Blockchain is a transformational technology which affects finance, Internet, and politics. However, many privacy protection problems for blockchain are waiting to be solved. In this study, we propose a novel linkable ring signature scheme with stealth addresses, which enables the payer and payee of the transaction to be anonymous and unlinkable in the cryptocurrency. The scheme is combined with an elliptic curve discrete logarithm (ECD logarithm)-based key encapsulation mechanism (KEM) stage and a lattice-based signature stage. The master public key and master secret key are much smaller compared with the previous scheme. Complete secure proof of the scheme is also presented in this study.

Multipartite secret sharing is an important research object in the area of secret sharing schemes. Compartmented access structures are an interesting class of multipartite access structures. The constructions of ideal linear schemes realizing compartmented access structures are studied by codes in this paper. We find that compartmented secret sharing is related to a class of codes called locally repairable codes which are being used widely in distributed and cloud storage systems. We study secret sharing schemes for compartmented access structures with upper bounds, compartmented access structures with lowers bounds and compartmented access structures with upper and lower bounds. We establish the relationships between secret sharing schemes for these compartmented access structures and locally repairable codes. Based on the relationships and some locally repairable codes, we obtain ideal linear schemes realizing these compartmented access structures by efficient methods.

Multipartite secret sharing schemes are those having a multipartite access structure, in which the set of participants is divided into several parts and all participants in the same part play an equivalent role. Secret sharing schemes for multipartite access structures have received considerable attention due to the fact that multipartite secret sharing can be seen as a natural and useful generalization of threshold secret sharing. This work deals with efficient and explicit constructions of ideal multipartite secret sharing schemes. Most ideal multipartite secret sharing schemes in the literature can be classified as either hierarchical or compartmented. The main results are the constructions for ideal hierarchical access structures, a family that contains every ideal hierarchical access structure as a particular case such as the disjunctive hierarchical threshold access structure and the conjunctive hierarchical threshold access structure, the constructions for three families of compartmented access structures, and the constructions for two families compartmented access structures with compartments. We present an efficient method to construct ideal linear schemes realizing these access structures by linear algebraic techniques on the basis of the relationship between multipartite secret sharing schemes, polymatroids and matroids.

Security challenges brought about by the upcoming 5G era should be taken seriously. Code-based cryptography leverages difficult problems in coding theory and is one of the main techniques enabling cryptographic primitives in the postquantum scenario. In this work, we propose the first efficient secure scheme based on polar codes (i.e., polarRLCE) which is inspired by the RLCE scheme, a candidate for the NIST postquantum cryptography standardization in the first round. In addition to avoiding some weaknesses of the RLCE scheme, we show that, with the proper choice of parameters, using polar codes, it is possible to design an encryption scheme to achieve the intended security level while retaining a reasonably small public key size. In addition, we also present a KEM version of the polarRLCE scheme that can attain a negligible decryption failure rate within the corresponding security parameters. It is shown that our proposal enjoys an apparent advantage to decrease the public key size, especially on the high-security level.

A code over a finite alphabet is called locally repairable codes (LRCs) if every symbol in the encoding is a function of a small number of other symbols of the codeword. In this paper, we study LRCs with heterogeneous locality constraints. We introduce (n, k, ri, δi, i ∈ [m]) LRCs which generalize the LRCs with equal (r, δ)-locality, and establish the Singleton-like bound for such codes. Then, we study how to construct optimal LRCs, namely, its minimum distance attains the proposed bound. In precisely, we redefine the notation of LRCs with maximal recoverability (MR-LRCs) based on the proposed LRCs and show that MR-LRCs are optimal LRCs. Finally, we construct a family of MR-LRCs which extend the construction of LRCs with equal locality presented by Rawat et al.