Fast Public Key Cryptosystem Research Articles

Development of a New Chaotic Maps Cryptosystem with Quadratic Residue Problem

A new fast public key cryptosystem is proposed, which is based on two dissimilar number-theoretic hard problems, namely the simultaneous chaotic maps (CM) problem and quadratic residue (QR) problem. The adversary has to solve the two hard problems simultaneously to recover the plaintext according to their knowledge about the public keys and the cipher-text. Cryptographic quadratic residue and chaotic system are employed to enhance the security of our cryptosystem scheme. The encryption, and decryption are discussed in details. Several security attacks are proposed to illustrate the system shield through chaotic maps and quadratic residue problems. The performance analysis of the proposed scheme show a much improved performance over existing techniques.

Decryption speed up of ElGamal with composite modulus.

Public key cryptosystems such as RSA, rebalanced RSA and ElGamal have the disadvantage of serious asymmetry between encryption and decryption speed. We reduced the CRT (Chinese Remainder Theorem) exponents maintaining full sized private exponent in ElGamal with composite modulus (CRT–ElGamal) for the fast decryption as in rebalanced RSA. In this case, unlike rebalanced RSA, decryption speed up can be obtained without losing of the fast encryption speed which is comparable to RSA with small public exponent. As a result, it is possible to propose the fast public key cryptosystem in which both encryption and decryption are fast, by reducing the asymmetry (i.e., fast encryption/slow decryption) in CRT–ElGamal encryption.

D-NTRU: More efficient and average-case IND-CPA secure NTRU variant

NTRU is a fast public key cryptosystem remaining unbroken. However, there is no known worst-to-average reduction for the original NTRU cryptosystem. Several provably secure NTRU modifications such as NAEP, pNE and NTRUCCA were proposed in the literature at the cost of inefficiency in encryption/decryption and enlarged ciphertext expansion. NAEP completes the IND-CCA security of the original NTRU under the average-case NTRU one-wayness intractability assumption. Both pNE and NTRUCCA obtain provable security goals under worst-case lattice assumptions. In this paper, a general framework for NTRU is considered, and a new PKC called D-NTRU is proposed. It is shown that the D-NTRU cryptosystem reduces the ciphertext expansion of the NTRU algorithm, and the encryption and decryption algorithms of D-NTRU perform even asymptotically faster than the NTRU algorithm only at the cost of slightly enlarged secret and public keys. The security of D-NTRU is proven in the standard model and under the average-case NTRU one-wayness assumption. The proof of the IND-CPA security of D-NTRU is completed by introducing another NTRU variant called C-NTRU as a bridge, defining some problems, and then proving the equivalence of these problems. So the proposed D-NTRU algorithm is more advantageous than the original NTRU algorithm, and much more efficient than all the provably secure variants of NTRU.

Cryptanalysis of NTRU with Two Public Keys

NTRU is a fast public key cryptosystem presented in 1996 by Hoffstein, Pipher and Silverman. It operates in the ring of truncated polynomials. In NTRU, a public key is a polynomial defined by the combination of two private polynomials. In this paper, we consider NTRU with two different public keys defined by different private keys. We present a lattice-based attack to recover the private keys assuming that the public keys share polynomials with a suitable number of common coefficients.

Security Analysis of Square Minus Scheme

The multivariate public key cryptosystem is a new and fast public key cryptosystem. This paper investigates the security of Square minus scheme, and presents a method to attack the scheme. The attack utilizes the affine parts of the private keys and the weakness caused by the structures of the private keys to find a large number of linear equations. The attack can recover the private keys efficiently when the parameters are small enough.

A New Public Key Cryptographic Scheme

The multivariate public key cryptosystem is a new and fast public key cryptosystem. This paper presents a multivariate public key cryptographic scheme over a finite field with odd prime characteristic. The idea of embedding and layering is manifested in its construction. The security of the scheme is analyzed in detail. The result indicates that the proposed scheme can resist all known attacks effectively.

Fast Public Key Cryptosystem Based Blind Signature Scheme

Compared with symmetric cryptosystem, asymmetric cryptosystem has much superiority in many application cases. Yet, the computation in a public key cryptosystem is much more complex than symmetric cryptosystem. In the paper, we applied HCC (Hyper-elliptic Curves Cryptosystem) as a typical fast public key cryptosystem into the designing of efficient blind signature scheme and presented an improved blind signature with fast cryptography algorithms. By utilizing probabilistic blinding algorithm, the scheme renders effective protection for the secrecy of original user, the signature generator or outer adversaries can not attack the secret message via the blinded information with effective polynomial algorithms. The scheme avoids the relevance between different signatures and interim parameters from the same original user, thus it effectively prevents signature forgery and replay attack. As security analysis for the scheme, we presented similar blind signature without relevant improving algorithms based on discrete logarithm cryptosystem. The analysis and comparison with other schemes both justify the security, reliability and high efficiency of the improved blind signature scheme regarding software and hardware application environment.

Improved Signcryption Schemes Based on Hyper-Elliptic Curves Cryptosystem

As a typical fast public key cryptosystem, HCC (Hyper-elliptic Curves Cryptosystem) provides efficient asymmetric algorithms for cryptography schemes. In the paper, we presented an improved authenticated encryption scheme based on HCC as a prototype of signcryption scheme. In the scheme, data encryption and signature generation can be achieved in a single formula and signature verifying protocol is also the decryption algorithm. Therefore, the scheme achieves secret message transmission and authentication simultaneously in one protocol. The scheme renders effective secrecy protection for message receiver; the attack on the authenticated signature and random parameters via the cipher-text is computationally infeasible. The designing strategy of message recovery signature reinforces the security and reliability of authenticated encryption and greatly improves its efficiency for software and hardware application. As a generalization of the authenticated encryption scheme, we presented a signcryption scheme based on HCC. The scheme makes full use of the superiority of fast asymmetric cryptosystem and effectively improves the application efficiency of signcryption for integrated environment.

Fast public-key encryption scheme based on Chinese remainder theorem

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.

Cryptanalysis of a public key cryptosystem based on two cryptographic assumptions

Baocang and Yupu proposed a relatively fast public key cryptosystem. The authors claim that the security of their system is based on two number-theoretic hard problems, namely the simultaneous Diophantine approximation problem and the integer factorisation problem. In this article we present a polynomial time heuristic attack that enables us to recover the private key from the public key. In particular, we show that breaking the system can be reduced to finding a short vector in a lattice which can be achieved using the L3-lattice reduction algorithm.

Public key cryptosystem based on two cryptographic assumptions

A new fast public key cryptosystem is proposed, which is based on two dissimilar number-theoretic hard problems, namely the simultaneous Diophantine approximation problem and integer factorisation problem. The adversary has to solve the two hard problems simultaneously to recover the plaintext according to their knowledge about the public keys and the cipher-text. Therefore, the scheme is expected to gain a high level of security. The newly-designed public key cryptosystem is efficient with respect to encryption and decryption. The encryption of this system is about three times faster than that of RSA, and the decryption is six times faster than that of RSA. The cipher-text expansion of the system is about 8:3.

Fast public-key cryptosystem using congruent polynomial equations

A fast public-key cryptosystem is proposed which is based on congruent polynomial equations. This scheme is much faster than the RSA scheme. Moreover, the encryption and decyption algorithms for this scheme are very simple. The task of breaking this scheme appears to be as difficult as that of factoring a large composite integer, although this has not yet been proven.

Fast public key cryptosystem based on matrix rings

A public key cryptosystem is proposed, which is based on the assumption that finding the square root of an element in a large finite ring is computationally infeasible in the absence of a knowledge of the ring structure. The encryption and decryption operations are very fast, and the data expansion is 1:2.