Abstract. We proposed a two-round protocol for solving the Millionaires' Problem in the setting of semi-honest parties. Our protocol uses either multiplicative or additive homomorphic encryptions. Previously proposed protocols used additive or XOR homomorphic encryption schemes only. The computation and communication costs of our protocol are in the same asymptotic order as those of the other efficient protocols. Nevertheless, since multiplicative homomorphic encryption scheme is more efficient than an additive one practically, our construction saves computation time and communication bandwidth in practicality.

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Fine-grained meter readings enable applications in an advanced metering infrastructure. However, those meter readings threaten personal privacy by implying a sketch of daily activities of households. The privacy issue has been addressed in smart metering systems by either a trusted third party assumption or cryptographic primitives. We address the privacy issue by using a trusted platform module and lightweight cryptographic primitives. Our smart metering system simultaneously supports the billing and load monitoring applications in a privacy preserving manner. It allows an electricity service provider obtain sums of meter readings over a time period and a monitoring center obtain sums of meter readings from meters in an area at some recent time unit while keeping individual meter reading private. Moreover, we formally prove that our system is privacy preserving. Our system provides a simple yet very practical solution to a privacy preserving smart metering system.

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In the application of cloud storage, a user no longer possesses his files in his local depository. Thus, he is concerned about the security of the stored files. Data confidentiality and data robustness are the main security issues. For data confidentiality, the user can first encrypt files and then store the encrypted files in a cloud storage. For data robustness, there are two concerns: service failure, and service corruption. We are concerned about data robustness in cloud storage services. Lin and Tzeng proposed a secure erasure code-based storage system with multiple key servers recently. Their system supports a repair mechanism, where a new storage server can compute a new ciphertext from the ciphertexts obtained from the remaining storage servers. Their system considers data confidentiality in the cloud, and data robustness against storage server failure. In this paper, we propose an integrity check scheme for their system to enhance data robustness against storage server corruption, which returns tampered ciphertexts. With our integrity check scheme, their storage system can deal with not only the problem of storage server failure, but also the problem of storage server corruption. The challenging part of our work is to have homomorphic integrity tags. New integrity tags can be computed from old integrity tags by storage servers without involvement of the user's secret key or backup servers. We prove the security of our integrity check scheme formally, and establish the parameters for achieving an overwhelming probability of a successful data retrieval. Index Terms-Dataconfidentiality, data robustness, homomorphism, integrity check, secure decentralized erasure code. NOTATION The security parameter The public parameter A -bit prime The operation of concatenating string and string into another string The operation of choosing element from set randomly and uniformly The bit size of element The number of storage servers The number of data blocks The number of key servers The threshold number of secret sharingThe number of storage servers that each ciphertext-tag tuple is dispatched to in the storing phase The number of storage servers that each key server queries in the retrieval phase The number of storage servers that a key server queries in the integrity check phase The number of storage servers that are failed or corrupted among the queried storage servers The proportion of storage servers that are failed or corrupted in the storage system The proportion of storage servers that are failed or corrupted among the queried storage servers: The predefined threshold for such that data are retrievable with overwhelming probability if Two small positive values such that if The public key of userThe secret key of userThe master verification key of userThe th storage serverThe th key serverThe identifier of data The share of secret key for key serverThe verification key of user for dataThe th block of dataThe ciphertext-tag tuple of blockThe encoded tuple stored in storage server 0018-9529