We propose a parallel pth powering method over an arbitrary finite field GF(pm). Using the proposed method, we present the explicit formulae for the computation of cubing over a ternary field GF(3m) which is defined by irreducible trinomials. We show that the field cubing computation for irreducible trinomials, which plays an important role in calculating pairing, can be implemented very efficiently.

A field multiplication in the extended binary field is often expressed using Toeplitz matrix-vector products (TMVPs), whose matrices have special properties such as symmetric or triangular. We show that such TMVPs can be efficiently implemented by taking advantage of some properties of matrices. This yields an efficient multiplier when a field multiplication involves such TMVPs. For example, we propose an efficient multiplier based on the Dickson basis which requires the reduced number of XOR gates by an average of 34% compared with previously known results.

Finding rare cases with medical data is important when hospitals or research institutes want to identify rare diseases. To extract meaningful information from a large amount of sensitive medical data, privacy-preserving data mining techniques can be used. A privacy-preserving t-repetition protocol can be used to find rare cases with distributed medical data. A privacy-preserving t-repetition protocol is to find elements which exactly t parties out of n parties have in common in their datasets without revealing their private datasets. A privacy-preserving t-repetition protocol can be used to find not only common cases with a high t but also rare cases with a low t. In 2011, Chun et al. suggested the generic set operation protocol which can be used to find t-repeated elements. In the paper, we first show that the Chun et al.'s protocol becomes infeasible for calculating t-repeated elements if the number of users is getting bigger. That is, the computational and communicational complexities of the Chun et al.'s protocol in calculating t-repeated elements grow exponentially as the number of users grows. Then, we suggest a polynomial-time protocol with respect to the number of users, which calculates t-repeated elements between users.

Distance bounding protocols permit a verifier to compute the distance to a prover by measuring the execution time of n rounds of challenge-response authentication. Many protocols have been proposed to reduce the false acceptance rate of the challenge-response procedure. Until now, it has been widely believed that the lowest bound of the false acceptance rate is (1/2)n when n is the number of rounds and the prover can send only one response bit for each round. In this paper, we propose a new distance bounding protocol whose false acceptance rate is (1/3)n against the distance fraud attacks and the mafia fraud attacks. To reduce the false acceptance rate, we use two challenge bits for each iteration and introduce a way of expressing three cases with the use of only one response bit, the same bit length as existing protocols. Our protocol is the first distance bounding protocol whose false acceptance rate is lower than the currently believed minimal bound without increasing the number of response bits for each round.

We propose subquadratic space complexity multipliers for any finite field $mathbb{F}_{q^n}$ over the base field $mathbb{F}_q$ using the Dickson basis, where q is a prime power. It is shown that a field multiplication in $mathbb{F}_{q^n}$ based on the Dickson basis results in computations of Toeplitz matrix vector products (TMVPs). Therefore, an efficient computation of a TMVP yields an efficient multiplier. In order to derive efficient $mathbb{F}_{q^n}$ multipliers, we develop computational schemes for a TMVP over $mathbb{F}_{q}$. As a result, the $mathbb{F}_{2^n}$ multipliers, as special cases of the proposed $mathbb{F}_{q^n}$ multipliers, have lower time complexities as well as space complexities compared with existing results. For example, in the case that n is a power of 3, the proposed $mathbb{F}_{2^n}$ multiplier for an irreducible Dickson trinomial has about 14% reduced space complexity and lower time complexity compared with the best known results.

In this paper, we derive a fast polynomial basis multiplier for GF(2m) defined by pentanomials xm+xk3+xk2+xk1+1 with 1 ≤ k1 < k2 < k3 ≤ m/2 using the presented method by Park and Chang. The proposed multiplier has the time delay TA+(2+⌈log2(m-1)⌉) TX or TA+(3+⌈log2(m-1)⌉) TX which is the lowest one compared with known multipliers for pentanomials except for special types, where TA and TX denote the delays of one AND gate and one XOR gate, respectively. On the other hand, its space complexity is very slightly greater than the best known results.

In this paper, we present a new three-way split formula for binary polynomial multiplication (PM) with five recursive multiplications. The scheme is based on a recently proposed multievaluation and interpolation approach using field extension. The proposed PM formula achieves the smallest space complexity. Moreover, it has about 40% reduced time complexity compared to best known results. In addition, using developed techniques for PM formulas, we propose a three-way split formula for Toeplitz matrix vector product with five recursive products which has a considerably improved complexity compared to previous known one.

In several important applications, we often encounter with the computation of a Toeplitz matrix vector product (TMVP). In this work, we propose a k-way splitting method for a TMVP over any field F, which is a generalization of that over GF(2) presented by Hasan and Negre. Furthermore, as an application of the TMVP method over F, we present the first subquadratic space complexity multiplier over any finite field GF(pn) defined by an irreducible trinomial.

Privacy preserving association rule mining algorithms have been designed for discovering the relations between variables in data while maintaining the data privacy. In this article we revise one of the recently introduced schemes for association rule mining using fake transactions (fs). In particular, our analysis shows that the fs scheme has exhaustive storage and high computation requirements for guaranteeing a reasonable level of privacy. We introduce a realistic definition of privacy that benefits from the average case privacy and motivates the study of a weakness in the structure of fs by fake transactions filtering. In order to overcome this problem, we improve the fs scheme by presenting a hybrid scheme that considers both privacy and resources as two concurrent guidelines. Analytical and empirical results show the efficiency and applicability of our proposed scheme.

Searchable encryption has many applications including e-mail systems and storage systems. The usefulness of searchable encryption derives from its support of keyword-testability. Keyword-testability means that a receiver of a ciphertext can test whether the ciphertext contains a specific keyword. Recently, Bellare et al. suggested an efficiently-searchable encryption scheme with keyword-recoverability as well as keyword-testability. Keyword-recoverability means that a receiver can extract the keyword from a ciphertext. All of the previous searchable encryption schemes have provided only keyword-testability. However, as explained by Bellare et al., no efficiently-searchable encryption scheme can provide even security against chosen keyword attacks. That is, Bellare et al.'s scheme assumes that no useful partial information about the keyword is known to the adversaries. In this paper, we suggest an SEKR (searchable encryption with keyword-recoverability) scheme which is secure even if the adversaries have any useful partial information about the keyword. Our scheme provides security against chosen ciphertext attacks which are stronger attacks than chosen keyword attacks. We also suggest an SEKR scheme for multi-keywords.