HCGraph

HCGraph is backed by Trias founding team’s research in the System Security group at University of Oxford since 2011 [1,2,3]. It integrates Heterogeneous TEE technologies (Trusted Execution Environment, includes Intel SGX, Intel TXT, ARM TrustZone, TCG TPM, etc.) and graph computation algorithms to achieve fast attestations among a large-scale network of distributed nodes.

The basic idea of the HCGraph is to enforce mutual attestations and gossip protocols among nodes, so that they collaboratively construct a web-of-trust, i.e. the Leviatom Network. The connections among each node on the web represent the nodes’ mutual attestation relationship. The strength of the connections is modelled to reflect the intensity of their mutual-attestations. This intensity represents how often a node’s integrity is examined by its peer. Therefore, by tracing the connections and evaluating the strength values, a node is able to deduce the integrity of another without performing direct attestation to it.

The above figure depicts the Leviatom’s conceptual model. A node attests the integrity of other nodes. It collects the attestation results, which are modelled as its Direct Trust to a target node and is stored in its local database, the Kernel. The direct trust is defined as follows:

$D i,j ​ (t)=∑_{t_n ​∈AH_j ​(t) ​}2^{k−Δ(t,t_n ​)}$

$Di,j(t)$is calculated by combining the timestamps maintained in the attestation history, which records the attestation tickets towards the neighbour (Nj). It is an integer interpreted as a bitmap vector with the length of k. Each bit represents a timestamp one step away from its higher adjacent bit, and the highest bit indicates the time t. A bit is set to 1 when an attestation is performed at the step it stands for. Thus, the direct trust, calculated as above, reflects all the recent successful attestations up to time t. AHj(t) denotes the attestation history for node Nj at time t. As a step is defined as minimum attestation interval, different timestamps t in AH do not indicate a same bit index. We can thus safely use summation instead of bitwise OR (“|”) for setting the corresponding bits.

This definition allows two evaluation values be compared. The larger one indicates the more recent an attestation is performed, and hence indicates a higher trust credibility. This property is used for modelling the Transitive Trust.

Direct trust values are propagated among the logical surrounding neighbours by exchanging the corresponding kernel contents using the gossip protocols. Therefore, from the kernel, a node is able to determine how its neighbours attest to each other. This thus helps modelling the Transitive Trust, which is represented by a path of connections.

The gossip protocols allow each node to disseminate the trust relationship it gathers to other related nodes, so that redundant attestations will be reduced. There are three ways of gossip disseminations in the Leviatom Network:

1. Gossip about gossip: when the local node and a target node only have few common in their Kernels, the gossip about gossip protocol is initiated to directly exchange their Kernels.

2. Gossip about reduced gossip: when the local node and a target node have much common in their Kernels, the gossip about reduced gossip protocol is initiated to only exchanged the complemental parts.

3. Targeted gossip: any time when a local node updates its Kernel, it identifies the set of target nodes who will be benefit from the updated data and sends the updated data package directly to the set of nodes.

Gossip about gossip enforces batched exchanges of attestation relationship data, this allows a new node to quickly obtain the up-to-date global data. Reduced gossip allows two “not-too-closed” nodes to exchange their data in batches, while reducing networking overheads. Targeted gossip allows new attestation relationship information to quickly propagate among the “closely-related” nodes to without putting too much burden on the network traffic.

The combination of these three gossip strategies achieves both quick information propagation rate with low networking overheads. With transitive trust relationship gathered by remote attestations and gossip protocols, HCGraph further builds a‘Conspiracy Breaching’ model for nodes to illustrate how intense a target node is attested by other nodes. This model helps locating the nodes who have the greatest ‘difficulties to lie’. Meanwhile, small world network algorithm improves the networks’ robustness.

Detailed algorithms and evaluations can be found in [1,2,3], and more experiment results will be published in the technical whitepaper.