of gravity for Generalized Peres spacetime and finally a wave like solution is obtained.

Over the last few years, among various alternatives to the Einstein theory of gravity, especially theories of gravity have received more importance due to number of interesting results in cosmology and astrophysics. Pandey [10] gave an theory of gravity to obtain conformally invariant gravitational waves in which field equations have the form given by (3). In this paper we have investigated Lyttleton Bondi Cosmological model in view of field equations of theory of gravity for Generalized Peres spacetime and finally a wave like solution is obtained.

Modified theories of Gravity have gained increased attention over the last few years due to combined motivation coming from various branches of physics. Among various alternatives to the Einstein theory of gravity, especially f (R) theories of gravity have received more importance due to number of interesting results in cosmology and astrophysics. Pandey [6] gave an f (R) theory of gravity to obtain comformally invariant gravitational waves in which field equations have the form given by (3). In this paper we have obtained a wave solution of f (R) theory of gravity in a special case of generalized Peres spacetime taken by Pandey [1] for n = 2. Some important features of the solution is discussed and is compared with the form of solution obtained by Pandey [1].

Now-a-days computational fluid mechanics has become very vital area in which obtained governing equations are differential equations. Sometimes, these governing equations cannot be easily solved by existing analytical methods. Due to this reason, we use various numerical techniques to find out approximate solution for such problems. Among these techniques, finite volume method is also being used for solving these governing equations here we are describing comparative study of Finite volume method and finite difference method.

Convection-Diffusion Problems occur very frequently in applied sciences and engineering. In this paper, the cru x of research articles published by numerous researchers during 2007-2011 in referred journals has been presented and this leads to conclusions and recommendations about what methods to use on Convection-Diffusion Problems. It is found that engineers and scientists are using finite element method, finite volu me method, finite volu me element method etc. in flu id mechanics. Here we discuss real life problems of fluid engineering solved by various numerical methods .which is very useful for finding solution of those type of governing equation, whose analytical solution are not easily found.

Convection-diffusion problems arise frequently in many areas of applied sciences and engineering. In this paper, we solve a convection-diffusion problem by central differencing scheme, upwinding differencing scheme (which are special cases of finite volume scheme) and finite difference scheme at various Peclet numbers. It is observed that when central differencing scheme is applied, the solution changes rapidly at high Peclet number because when velocity is large, the flow term becomes large, and the convection term dominates. Similarly, when velocity is low, the diffusion term dominates and the solution diverges, i.e., mathematically the system does not satisfy the criteria of consistency. On applying upwinding differencing scheme, we conclude that the criteria of consistency is satisfied because in this scheme the flow direction is also considered. To support our study, a test example is taken and comparison of the numerical solutions with the analytical solutions is done.

The single-phase pressure drop and heat transfer in a rotor-assembled strand inserted tube were measured using water as the working fluid. Experiment using a smooth tube was carried out to calibrate the experimental system and the data reduction method. In the experiment, fixed mounts were used to eliminate the entrance effect. The experimental results of smooth tube show that employment of fixed mounts leads to a visible bias of friction factor at relative low Reynolds numbers, although it does not significantly affect the Nusselt numbers. The measured data of inserted tube reveal that rotor-assembled strand can significantly improve heat transfer with the Nusselt number increased by 101.6% 106.6% and the overall heat transfer coefficient increased by 58.1% 67.4% within the Reynolds number range of 20000 to 36000. Meanwhile, friction factor increases by 52.2% 84.2% within the same Reynolds number range. The correlations of Nusselt number and friction factor as function of the Reynolds number and Prandtl number were determined through multivariant linear normal regression.

An e# cient and semantically secure public key cryptosystem based on singular cubic curve is proposed in this paper. It is about two times faster than the cryptosystem of David at the same security label and more e# cient than the Koyama scheme at high security level. Further, the partially known plaintext attack and the linearly related plaintext attacks are analyzed and concluded that those are not possible in the proposed scheme.

Abstract: The standard RSA cryptosystem is not semantically secure. Pointcheviel proposed a variant of RSA cryptosystem with the property of semantic security by introducing a new problem known as DRSA problem. He called it DRSA scheme. In this paper, we underlined a shortcoming of that scheme and proposed an alternative DRSA public key cryptosystem. Keywords: Public key cryptosystem, RSA, DRSA, semantically secure.

Digital signatures are efficient tools for source authenticationin cryptography. The concept of proxy signature enables a signer todelegate its signing capability to any other party, called proxy signer. Inthis paper, an efficient multi-proxy signature scheme is proposed frombilinear pairing, using the Boneh, Lynn and Shacham's (BLS) shortsignature 1 and ID-based signature of Xun Yi 2. The size of signature inour scheme is less than those of other existing schemes 3-4. Furthermore, our scheme satisfies all the security ...

In this paper we revisit Meng et. al [9] method to find new weakness in RSA. Let N= pq be an LSBS-RSA modulus where p and q have same bit length. Let p and ρq share the m least significant bits, where ρ (1≤ ρ≤ 2) is known to the attacker. In this paper, under some assumption, we show that the number of weak keys e is at least N 3 4+ θ− ϵ, and there exist a probabilistic algorithm that can factor N in time

Abstract: Identity-based (ID-based) public key settings are very good alternatives for the certificate based public key settings. Proxy signatures are good tools to delegate the signing capability by original signer to any other parties. The concept of bilinear pairing is very useful in many signature protocols for the ease of computation. Here, we propose an ID-based multi-proxy multi-signature scheme using bilinear pairing and replacing the certificate generation of Li and Chen scheme [5], by delegation generation. Our scheme is more ...

Abstract. RSA type public key cryptosystems based on the Pell's equation are proposed in the honor of an Indian mathematician Brahmgupta who studied Pell's equation long before European mathematicians came to know about it. Three RSA type schemes are proposed, first two are not semantically secure where as the other two schemes are semantically secure. The decryption speed of the proposed schemes is about two times as fast as RSA for a 2 log n-bit message. It is shown that the proposed schemes are more secure than the ...

An efficient and semantically secure public key cryptosystem based on singular cubic curve is proposed in this paper. It is about two times faster than the cryptosystem of David at the same security label and more efficient than the Koyama scheme at high security level. Further, the partially known plaintext attack and the linearly related plaintext attacks are analyzed and concluded that those are not possible in the proposed scheme.

An attack is possible upon all three RSA analogue PKCs based on singular cubic curves given by Koyama. While saying so, Seng et al observed that the scheme become insecure if a linear relation is known between two plaintexts. In this case, attacker has to compute greatest common divisor of two polynomials corresponding to those two plaintexts. However, the computation of greatest common divisor of two polynomials is not efficient. For the reason, the degree e of both polynomials, an encryption exponent, is quite large. In this ...

Proxy signature is useful in situation when a user wants to authorize an agent called proxy signer to sign any document on his behalf. Multi-proxy multi-signature is one of the primitives of proxy signature. Bilinear pairing makes the system efficient and provides an ease in computation. In this paper, we propose an ID-based multi-proxy multi-signature scheme from bilinear pairings based on Computational Diffie-Hellman Problem (CDHP), replacing the certificate generation of Li and Chen's scheme by delegation generation. Our scheme is proxy protected and computationally more efficient than the ID-based multi-proxy multi-signature scheme of Li and Chen. We also analyze the security properties of our scheme and show that the proposed scheme satisfies all the security requirements of a safe proxy signature scheme.

Key agreement (KA) allows two or more users to negotiate a secret session key among them over an open network. Authenticated key agreement (AKA) is a KA protocol enhanced to prevent active attacks. AKA can be achieved using a public-key infrastructure (PKI) or identity-based cryptography. However, the former suffers from a heavy certificate management burden while the latter is subject to the so-called key escrow problem. Recently, certificateless cryptography was introduced to mitigate these limitations. We propose an efficient certificateless two-party AKA protocol. Security is proven under the standard computational Diffie-Hellman (CDH) and bilinear Diffie-Hellman (BDH) assumptions. Our protocol is efficient and practical, because it requires only one pairing operation and three scale multiplications by each party. Moreover, the pairing operation and one scale multiplication scale can be precomputed, then only two scale multiplications are needed to finished the key agreement.

The cryptosystem proposed by Koyama is not semantically secure. Also, it is not secure against partial known plaintext attack, linearly related plaintext attack and low exponent attack. In this paper we propose a cryptosystem over singular cubic curve using ...

Proxy signature is an active research area in cryptography. A proxy signature scheme allows an entity to delegate his or her signing capability to another entity in such a way that the latter can sign messages on behalf of the former. Many proxy signature schemes using bilinear pairings have been proposed. But the relative computation cost of the pairing is more than 10 times of the scalar multiplication over elliptic curve group. In order to save the running time and the size of the signature, we propose a proxy signature scheme without bilinear pairings and prove its security against adaptive chosen-message attack in random oracle model. The security of our scheme is based on the hardness of the elliptic curve discrete logarithm problem. With the running time being saved greatly, our scheme is more practical than the previous related scheme for practical applications.