SETUP in Secret Sharing Schemes using Random Values

Secret sharing schemes divide a secret among multiple participants so that only authorized subsets of parties can reconstruct it. We show that SETUP (Secretly Embedded Trapdoor with Universal Protection) attack can be embedded in secret sharing schemes that employ enough randomness to give the attacker an overwhelming advantage to access the secret. In case of ideal schemes, a coalition of a few participants (within at least one is the attacker) can succeed the attack, while in case of non-ideal schemes the attacker\u27s knowledge can be enough to reveal the secret. We exemplify the attack against Shamir\u27s threshold scheme, which is the most well-known and used secret sharing scheme. Finally, we consider some prevention techniques against the proposed attack

CHURP: Dynamic-Committee Proactive Secret Sharing

We introduce CHURP (CHUrn-Robust Proactive secret sharing). CHURP enables secure secret-sharing in dynamic settings, where the committee of nodes storing a secret changes over time. Designed for blockchains, CHURP has lower communication complexity than previous schemes: $O(n)$ on-chain and $O(n^2)$ off-chain in the optimistic case of no node failures. CHURP includes several technical innovations: An efficient new proactivization scheme of independent interest, a technique (using asymmetric bivariate polynomials) for efficiently changing secret-sharing thresholds, and a hedge against setup failures in an efficient polynomial commitment scheme. We also introduce a general new technique for inexpensive off-chain communication across the peer-to-peer networks of permissionless blockchains. We formally prove the security of CHURP, report on an implementation, and present performance measurements

Secret-Sharing for NP

A computational secret-sharing scheme is a method that enables a dealer, that has a secret, to distribute this secret among a set of parties such that a "qualified" subset of parties can efficiently reconstruct the secret while any "unqualified" subset of parties cannot efficiently learn anything about the secret. The collection of "qualified" subsets is defined by a Boolean function. It has been a major open problem to understand which (monotone) functions can be realized by a computational secret-sharing schemes. Yao suggested a method for secret-sharing for any function that has a polynomial-size monotone circuit (a class which is strictly smaller than the class of monotone functions in P). Around 1990 Rudich raised the possibility of obtaining secret-sharing for all monotone functions in NP: In order to reconstruct the secret a set of parties must be "qualified" and provide a witness attesting to this fact. Recently, Garg et al. (STOC 2013) put forward the concept of witness encryption, where the goal is to encrypt a message relative to a statement "x in L" for a language L in NP such that anyone holding a witness to the statement can decrypt the message, however, if x is not in L, then it is computationally hard to decrypt. Garg et al. showed how to construct several cryptographic primitives from witness encryption and gave a candidate construction. One can show that computational secret-sharing implies witness encryption for the same language. Our main result is the converse: we give a construction of a computational secret-sharing scheme for any monotone function in NP assuming witness encryption for NP and one-way functions. As a consequence we get a completeness theorem for secret-sharing: computational secret-sharing scheme for any single monotone NP-complete function implies a computational secret-sharing scheme for every monotone function in NP

KALwEN+: Practical Key Management Schemes for Gossip-Based Wireless Medical Sensor Networks

The constrained resources of sensors restrict the design of a key management scheme for wireless sensor networks (WSNs). In this work, we first formalize the security model of ALwEN, which is a gossip-based wireless medical sensor network (WMSN) for ambient assisted living. Our security model considers the node capture, the gossip-based network and the revocation problems, which should be valuable for ALwEN-like applications. Based on Shamir's secret sharing technique, we then propose two key management schemes for ALwEN, namely the KALwEN+ schemes, which are proven with the security properties defined in the security model. The KALwEN+ schemes not only fit ALwEN, but also can be tailored to other scalable wireless sensor networks based on gossiping

PROPYLA: Privacy Preserving Long-Term Secure Storage

An increasing amount of sensitive information today is stored electronically and a substantial part of this information (e.g., health records, tax data, legal documents) must be retained over long time periods (e.g., several decades or even centuries). When sensitive data is stored, then integrity and confidentiality must be protected to ensure reliability and privacy. Commonly used cryptographic schemes, however, are not designed for protecting data over such long time periods. Recently, the first storage architecture combining long-term integrity with long-term confidentiality protection was proposed (AsiaCCS'17). However, the architecture only deals with a simplified storage scenario where parts of the stored data cannot be accessed and verified individually. If this is allowed, however, not only the data content itself, but also the access pattern to the data (i.e., the information which data items are accessed at which times) may be sensitive information. Here we present the first long-term secure storage architecture that provides long-term access pattern hiding security in addition to long-term integrity and long-term confidentiality protection. To achieve this, we combine information-theoretic secret sharing, renewable timestamps, and renewable commitments with an information-theoretic oblivious random access machine. Our performance analysis of the proposed architecture shows that achieving long-term integrity, confidentiality, and access pattern hiding security is feasible.Comment: Few changes have been made compared to proceedings versio

Economical (k,m)-threshold controlled quantum teleportation

We study a (k,m)-threshold controlling scheme for controlled quantum teleportation. A standard polynomial coding over GF(p) with prime p > m-1 needs to distribute a d-dimensional qudit with d >= p to each controller for this purpose. We propose a scheme using m qubits (two-dimensional qudits) for the controllers' portion, following a discussion on the benefit of a quantum control in comparison to a classical control of a quantum teleportation.Comment: 11 pages, 2 figures, v2: minor revision, discussions improved, an equation corrected in procedure (A) of section 4.3, v3: major revision, protocols extended, citations added, v4: minor grammatical revision, v5: minor revision, discussions extende