In this thesis we study a problem of doing Verifiable Secret Sharing (VSS) and Multiparty Computations (MPC) in a model where private channels between the players and a broadcast channel is available. The adversary is active, adaptive and has an unbounded computing power. The thesis is based on two papers [CDD00, CDD 99]. In [CDD00] we assume that the adversary can corrupt any set from a given adversary structure. In this setting we study a problem of doing efficient VSS and MPC given an access to a secret sharing scheme (SS). For all adversary structures where VSS is possible at all, we show that, up to a polynomial time black-box reduction, the complexity of adaptively secure VSS is the same as that of ordinary secret sharing (SS), where security is only required against a passive, static adversary. Previously, such a connection was only known for linear secret sharing and VSS schemes. We then showIn this thesis we study a problem of doing Verifiable Secret Sharing (VSS) and Multiparty Computations (MPC) in a model where private channels between the players and a broadcast channel is available. The adversary is active, adaptive and has an unbounded computing power. The thesis is based on two papers [CDD00, CDD 99]. In [CDD00] we assume that the adversary can corrupt any set from a given adversary structure. In this setting we study a problem of doing efficient VSS and MPC given an access to a secret sharing scheme (SS). For all adversary structures where VSS is possible at all, we show that, up to a polynomial time black-box reduction, the complexity of adaptively secure VSS is the same as that of ordinary secret sharing (SS), where security is only required against a passive, static adversary. Previously, such a connection was only known for linear secret sharing and VSS schemes. We then show

Jan 1, 20020 citations

Split-State Non-Malleable Codes and Secret Sharing Schemes for Quantum Messages

Naresh Goud Boddu, Vipul Goyal, Rahul Jain +1 more

Non-malleable codes are fundamental objects at the intersection of cryptography and coding theory. These codes provide security guarantees even in settings where error correction and detection are impossible, and have found applications to several other cryptographic tasks. One of the strongest and most well-studied adversarial tampering models is $2$ -split-state tampering. Here, a codeword is split into two parts and the adversary can then independently tamper with each part using arbitrary functions. This model can be naturally extended to the secret sharing setting with several parties by having the adversary independently tamper with each share. Previous works on non-malleable coding and secret sharing in the split-state tampering model only considered the encoding of \emph{classical} messages. Furthermore, until recent work by Aggarwal, Boddu, and Jain (IEEE Trans.\ Inf.\ Theory 2024), adversaries with quantum capabilities and \emph{shared entanglement} had not been considered, and it is a priori not clear whether previous schemes remain secure in this model. In this work, we introduce the notions of split-state non-malleable codes and secret sharing schemes for quantum messages secure against quantum adversaries with shared entanglement. Then, we present explicit constructions of such schemes that achieve low-error non-malleability. More precisely, we construct efficiently encodable and decodable split-state non-malleable codes and secret sharing schemes for quantum messages preserving entanglement with external systems and achieving security against quantum adversaries having shared entanglement with codeword length $n$ , any message length at most $n^{Ω(1)}$ , and error $ε=2^{-{n^{Ω(1)}}}$ . In the easier setting of \emph{average-case} non-malleability, we achieve efficient non-malleable coding with rate close to $1/11$ .Non-malleable codes are fundamental objects at the intersection of cryptography and coding theory. These codes provide security guarantees even in settings where error correction and detection are impossible, and have found applications to several other cryptographic tasks. One of the strongest and most well-studied adversarial tampering models is $2$-split-state tampering. Here, a codeword is split into two parts and the adversary can then independently tamper with each part using arbitrary functions. This model can be naturally extended to the secret sharing setting with several parties by having the adversary independently tamper with each share. Previous works on non-malleable coding and secret sharing in the split-state tampering model only considered the encoding of \emph{classical} messages. Furthermore, until recent work by Aggarwal, Boddu, and Jain (IEEE Trans.\ Inf.\ Theory 2024), adversaries with quantum capabilities and \emph{shared entanglement} had not been considered, and it is a priori not clear whether previous schemes remain secure in this model. In this work, we introduce the notions of split-state non-malleable codes and secret sharing schemes for quantum messages secure against quantum adversaries with shared entanglement. Then, we present explicit constructions of such schemes that achieve low-error non-malleability. More precisely, we construct efficiently encodable and decodable split-state non-malleable codes and secret sharing schemes for quantum messages preserving entanglement with external systems and achieving security against quantum adversaries having shared entanglement with codeword length $n$, any message length at most $n^{Ω(1)}$, and error $ε=2^{-{n^{Ω(1)}}}$. In the easier setting of \emph{average-case} non-malleability, we achieve efficient non-malleable coding with rate close to $1/11$.

arXiv:2308.06466Aug 12, 20231 citation

2

-split-state tampering. Here, a codeword is split into two parts and the adversary can then independently tamper with each part using arbitrary functions. This model can be naturally extended to the secret sharing setting with several parties by having the adversary independently tamper with each share. Previous works on non-malleable coding and secret sharing in the split-state tampering model only considered the encoding of \emph{classical} messages. Furthermore, until recent work by Aggarwal, Boddu, and Jain (IEEE Trans.\ Inf.\ Theory 2024), adversaries with quantum capabilities and \emph{shared entanglement} had not been considered, and it is a priori not clear whether previous schemes remain secure in this model. In this work, we introduce the notions of split-state non-malleable codes and secret sharing schemes for quantum messages secure against quantum adversaries with shared entanglement. Then, we present explicit constructions of such schemes that achieve low-error non-malleability. More precisely, we construct efficiently encodable and decodable split-state non-malleable codes and secret sharing schemes for quantum messages preserving entanglement with external systems and achieving security against quantum adversaries having shared entanglement with codeword length

n

, any message length at most

n^{Ω(1)}

, and error

ε=2^{-{n^{Ω(1)}}}

. In the easier setting of \emph{average-case} non-malleability, we achieve efficient non-malleable coding with rate close to

1/11