Fast public-key encryption scheme based on Chinese remainder theorem

Abstract

Traditional public-key cryptosystems suffer from a relatively low encryption/decryption speed, which hampers their applications in resource-constrained environments. A fast public-key cryptosystem is proposed to remedy this drawback. The new algorithm uses Chinese remainder theorem to hide the trapdoor information. The encryption of the system only carries out several modular multiplication operations, and the decryption only needs a modular multiplication and a low-dimensional matrixvector multiplication, which makes the speed of the encryption and the decryption of the scheme very high. The security of the system is based on two difficult number-theoretic problems. The attacker has to solve the integer factorization problem and the simultaneous Diophantine approximation problem simultaneously to recover the secret key from the public key. The proposed cryptosystem is also shown to be secure against lattice attack. The analysis shows that the encryption algorithm is a secure, fast and efficient public-key cryptosystem.

Enhancing Data Privacy and Access Anonymity in Cloud Computing

“…These factors could be carefully designed to get less impact on the efficiency of our method. In general, computing the Chines Reminder Theorem solution is efficient compared to other cryptography methods used in cryptography access control as it uses simple modulus operations without exponential operation (Wang, Wei and Hu 2009).…”

Cryptanalysis of two cryptosystems based on multiple intractability assumptions

“…In this section, we describe the two cryptosystems with multiple intractability assumptions. For detailed information on the design, please refer to the papers [8,9].…”

“…Some designers of cryptosystems think that a system based on multiple intractable problems should be more secure since these problems are very hard to be solved simultaneously. With this idea considered, two public key cryptosystems with two intractable problems, integer factorisation and simultaneous Diophantine approximation problems, mixed in their design were proposed by Hu in 2005 and2009, respectively, [8,9]. The simultaneous Diophantine approximation problem is, roughly speaking, a problem of finding n rational fractions with a same denominator to approximate, respectively, the given n real numbers.…”

“…Under some conditions, certain simultaneous Diophantine approximation problems are NP-hard [10]. Wang and Hu [8,9] constructed some modular equations with small unknowns and with modulus being unknown prime divisors of some given large integer N. For the security of these two schemes and to break the schemes, they claimed that an attacker should first factor N and then solve the simultaneous Diophantine approximation problem which is reduced from finding small roots of these modular equations. They also considered some known attacks including direct lattice basis reduction attacks and simultaneous Diophantine approximation attacks.…”

An Efficient Method for Improving the Computational Performance of the Cubic Lucas Cryptosystem

“…Thus, to remedy this drawback, some fast public key cryptosystems have been proposed, including the NTRU cryptosystem which is based on algebraic structures of certain polynomial rings [6] and the Braid groups based cryptosystem [5]. Other research has investigated improving some strong existing public key cryptosystems, such as the RSA and the elliptic curve, using mathematical techniques and computational algorithms [13,17].…”