Multilevel Threshold Secret and Function Sharing based on the Chinese Remainder Theorem

A recent work of Harn and Fuyou presents the first multilevel (disjunctive) threshold secret sharing scheme based on the Chinese Remainder Theorem. In this work, we first show that the proposed method is not secure and also fails to work with a certain natural setting of the threshold values on compartments. We then propose a secure scheme that works for all threshold settings. In this scheme, we employ a refined version of Asmuth-Bloom secret sharing with a special and generic Asmuth-Bloom sequence called the {\it anchor sequence}. Based on this idea, we also propose the first multilevel conjunctive threshold secret sharing scheme based on the Chinese Remainder Theorem. Lastly, we discuss how the proposed schemes can be used for multilevel threshold function sharing by employing it in a threshold RSA cryptosystem as an example

Actively Secure Two-Party Computation: Efficient Beaver Triple Generation

Töö kombineerib erinevaid ideid, et saavutada aktiivses mudelis turvalist kahe osapoolega ühisarvutust. Töö käigus defineerime Sharemindi raamistikku kaks uut turvaala. Kasutame aditiivset ühissalastust, sõnumiautentimisskeeme, aditiivselt homomorfset krüptosüsteemi ning nullteadmustõestusi. Protokollistikud jagame kahte osasse, vastavalt ettearvutamise ja töö faas. Ettearvutamise ajal valmistatakse ette juhuslikke väärtusi, mis võimaldavad töö faasis arvutusi kiirendada. Eelkõige keskendume korrutamise jaoks vajalike Beaveri kolmikute genereerimisele.This thesis combines currently popular ideas in actively secure multi-party computation to define two actively secure two-party protocol sets for Sharemind secure multi-party computation framework. This includes additive secret sharing, dividing work as online and precomputation phase, using Beaver triples for multiplication and using message authentication codes for integrity checks. Our protocols use additively homomorphic Paillier cryptosystem, especially in the precomputation phase. The thesis includes two different setups for secure two-party computation which are also implemented and compared to each other. In addition, we propose new ideas to use additively homomorphic cryptosystem to generate Beaver triples for any chosen modulus. The important aspects of Beaver triple generation are maximising the amount of useful bits we get from one generation and assuring that these triples are correct

Cryptography with Weights: MPC, Encryption and Signatures

The security of several cryptosystems rests on the trust assumption that a certain fraction of the parties are honest. This trust assumption has enabled a diverse of cryptographic applications such as secure multiparty computation, threshold encryption, and threshold signatures. However, current and emerging practical use cases suggest that this paradigm of one-person-one-vote is outdated. In this work, we consider {\em weighted} cryptosystems where every party is assigned a certain weight and the trust assumption is that a certain fraction of the total weight is honest. This setting can be translated to the standard setting (where each party has a unit weight) via virtualization. However, this method is quite expensive, incurring a multiplicative overhead in the weight. We present new weighted cryptosystems with significantly better efficiency. Specifically, our proposed schemes incur only an {\em additive} overhead in weights. \begin{itemize} \item We first present a weighted ramp secret-sharing scheme where the size of the secret share is as short as $O(w)$ (where $w$ corresponds to the weight). In comparison, Shamir\u27s secret sharing with virtualization requires secret shares of size $w\cdot\lambda$, where $\lambda=\log |\mathbb{F}|$ is the security parameter. \item Next, we use our weighted secret-sharing scheme to construct weighted versions of (semi-honest) secure multiparty computation (MPC), threshold encryption, and threshold signatures. All these schemes inherit the efficiency of our secret sharing scheme and incur only an additive overhead in the weights. \end{itemize} Our weighted secret-sharing scheme is based on the Chinese remainder theorem. Interestingly, this secret-sharing scheme is {\em non-linear} and only achieves statistical privacy. These distinct features introduce several technical hurdles in applications to MPC and threshold cryptosystems. We resolve these challenges by developing several new ideas

Privacy enhancing technologies : protocol verification, implementation and specification

In this thesis, we present novel methods for verifying, implementing and specifying protocols. In particular, we focus properties modeling data protection and the protection of privacy. In the first part of the thesis, the author introduces protocol verification and presents a model for verification that encompasses so-called Zero-Knowledge (ZK) proofs. These ZK proofs are a cryptographic primitive that is particularly suited for hiding information and hence serves the protection of privacy. The here presented model gives a list of criteria which allows the transfer of verification results from the model to the implementation if the criteria are met by the implementation. In particular, the criteria are less demanding than the ones of previous work regarding ZK proofs. The second part of the thesis contributes to the area of protocol implementations. Hereby, ZK proofs are used in order to improve multi-party computations. The third and last part of the thesis explains a novel approach for specifying data protection policies. Instead of relying on policies, this approach relies on actual legislation. The advantage of relying on legislation is that often a fair balancing is introduced which is typically not contained in regulations or policies.In dieser Arbeit werden neue Methoden zur Verifikation, Implementierung und Spezifikation im von Protokollen vorgestellt. Ein besonderer Fokus liegt dabei auf Datenschutz-Eigenschaften und dem Schutz der Privatsph¨are. Im ersten Teil dieser Arbeit geht der Author auf die Protokoll- Verifikation ein und stellt ein Modell zur Verifikation vor, dass sogenannte Zero-Knowledge (ZK) Beweise enth¨alt. Diese ZK Beweise sind ein kryptographisches primitiv, dass insbesondere zum Verstecken von Informationen geeignet ist und somit zum Schutz der Privatsph¨are dient. Das hier vorgestellte Modell gibt eine Liste von Kriterien, welche eine Implementierung der genutzten kryptographischen Primitive erf¨ullen muss, damit die verifikationen im Modell sich auf Implementierungen ¨ubertragen lassen. In Bezug auf ZK Beweise sind diese Kriterien sch¨acher als die vorangegangener Arbeiten. Der zweite Teil der Arbeit wendet sich der Implementierung von Protokollen zu. Hierbei werden dann ZK Beweise verwendet um sichere Mehrparteienberechnungen zu verbessern. Im dritten und letzten Teil der Arbeit wird eine neuartige Art der Spezifikation von Datenschutz-Richtlinien erl¨autert. Diese geht nicht von Richtlinien aus, sondern von der Rechtsprechung. Der Vorteil ist, dass in der Rechtsprechung konkrete Abw¨agungen getroffen werden, die Gesetze und Richtlinien nicht enthalten

Improving the Efficiency of Homomorphic Encryption Schemes

In this dissertation, we explore different approaches to practical homomorphic encryption schemes. For partial homomorphic encryption schemes, we observe that the versatility is the main bottleneck. To solve this problem, we propose general approaches to improve versatility of them by either extending the range of supported circuits or extending the message space. These general approaches can be applied to a wide range of partial HE schemes and greatly increase the number of applications that they support. For fully homomorphic encryption schemes, the slow running speed and the large ciphertext are the main challenges. Therefore, we propose efficient implementations as well as methods to compress the ciphertext. In detail, the Gentry Halevi FHE scheme and the LTV FHE scheme are implemented and the resulting performance shows significant improvement over previous works. For ciphertext compression, the concept of scheme conversion is proposed. Given a scheme converter, we can convert between schemes with compact ciphertext for communication and homomorphic schemes for computation

On Improving Communication Complexity in Cryptography

Cryptography grew to be much more than "the study of secret writing". Modern cryptography is concerned with establishing properties such as privacy, integrity and authenticity in protocols for secure communication and computation. This comes at a price: Cryptographic tools usually introduce an overhead, both in terms of communication complexity (that is, number and size of messages transmitted) and computational efficiency (that is, time and memory required). As in many settings communication between the parties involved is the bottleneck, this thesis is concerned with improving communication complexity in cryptographic protocols. One direction towards this goal is scalable cryptography: In many cryptographic schemes currently deployed, the security degrades linearly with the number of instances (e.g. encrypted messages) in the system. As this number can be huge in contexts like cloud computing, the parameters of the scheme have to be chosen considerably larger - and in particular depending on the expected number of instances in the system - to maintain security guarantees. We advance the state-of-the-art regarding scalable cryptography by constructing schemes where the security guarantees are independent of the number of instances. This allows to choose smaller parameters, even when the expected number of instances is immense. - We construct the first scalable encryption scheme with security against active adversaries which has both compact public keys and ciphertexts. In particular, we significantly reduce the size of the public key to only about 3% of the key-size of the previously most efficient scalable encryption scheme. (Gay,Hofheinz, and Kohl, CRYPTO, 2017) - We present a scalable structure-preserving signature scheme which improves both in terms of public-key and signature size compared to the previously best construction to about 40% and 56% of the sizes, respectively. (Gay, Hofheinz, Kohl, and Pan, EUROCRYPT, 2018) Another important area of cryptography is secure multi-party computation, where the goal is to jointly evaluate some function while keeping each party’s input private. In traditional approaches towards secure multi-party computation either the communication complexity scales linearly in the size of the function, or the computational efficiency is poor. To overcome this issue, Boyle, Gilboa, and Ishai (CRYPTO, 2016) introduced the notion of homomorphic secret sharing. Here, inputs are shared between parties such that each party does not learn anything about the input, and such that the parties can locally evaluate functions on the shares. Homomorphic secret sharing implies secure computation where the communication complexity only depends on the size of the inputs, which is typically much smaller than the size of the function. A different approach towards efficient secure computation is to split the protocol into an input-independent preprocessing phase, where long correlated strings are generated, and a very efficient online phase. One example for a useful correlation are authenticated Beaver triples, which allow to perform efficient multiplications in the online phase such that privacy of the inputs is preserved and parties deviating the protocol can be detected. The currently most efficient protocols implementing the preprocessing phase require communication linear in the number of triples to be generated. This results typically in high communication costs, as the online phase requires at least one authenticated Beaver triple per multiplication. We advance the state-of-the art regarding efficient protocols for secure computation with low communication complexity as follows. - We construct the first homomorphic secret sharing scheme for computing arbitrary functions in NC 1 (that is, functions that are computably by circuits with logarithmic depth) which supports message spaces of arbitrary size, has only negligible correctness error, and does not require expensive multiplication on ciphertexts. (Boyle, Kohl, and Scholl, EUROCRYPT, 2019) - We introduce the notion of a pseudorandom correlation generator for general correlations. Pseudorandom correlation generators allow to locally extend short correlated seeds into long pseudorandom correlated strings. We show that pseudorandom correlation generators can replace the preprocessing phase in many protocols, leading to a preprocessing phase with sublinear communication complexity. We show connections to homomorphic secret sharing schemes and give the first instantiation of pseudorandom correlation generators for authenticated Beaver triples at reasonable computational efficiency. (Boyle, Couteau, Gilboa, Ishai, Kohl, and Scholl, CRYPTO, 2019

An Efficient Threshold Access-Structure for RLWE-Based Multiparty Homomorphic Encryption

We propose and implement a multiparty homomorphic encryption (MHE) scheme with a $t$-out-of-$N$-threshold access-structure that is efficient and does not require a trusted dealer in the common random-string model. We construct this scheme from the ring-learning-with-error (RLWE) assumptions, and as an extension of the MHE scheme of Mouchet et al. (PETS 21). By means of a specially adapted share re-sharing procedure, this extension can be used to relax the $N$-out-of-$N$-threshold access structure of the original scheme into a $t$-out-of-$N$-threshold one. This procedure introduces only a single round of communication during the setup phase, after which any set of at least $t$ parties can compute a $t$-out-of-$t$ additive sharing of the secret key with no interaction; this new sharing can be used directly in the scheme of Mouchet et al. We show that, by performing Shamir re-sharing over the MHE ciphertext-space ring with a carefully chosen exceptional set, this reconstruction procedure can be made secure and has negligible overhead. Moreover, it only requires the parties to store a constant-size state after its setup phase. Hence, in addition to fault tolerance, lowering the corruption threshold also yields considerable efficiency benefits, by enabling the distribution of batched secret-key operations among the online parties. We implemented and open-sourced our scheme in the Lattigo library

An Efficient Secure Message Transmission in Mobile Ad Hoc Networks using Enhanced Homomorphic Encryption Scheme

In MANETs the nodes are capable of roaming independently. The node with inadequate physical protection can be easily captured, compromised and hijacked. Due to this huge dependency's on the nodes, there are more security problems. Therefore the nodes in the network must be prepared to work in a mode that trusts no peer. In this paper we look at the current scheme to transmit the data in MANETs. We then propose a new scheme for secure transmission of message in MANETs as Alternative scheme for DF2019;s new Ph and DF2019;s additive and multiplicative PH. Here we also provide the computational cost of the homomorphic encryption schemes. We also provide the implementation issues of our new scheme in MANETs. For the entire message to be recoverd by the attacker, the attacker needs to compromise atleast g nodes, one node from each group g and know the encryption keys to decrypt the message. The success rate of our proposed new scheme is 100% if there are more number of active paths in each group of the network