On Proactive Verifiable Secret Sharing Schemes

The paper has been presented at the International Conference Pioneers of Bulgarian Mathematics, Dedicated to Nikola Obreshkoff and Lubomir Tschakaloff , Sofia, July, 2006. The material in this paper was presented in part at the 11th Workshop on Selected Areas in Cryptography (SAC) 2004This paper investigates the security of Proactive Secret Sharing Schemes. We first consider the approach of using commitment to 0 in the renewal phase in order to refresh the player's shares and we present two types of attacks in the information theoretic case. Then we prove the conditions for the security of such a proactive scheme. Proactivity can be added also using re-sharing instead of commitment to 0. We investigate this alternative approach too and describe two protocols. We also show that both techniques are not secure against a mobile adversary. To summarize we generalize the existing threshold protocols to protocols for general access structure. Besides this, we propose attacks against the existing proactive verifiable secret sharing schemes, and give modifications of the schemes that resist these attacks

General dd-level quantum multi-secret sharing scheme with cheating identification

This work proposes a $d$-dimensional quantum multi-secret sharing (QMSS) scheme with a cheat detection mechanism. The dealer creates the secret shares using multi access structures and a monotone span program. To detect the participant's deceit, the dealer distributes secret share shadows derived from a random invertible matrix $X$ to the participants, stored in the Black box. The cheat detection mechanism of the Black box identifies the participant's deceitful behavior during the secret recovery phase. Only honest participants authenticated by the Black box acquire their secret shares to recover the multiple secrets. After the Black box cheating verification, the participants reconstruct the secrets by utilizing the unitary operations and quantum Fourier transform. The proposed protocol is reliable to prevent attacks from eavesdroppers and participants. The proposed protocol provides greater versatility, security, and practicality

Distributed Protocols with Threshold and General Trust Assumptions

Distributed systems today power almost all online applications. Consequently, a wide range of distributed protocols, such as consensus, and distributed cryptographic primitives are being researched and deployed in practice. This thesis addresses multiple aspects of distributed protocols and cryptographic schemes, enhancing their resilience, efficiency, and scalability. Fundamental to every secure distributed protocols are its trust assumptions. These assumptions not only measure a protocol's resilience but also determine its scope of application, as well as, in some sense, the expressiveness and freedom of the participating parties. Dominant in practice is so far the threshold setting, where at most some f out of the n parties may fail in any execution. However, in this setting, all parties are viewed as identical, making correlations indescribable. These constraints can be surpassed with general trust assumptions, which allow arbitrary sets of parties to fail in an execution. Despite significant theoretical efforts, relevant practical aspects of this setting are yet to be addressed. Our work fills this gap. We show how general trust assumptions can be efficiently specified, encoded, and used in distributed protocols and cryptographic schemes. Additionally, we investigate a consensus protocol and distributed cryptographic schemes with general trust assumptions. Moreover, we show how the general trust assumptions of different systems, with intersecting or disjoint sets of participants, can be composed into a unified system. When it comes to decentralized systems, such as blockchains, efficiency and scalability are often compromised due to the total ordering of all user transactions. Guerraoui (Distributed Computing, 2022) have contradicted the common design of major blockchains, proving that consensus is not required to prevent double-spending in a cryptocurrency. Modern blockchains support a variety of distributed applications beyond cryptocurrencies, which let users execute arbitrary code in a distributed and decentralized fashion. In this work we explore the synchronization requirements of a family of Ethereum smart contracts and formally establish the subsets of participants that need to synchronize their transactions. Moreover, a common requirement of all asynchronous consensus protocols is randomness. A simple and efficient approach is to employ threshold cryptography for this. However, this necessitates in practice a distributed setup protocol, often leading to performance bottlenecks. Blum (TCC 2020) propose a solution bypassing this requirement, which is, however, practically inefficient, due to the employment of fully homomorphic encryption. Recognizing that randomness for consensus does not need to be perfect (that is, always unpredictable and agreed-upon) we propose a practical and concretely-efficient protocol for randomness generation. Lastly, this thesis addresses the issue of deniability in distributed systems. The problem arises from the fact that a digital signature authenticates a message for an indefinite period. We introduce a scheme that allows the recipients to verify signatures, while allowing plausible deniability for signers. This scheme transforms a polynomial commitment scheme into a digital signature scheme

New results and applications for multi-secret sharing schemes

In a multi-secret sharing scheme (MSSS), different secrets are distributed among the players in some set , each one according to an access structure. The trivial solution to this problem is to run independent instances of a standard secret sharing scheme, one for each secret. In this solution, the length of the secret share to be stored by each player grows linearly with (when keeping all other parameters fixed). Multi-secret sharing schemes have been studied by the cryptographic community mostly from a theoretical perspective: different models and definitions have been proposed, for both unconditional (information-theoretic) and computational security. In the case of unconditional security, there are two different definitions. It has been proved that, for some particular cases of access structures that include the threshold case, a MSSS with the strongest level of unconditional security must have shares with length linear in . Therefore, the optimal solution in this case is equivalent to the trivial one. In this work we prove that, even for a more relaxed notion of unconditional security, and for some kinds of access structures (in particular, threshold ones), we have the same efficiency problem: the length of each secret share must grow linearly with . Since we want more efficient solutions, we move to the scenario of MSSSs with computational security. We propose a new MSSS, where each secret share has constant length (just one element), and we formally prove its computational security in the random oracle model. To the best of our knowledge, this is the first formal analysis on the computational security of a MSSS. We show the utility of the new MSSS by using it as a key ingredient in the design of two schemes for two new functionalities: multi-policy signatures and multi-policy decryption. We prove the security of these two new multi-policy cryptosystems in a formal security model. The two new primitives provide similar functionalities as attribute-based cryptosystems, with some advantages and some drawbacks that we discuss at the end of this work.Peer ReviewedPostprint (author’s final draft