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An outsourcing re-encryption program can help a ciphertext owner (delegator) transform his/her ciphertext into another ciphertext of delegatee. For example, an e-mail receiver can re-transfer an encrypted e-mail to his secretary while allowing the e-mail to be readable for her. For a multi-hop re-encryption, the delegatee can re-encrypt the ciphertext to another user in delegation chain, repeatedly. Traditionally, this transformation is usually conducted by a proxy or an outsourcing server. However, the proxy or outsourcing server needs a re-encryption key (i.e., re-key) and the re-encryption program must execute in a black-box manner (cannot trace into or debug and monitor the program), and thus the outsource server must be semi-trusted. Actually, as the outsource program was run and fully controlled by the server, in this paper, we consider a stronger attack in the case that the re-encryption program was run on an untrusted/malicious server and even the server can trace into the codes and monitor the variables during the executing. We design a secure multi-hop re-encryption scheme, and then convert the re-encryption program into an obfuscated version with constant-hiding to ensure no sensitive information be revealed. The obfuscator of multi-hop re-encryption is to faithfully hide the program and its sensitive data that takes a re-encryption program/circuit as input and outputs another program with the same functionality, while revealing no more sensitive information (i.e., sensitive key and plaintext) than learns from the blackbox oracle access to the original program. We also present a flexible and controllable construction of re-encryption scheme, functionality model and its obfuscation version in leveled multilinear groups, and exemplify some scenarios to deploy in various applications. Finally, we provide the performance analysis of the obfuscator, such as functionality preservation of consistency, polynomial slowdown of performance, and average-case virtual black-box of security, and show that the obfuscator is efficient and practical in use.

With the development of cloud computing and big data,it had important practical significance for how to outsource private data and verify the computing result efficiently.A verifiably outsourcing scheme for multivariate polynomial evaluation based on multilinear maps and homomorphic encryption was proposed where the user could verify the computing result exactly.The proposed scheme is provably secure without random oracles and the multivariate polynomial itself and the input of the function are private for the server.Moreover,the cost of the user is much smaller than that of the server,and it is much smaller than that of computing the multivariate polynomial directly.

We present the first linkable ring signature scheme with both unconditional anonymity and forward-secure key update: a powerful tool which has direct applications in elegantly addressing a number of simultaneous constraints in remote electronic voting. We propose a comprehensive security model, and construct a scheme based on the hardness of finding discrete logarithms, and (for forward security) inverting bilinear or multilinear maps of moderate degree to match the time granularity of forward security. We prove efficient security reductions—which, of independent interest, apply to, and are much tighter than, linkable ring signatures without forward security, thereby vastly improving the provable security of these legacy schemes. If efficient multilinear maps should ever admit a secure realisation, our contribution would elegantly address a number of problems heretofore unsolved in the important application of (multi-election) practical Internet voting. Even if multilinear maps are never obtained, our minimal two-epoch construction instantiated from bilinear maps can be combinatorially boosted to synthesise a polynomial time granularity, which would be sufficient for Internet voting and more.