In some applications, a short private exponent d is chosen to improve the decryption or signing process for RSA public key cryptosystem. However, in a typical RSA, if the private exponent d is selected first, the public exponent e should be of the same order of magnitude as φ(N). Sun et al. devised three RSA variants using unbalanced prime factors p and q to lower the computational cost. Unfort...

At the beginning some results from the field of graph theory are presented. Next we show how to share a secret that is proper n-coloring of the graph, with the known structure. The graph is described and converted to the form, where colors assigned to vertices form the number with entries from Zn. A secret sharing scheme (SSS) for the graph coloring is proposed. The proposed method is applied t...

RSA is an algorithm for public-key cryptography that is based on the presumed difficulty of factoring large integers, the factoring problem. RSA stands for Ron Rivest, Adi Shamir and Leonard, who first publicly described it in 1978. A user of RSA creates and then publishes the product of two large prime numbers, along with an auxiliary value, as their public key. The prime factors must be kept ...

Recently, Tao et al. presented a new simple and efficient multivariate pubic key encryption scheme based on matrix multiplication, which is called Simple Matrix Scheme or ABC. Using linearization equation attack, we propose a polynomial time algorithm, which directly recovers an equivalent private key from the public key of ABC. Furthermore, our attack can also be applied to the variants of ABC...

This paper presents a concept for an UHF tag supporting cryptographically strong authentication which is based on the Rabin-Montgomery public key cryptosystem in accordance with the framework of ISO/IEC 29167-1. It uses an easily computable long integer square operation for the public key encryption of a tag ID record. Only a legitimate interrogator who is in possession of the private key can d...

Guo et al. recently presented a reaction attack against the QC-MDPC McEliece cryptosystem. Their attack is based on the observation that when a bit-flipping decoding algorithm is used in the QC-MDPC McEliece, then there exists a dependence between the secret matrix H and the failure probability of the bit-flipping algorithm. This dependence can be exploited to reveal the matrix H which constitu...

We introduce the notion of computational security, in contrast to the perfect security of last lecture, which was an information-theoretic, rather than computational notion. We review the notions of algorithm running time, assymptotic notation, and polynomial time algorithms. We introduce notions of efficient algorithms, negligible probabilities, and adversarial advantage in attacking a cryptos...

Hwang, Lu and Lin (2003) proposed a (t, n) threshold proxy signature scheme, based on the RSA cryptosystem. Later, Wang et al. (2004a) indicated that this scheme was insecure because the original signer’s private key could be derived. Moreover, the delegates’ identities had to be chosen carefully. In this paper, we propose an improved RSA-based (t, n) threshold proxy signature scheme, which wit...

The security issue has become an important concern of grid computing. To prevent the grid resources from being illegally visited, the strong mutual authentication is needed for user and server. In this paper, based on the elliptic curve cryptosystem, we would like to propose an efficient user authentication scheme for grid computing. The proposed scheme only requires a one-way hash function and...