Verifiable multi-secret sharing schemes for multiple threshold access structures

A multi-secret sharing scheme allows several secrets to be shared amongst a group of participants. In 2005, Shao and Cao developed a verifiable multi-secret sharing scheme where each participant’s share can be used several times which reduces the number of interactions between the dealer and the group members. In addition some secrets may require a higher security level than others involving the need for different threshold values. Recently Chan and Chang designed such a scheme but their construction only allows a single secret to be shared per threshold value. In this article we combine the previous two approaches to design a multiple time verifiable multi-secret sharing scheme where several secrets can be shared for each threshold value. Since the running time is an important factor for practical applications, we will provide a complexity comparison of our combined approach with respect to the previous schemes.

Algebraic Cryptanalysis of CTRU Cryptosystem

CTRU, a public key cryptosystem was proposed by Gaborit, Ohler and Sole. It is analogue of NTRU, the ring of integers replaced by the ring of polynomials $\mathbb{F}_2[T]$ . It attracted attention as the attacks based on either LLL algorithm or the Chinese Remainder Theorem are avoided on it, which is most common on NTRU. In this paper we presents a polynomial-time algorithm that breaks CTRU for all recommended parameter choices that were derived to make CTRU secure against popov normal form attack. The paper shows if we ascertain the constraints for perfect decryption then either plaintext or private key can be achieved by polynomial time linear algebra attack.

Nonhomogeneous subalgebras of Lie and special Jordan superalgebras

We consider polynomial identities satisfied by nonhomogeneous subalgebras of Lie and special Jordan superalgebras: we ignore the grading and regard the superalgebra as an ordinary algebra. The Lie case has been studied by Volichenko and Baranov: they found identities in degrees 3, 4 and 5 which imply all the identities in degrees <= 6. We simplify their identities in degree 5, and show that there are no new identities in degree 7. The Jordan case has not previously been studied: we find identities in degrees 3, 4, 5 and 6 which imply all the identities in degrees <= 6, and demonstrate the existence of further new identities in degree 7. our proofs depend on computer algebra: we use the representation theory of the symmetric group, the Hermite normal form of an integer matrix, the LLL algorithm for lattice basis reduction, and the Chinese remainder theorem. (C) 2009 Elsevier Inc. All rights reserved.

Sturm Sequences and Modified Subresultant Polynomial Remainder Sequences

ACM Computing Classification System (1998): F.2.1, G.1.5, I.1.2.

Peer to peer English/Chinese cross-language information retrieval

Peer to peer systems have been widely used in the internet. However, most of the peer to peer information systems are still missing some of the important features, for example cross-language IR (Information Retrieval) and collection selection / fusion features. Cross-language IR is the state-of-art research area in IR research community. It has not been used in any real world IR systems yet. Cross-language IR has the ability to issue a query in one language and receive documents in other languages. In typical peer to peer environment, users are from multiple countries. Their collections are definitely in multiple languages. Cross-language IR can help users to find documents more easily. E.g. many Chinese researchers will search research papers in both Chinese and English. With Cross-language IR, they can do one query in Chinese and get documents in two languages. The Out Of Vocabulary (OOV) problem is one of the key research areas in crosslanguage information retrieval. In recent years, web mining was shown to be one of the effective approaches to solving this problem. However, how to extract Multiword Lexical Units (MLUs) from the web content and how to select the correct translations from the extracted candidate MLUs are still two difficult problems in web mining based automated translation approaches. Discovering resource descriptions and merging results obtained from remote search engines are two key issues in distributed information retrieval studies. In uncooperative environments, query-based sampling and normalized-score based merging strategies are well-known approaches to solve such problems. However, such approaches only consider the content of the remote database but do not consider the retrieval performance of the remote search engine. This thesis presents research on building a peer to peer IR system with crosslanguage IR and advance collection profiling technique for fusion features. Particularly, this thesis first presents a new Chinese term measurement and new Chinese MLU extraction process that works well on small corpora. An approach to selection of MLUs in a more accurate manner is also presented. After that, this thesis proposes a collection profiling strategy which can discover not only collection content but also retrieval performance of the remote search engine. Based on collection profiling, a web-based query classification method and two collection fusion approaches are developed and presented in this thesis. Our experiments show that the proposed strategies are effective in merging results in uncooperative peer to peer environments. Here, an uncooperative environment is defined as each peer in the system is autonomous. Peer like to share documents but they do not share collection statistics. This environment is a typical peer to peer IR environment. Finally, all those approaches are grouped together to build up a secure peer to peer multilingual IR system that cooperates through X.509 and email system.