Intrusion detection system for encrypted networks using secret-sharing schemes

Secret-sharing schemes describe methods to securely share a secret among a group of participants. A properly constructed secret-sharing scheme guarantees that the share belonging to one participant does not reveal anything about the shares of others or even the secret itself. Besides the obvious feature which is to distribute a secret, secret-sharing schemes have also been used in secure multi-party computations and redundant residue number systems for error correction codes. In this paper, we propose that the secret-sharing scheme be used as a primitive in a Network-based Intrusion Detection System (NIDS) to detect attacks in encrypted networks. Encrypted networks such as Virtual Private Networks (VPNs) fully encrypt network traffic which can include both malicious and non-malicious traffic. Traditional NIDS cannot monitor encrypted traffic. Our work uses a combination of Shamir's secret-sharing scheme and randomised network proxies to enable a traditional NIDS to function normally in a VPN environment. In this paper, we introduce a novel protocol that utilises a secret-sharing scheme to detect attacks in encrypted networks.

Detecting attacks in encrypted networks using secret-sharing schemes

Secret-sharing schemes describe methods to securely share a secret among a group of participants. A properly constructed secret-sharing scheme guarantees that the share belonging to one participant does not reveal anything about the shares of others or even the secret itself. Besides being used to distribute a secret, secret-sharing schemes have also been used in secure multi-party computations and redundant residue number systems for error correction codes. In this paper, we propose that the secret-sharing scheme be used as a primitive in a Network-based Intrusion Detection System (NIDS) to detect attacks in encrypted Networks. Encrypted networks such as Virtual Private Networks (VPNs) fully encrypt network traffic which can include both malicious and non-malicious traffic. Traditional NIDS cannot monitor such encrypted traffic. We therefore describe how our work uses a combination of Shamir's secret-sharing scheme and randomised network proxies to enable a traditional NIDS to function normally in a VPN environment.

Quantum direct secret sharing with efficient eavesdropping-check and authentication based on distributed fountain codes

We propose to use a simple and effective way to achieve secure quantum direct secret sharing. The proposed scheme uses the properties of fountain codes to allow a realization of the physical conditions necessary for the implementation of no-cloning principle for eavesdropping-check and authentication. In our scheme, to achieve a variety of security purposes, nonorthogonal state particles are inserted in the transmitted sequence carrying the secret shares to disorder it. However, the positions of the inserted nonorthogonal state particles are not announced directly, but are obtained by sending degrees and positions of a sequence that are pre-shared between Alice and each Bob. Moreover, they can confirm that whether there exists an eavesdropper without exchanging classical messages. Most importantly, without knowing the positions of the inserted nonorthogonal state particles and the sequence constituted by the first particles from every EPR pair, the proposed scheme is shown to be secure.

Multi-party computation with conversion of secret sharing

Classical results in unconditionally secure multi-party computation (MPC) protocols with a passive adversary indicate that every n-variate function can be computed by n participants, such that no set of size t < n/2 participants learns any additional information other than what they could derive from their private inputs and the output of the protocol. We study unconditionally secure MPC protocols in the presence of a passive adversary in the trusted setup (‘semi-ideal’) model, in which the participants are supplied with some auxiliary information (which is random and independent from the participant inputs) ahead of the protocol execution (such information can be purchased as a “commodity” well before a run of the protocol). We present a new MPC protocol in the trusted setup model, which allows the adversary to corrupt an arbitrary number t < n of participants. Our protocol makes use of a novel subprotocol for converting an additive secret sharing over a field to a multiplicative secret sharing, and can be used to securely evaluate any n-variate polynomial G over a field F, with inputs restricted to non-zero elements of F. The communication complexity of our protocol is O(ℓ · n 2) field elements, where ℓ is the number of non-linear monomials in G. Previous protocols in the trusted setup model require communication proportional to the number of multiplications in an arithmetic circuit for G; thus, our protocol may offer savings over previous protocols for functions with a small number of monomials but a large number of multiplications.

Decomposition construction for secret sharing schemes with graph access structures in polynomial time

The purpose of this paper is to describe a new decomposition construction for perfect secret sharing schemes with graph access structures. The previous decomposition construction proposed by Stinson is a recursive method that uses small secret sharing schemes as building blocks in the construction of larger schemes. When the Stinson method is applied to the graph access structures, the number of such “small” schemes is typically exponential in the number of the participants, resulting in an exponential algorithm. Our method has the same flavor as the Stinson decomposition construction; however, the linear programming problem involved in the construction is formulated in such a way that the number of “small” schemes is polynomial in the size of the participants, which in turn gives rise to a polynomial time construction. We also show that if we apply the Stinson construction to the “small” schemes arising from our new construction, both have the same information rate.

Verifiable multi-secret sharing schemes for multiple threshold access structures

A multi-secret sharing scheme allows several secrets to be shared amongst a group of participants. In 2005, Shao and Cao developed a verifiable multi-secret sharing scheme where each participant’s share can be used several times which reduces the number of interactions between the dealer and the group members. In addition some secrets may require a higher security level than others involving the need for different threshold values. Recently Chan and Chang designed such a scheme but their construction only allows a single secret to be shared per threshold value. In this article we combine the previous two approaches to design a multiple time verifiable multi-secret sharing scheme where several secrets can be shared for each threshold value. Since the running time is an important factor for practical applications, we will provide a complexity comparison of our combined approach with respect to the previous schemes.

Cheating immune secret sharing

We consider secret sharing with binary shares. This model allows us to use the well developed theory of cryptographically strong boolean functions. We prove that for given secret sharing, the average cheating probability over all cheating and original vectors, i.e., ρ ¯= 1 n ⋅ 2 −n ∑ n c=1 ∑ α∈Vn ρ c,α , satisfies ρ ¯⩾ 1 2 , and the equality holds ⇔ ρc,α satisfies ρc,α = 1/2 for every cheating vector δc and every original vector α. In this case the secret sharing is said to be cheating immune. We further establish a relationship between cheating-immune secret sharing and cryptographic criteria of boolean functions. This enables us to construct cheating-immune secret sharing.

Cheating prevention in linear secret sharing

Cheating detection in linear secret sharing is considered. The model of cheating extends the Tompa-Woll attack and includes cheating during multiple (unsuccessful) recovery of the secret. It is shown that shares in most linear schemes can be split into subshares. Subshares can be used by participants to trade perfectness of the scheme with cheating prevention. Evaluation of cheating prevention is given in the context of different strategies applied by cheaters.

Cheating prevention in secret sharing over GF(pt)

The work investigates cheating prevention in secret sharing. It is argued that cheating is immune against cheating if the cheaters gain no advantage over honest participants by submitting invalid shares to the combiner. This work addresses the case when shares and the secret are taken from GF(pt). Two models are considered. The first one examines the case when cheaters consistently submit always invalid shares. The second modeldeal s with cheaters who submit a mixture of valid and invalid shares. For these two models, cheating immunity is defined, properties of cheating immune secret sharing are investigated and their constructions are given.

Constructions of cheating immune secret sharing

The work addresses the problem of cheating prevention in secret sharing. Two cheating scenarios are considered. In the first one, the cheaters always submit invalid shares to the combiner. In the second one, the cheaters collectively decide which shares are to be modified so the combiner gets a mixture of valid and invalid shares from the cheaters. The secret scheme is said to be k-cheating immune if any group of k cheaters has no advantage over honest participants. The paper investigates cryptographic properties of the defining function of secret sharing so the scheme is k-cheating immune. Constructions of secret sharing immune against k cheaters are given.

Generalised cumulative arrays in secret sharing

Cumulative arrays have played an important role in the early development of the secret sharing theory. They have not been subject to extensive study so far, as the secret sharing schemes built on them generally result in much larger sizes of shares, when compared with other conventional approaches. Recent works in threshold cryptography show that cumulative arrays may be the appropriate building blocks in non-homomorphic threshold cryptosystems where the conventional secret sharing methods are generally of no use. In this paper we study several extensions of cumulative arrays and show that some of these extensions significantly improve the performance of conventional cumulative arrays. In particular, we derive bounds on generalised cumulative arrays and show that the constructions based on perfect hash families are asymptotically optimal. We also introduce the concept of ramp perfect hash families as a generalisation of perfect hash families for the study of ramp secret sharing schemes and ramp cumulative arrays.

Ideal secret sharing schemes from permutations

The work presents a new method for the design of ideal secret sharing. The method uses regular mappings that are well suited for construction of perfect secret sharing. The restriction of regular mappings to permutations gives a convenient tool for investigation of the relation between permutations and ideal secret sharing generated by them.

Lattice-based threshold-changeability for standard CRT secret-sharing schemes

We consider the problem of increasing the threshold parameter of a secret-sharing scheme after the setup (share distribution) phase, without further communication between the dealer and the shareholders. Previous solutions to this problem require one to start off with a non-standard scheme designed specifically for this purpose, or to have secure channels between shareholders. In contrast, we show how to increase the threshold parameter of the standard CRT secret-sharing scheme without secure channels between the shareholders. Our method can thus be applied to existing CRT schemes even if they were set up without consideration to future threshold increases. Our method is a positive cryptographic application for lattice reduction algorithms, and we also use techniques from lattice theory (geometry of numbers) to prove statements about the correctness and information-theoretic security of our constructions.

Lattice-based threshold-changeability for standard Shamir secret-sharing schemes

We consider the problem of increasing the threshold parameter of a secret-sharing scheme after the setup (share distribution) phase, without further communication between the dealer and the shareholders. Previous solutions to this problem require one to start off with a non-standard scheme designed specifically for this purpose, or to have communication between shareholders. In contrast, we show how to increase the threshold parameter of the standard Shamir secret-sharing scheme without communication between the shareholders. Our technique can thus be applied to existing Shamir schemes even if they were set up without consideration to future threshold increases. Our method is a new positive cryptographic application for lattice reduction algorithms, inspired by recent work on lattice-based list decoding of Reed-Solomon codes with noise bounded in the Lee norm. We use fundamental results from the theory of lattices (Geometry of Numbers) to prove quantitative statements about the information-theoretic security of our construction. These lattice-based security proof techniques may be of independent interest.