Cryptography is the study that provides security service. It concerns with confidentiality, integrity, and authentication. Public key cryptography provides an enormous revolution in the field of the cryptosystem. It u...Cryptography is the study that provides security service. It concerns with confidentiality, integrity, and authentication. Public key cryptography provides an enormous revolution in the field of the cryptosystem. It uses two different keys where keys are related in such a way that, the public key can use to encrypt the message and private key can be used to decrypt the message. This paper proposed an enhanced and modified approach of RSA cryptosystem based on “n” distinct prime number. This existence of “n” prime number increases the difficulty of the factoring of the variable “N” which increases the complexity of the algorithm. In this approach, two different public key and private key generated from the large factor of the variable “N” and perform a double encryption-decryption operation which affords more security. Experiment on a set of a random number provided that the key generation time, analysis of variable “N”, encryption and decryption will take a long time compared to traditional RSA. Thus, this approach is more efficient, highly secured and not easily breakable.展开更多
RSA public key cryptosystem is extensively used in information security systems. However, key generation for RSA cryptosystem requires multiplicative inversion over finite field, which has higher computational complex...RSA public key cryptosystem is extensively used in information security systems. However, key generation for RSA cryptosystem requires multiplicative inversion over finite field, which has higher computational complexity, compared with either multiplication in common sense or modular multiplication over finite field. In order to improve the performance of key generation, we propose a batch private keys generation method in this paper. The method derives efficiency from cutting down multiplicative inversions over finite field. Theoretical analysis shows that the speed of batch private keys generation for s users is faster than that of s times solo private key generation. It is suitable for applications in those systems with large amount of users.展开更多
The security of the RSA system with the prime pairs of some special form is investigated. A new special-purpose algorithm for factoring RSA numbers is proposed. The basic idea of the method is to factor RSA numbers by...The security of the RSA system with the prime pairs of some special form is investigated. A new special-purpose algorithm for factoring RSA numbers is proposed. The basic idea of the method is to factor RSA numbers by factoring a well-chosen quadratic polynomial with integral coefficients. When viewed as a general-purpose algorithm, the new algorithm has a high computational complexity. It is shown thai the RSA number n = pq can be easily factored if p and q have the special form of p = as＋b, q=cs＋d, where a, b, c, d are relatively small numbers. Such prime pairs （p, q） are the weak keys of RSA, so when we generate RSA modulus, we should avoid using such prime pairs （p, q）.展开更多
In key escrow field it is important to solve the problem thatuser's secret key completely depends on the trusted escrow agency. In 1995, some methods of solving the problem were presented. But these methods are no...In key escrow field it is important to solve the problem thatuser's secret key completely depends on the trusted escrow agency. In 1995, some methods of solving the problem were presented. But these methods are no better than that of directly using threshold cryptography. In this paper, we present a common pattern of threshold key escrow scheme based on public key cryptosystem, and a detailed design based on the improved RSA algorithm is given. The above problem is solved by this scheme.展开更多
A new fast algorithm to compute modular exponentiation for very large integers is proposed in this paper, which is an improvement of the fast RSA algorithm based on Symmetry of Modular Multiplication(SMM). The SMM alg...A new fast algorithm to compute modular exponentiation for very large integers is proposed in this paper, which is an improvement of the fast RSA algorithm based on Symmetry of Modular Multiplication(SMM). The SMM algorithm obtains the speed improvement by conditional substitution on every basic operation to decrease the absolute value of product and the operation numbers of modular reductions. The proposed algorithm can get faster operation speed by decreasing the numbers of basic operations. Compared to conventional binary representation, a speed improvement of approximately 47.5% would be expected using the proposed algorithm.展开更多
In this paper,we propose a. practical parallel algorithm for computing ab mod c. The algorithm is based on RES representations of integers. In particular, a technique is introduced for avoiding overflow.The algorithm ...In this paper,we propose a. practical parallel algorithm for computing ab mod c. The algorithm is based on RES representations of integers. In particular, a technique is introduced for avoiding overflow.The algorithm is easy to be implemented on hardware and achieves linear speedup.展开更多
This paper describes an algorithm for secure transmission of information via open communication channels based on the discrete logarithm problem. The proposed algorithm also provides sender identification (digital sig...This paper describes an algorithm for secure transmission of information via open communication channels based on the discrete logarithm problem. The proposed algorithm also provides sender identification (digital signature). It is twice as fast as the RSA algorithm and requires fifty per cent fewer exponentiations than the ElGamal cryptosystems. In addition, the algorithm requires twice less bandwidth than the ElGamal algorithm. Numerical examples illustrate all steps of the proposed algorithm: system design (selection of private and public keys), encryption, transmission of information, decryption and information recovery.展开更多
文摘Cryptography is the study that provides security service. It concerns with confidentiality, integrity, and authentication. Public key cryptography provides an enormous revolution in the field of the cryptosystem. It uses two different keys where keys are related in such a way that, the public key can use to encrypt the message and private key can be used to decrypt the message. This paper proposed an enhanced and modified approach of RSA cryptosystem based on “n” distinct prime number. This existence of “n” prime number increases the difficulty of the factoring of the variable “N” which increases the complexity of the algorithm. In this approach, two different public key and private key generated from the large factor of the variable “N” and perform a double encryption-decryption operation which affords more security. Experiment on a set of a random number provided that the key generation time, analysis of variable “N”, encryption and decryption will take a long time compared to traditional RSA. Thus, this approach is more efficient, highly secured and not easily breakable.
基金Supported by National Laboratory for Modern Communications Foundation (No. 5143 6010404DZ0235)
文摘RSA public key cryptosystem is extensively used in information security systems. However, key generation for RSA cryptosystem requires multiplicative inversion over finite field, which has higher computational complexity, compared with either multiplication in common sense or modular multiplication over finite field. In order to improve the performance of key generation, we propose a batch private keys generation method in this paper. The method derives efficiency from cutting down multiplicative inversions over finite field. Theoretical analysis shows that the speed of batch private keys generation for s users is faster than that of s times solo private key generation. It is suitable for applications in those systems with large amount of users.
基金Supported by the National Natural Science Foun-dation of China (60473029)
文摘The security of the RSA system with the prime pairs of some special form is investigated. A new special-purpose algorithm for factoring RSA numbers is proposed. The basic idea of the method is to factor RSA numbers by factoring a well-chosen quadratic polynomial with integral coefficients. When viewed as a general-purpose algorithm, the new algorithm has a high computational complexity. It is shown thai the RSA number n = pq can be easily factored if p and q have the special form of p = as＋b, q=cs＋d, where a, b, c, d are relatively small numbers. Such prime pairs （p, q） are the weak keys of RSA, so when we generate RSA modulus, we should avoid using such prime pairs （p, q）.
基金This work was supported by the National Natural Science Foundation of China (Grant Nos. 69772037, 60072018).
文摘In key escrow field it is important to solve the problem thatuser's secret key completely depends on the trusted escrow agency. In 1995, some methods of solving the problem were presented. But these methods are no better than that of directly using threshold cryptography. In this paper, we present a common pattern of threshold key escrow scheme based on public key cryptosystem, and a detailed design based on the improved RSA algorithm is given. The above problem is solved by this scheme.
文摘A new fast algorithm to compute modular exponentiation for very large integers is proposed in this paper, which is an improvement of the fast RSA algorithm based on Symmetry of Modular Multiplication(SMM). The SMM algorithm obtains the speed improvement by conditional substitution on every basic operation to decrease the absolute value of product and the operation numbers of modular reductions. The proposed algorithm can get faster operation speed by decreasing the numbers of basic operations. Compared to conventional binary representation, a speed improvement of approximately 47.5% would be expected using the proposed algorithm.
文摘In this paper,we propose a. practical parallel algorithm for computing ab mod c. The algorithm is based on RES representations of integers. In particular, a technique is introduced for avoiding overflow.The algorithm is easy to be implemented on hardware and achieves linear speedup.
文摘This paper describes an algorithm for secure transmission of information via open communication channels based on the discrete logarithm problem. The proposed algorithm also provides sender identification (digital signature). It is twice as fast as the RSA algorithm and requires fifty per cent fewer exponentiations than the ElGamal cryptosystems. In addition, the algorithm requires twice less bandwidth than the ElGamal algorithm. Numerical examples illustrate all steps of the proposed algorithm: system design (selection of private and public keys), encryption, transmission of information, decryption and information recovery.
