**Privacy Preserving Reputation Calculation in P2P Systems with Homomorphic Encryption**

FUJITA Satoshi

Graduate School of Advanced Science and Engineering, Hiroshima

University, Kagamiyama 1-4-1, Higashi-Hiroshima, 739-8527, Japan

**Abstract**

In this paper, we consider the problem of calculating the node reputation in a Peer-toPeer (P2P) system from fragments of partial knowledge concerned with the trustfulness of nodes which are subjectively given by each node (i.e., evaluator) participating in the system. We are particularly interested in the distributed processing of the calculation of reputation scores while preserving the privacy of evaluators. The basic idea of the proposed method is to extend the EigenTrust reputation management system with the notion of homomorphic cryptosystem. More specifically, it calculates the main eigenvector of a linear system which models the trustfulness of the users (nodes) in the P2P system in a distributed manner, in such a way that: 1) it blocks accesses to the trust value by the nodes to have the secret key used for the decryption, 2) it improves the efficiency of calculation by offloading a part of the task to the participating nodes, and 3) it uses different public keys during the calculation to improve the robustness against the leave of nodes. The performance of the proposed method is evaluated through numerical calculations.

**Keywords**

P2P reputation management, homomorphic cryptosystem, EigenTrust, Paillier cryptosystem.

**Table 1**. . Execution time required for the encoding/decoding in the Paillier cryptosystem. Two values in each cell show the mean and the sample standard deviation over 1000 runs, respectively.

where ⃗ci = (ci1, . . . , cin) T . Although the above ⃗ti = (ti1, ti2, . . . , tin) T is the reputation of nodes through a chain of length two from i, it can be easily extended to the chain of length n so that ⃗ti := C n⃗ci . Vector ⃗ti is known to converge to the main eigenvector of matrix C as n → ∞ (i.e., to the eigenvector such that the eigenvalue is one) regardless of the value of ci , as long as matrix C is irreducible and acyclic, and the existence of such an eigenvector is guaranteed by the Peron Frobenius Theorem. It is worth noting that ⃗t = limn→∞ C n⃗c corresponds to the stationary distribution of Markov chain in such a way that the transition probability between states is given by C. Although such ⃗t can be obtained algebraically by solving the

**Fig 1**. Two partitions of the set of nodes V = {1, 2, . . . , 24} with k = 4. Four subsets in U
are represented by dashed blue rectangles and six subsets in V are represented by dashed red rectangles.

**Authors**

**Jung Sub Ahn** received the B.S. degree in computer engineering from Kyunil University in 2016 and now doing Ph.D. degree in Department of Electrical and Computer Engineering from Sungkyunkwan University, Republic of Korea. His research interests include wireless sensor network security, modelling & simulation, IoT security

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