With the many benefits of cloud computing, an entity may want to outsource its data and their related analytics tasks to a cloud. When data are sensitive, it is in the interest of the entity to outsource encrypted data to the cloud; however, this limits the types of operations that can be performed on the cloud side. Especially, evaluating queries over the encrypted data stored on the cloud without the entity performing any computation and without ever decrypting the data become a very challenging problem. In this paper, we propose solutions to conduct range queries over outsourced encrypted data. The existing methods leak valuable information to the cloud which can violate the security guarantee of the underlying encryption schemes. In general, the main security primitive used to evaluate range queries is secure comparison (SC) of encrypted integers. However, we observe that the existing SC protocols are not very efficient. To this end, we first propose a novel SC scheme that takes encrypted integers and outputs encrypted comparison result. We empirically show its practical advantage over the current state-of-the-art. We then utilize the proposed SC scheme to construct two new secure range query protocols. Our protocols protect data confidentiality, privacy of user's query, and also preserve the semantic security of the encrypted data; therefore, they are more secure than the existing protocols. Furthermore, our second protocol is lightweight at the user end, and it can allow an authorized user to use any device with limited storage and computing capability to perform the range queries over outsourced encrypted data.
On the other hand, there exist a large number of custom-designed SC protocols (e.g., @cite_54 @cite_23 @cite_2 ) that directly operate on encrypted inputs. Since the goal of this paper is not to investigate all the existing SC protocols, we simply refer to the most efficient known implementation of SC (here we consider methods based on Paillier cryptosystem to have a fair comparison with our scheme) that was proposed by @cite_2 . We emphasize that the SC protocol given in @cite_2 requires the encryptions of individual bits of @math and @math as the input rather than @math . Though their protocol is efficient than the above garbled-circuit based SC method (i.e., ) for smaller input domain sizes, we show that our SC scheme outperforms both the methods for all practical values of input domain sizes (see Section for details). Also, it is worth pointing out that the protocol in @cite_2 leaks the comparison result @math to at least one of the involved parties. However, by using the techniques in @cite_23 , we can easily modify (at the expense of extra cost) the protocol of @cite_2 to generate @math as the output without revealing @math to both parties.
@cite_54 @cite_23 @cite_2
2402235285 2088492763 2156001253 2101207956
We propose a general multiparty computation protocol secure against an active adversary corrupting up to @math of the n players. The protocol may be used to compute securely arithmetic circuits over any finite field @math . Our protocol consists of a preprocessing phase that is both independent of the function to be computed and of the inputs, and a much more efficient online phase where the actual computation takes place. The online phase is unconditionally secure and has total computational and communication complexity linear in n, the number of players, where earlier work was quadratic in n. Moreover, the work done by each player is only a small constant factor larger than what one would need to compute the circuit in the clear. We show this is optimal for computation in large fields. In practice, for 3 players, a secure 64-bit multiplication can be done in 0.05 ms. Our preprocessing is based on a somewhat homomorphic cryptosystem. We extend a scheme by , so that we can perform distributed decryption and handle many values in parallel in one ciphertext. The computational complexity of our preprocessing phase is dominated by the public-key operations, we need @math operations per secure multiplication where s is a parameter that increases with the security parameter of the cryptosystem. Earlier work in this model needed @math operations. In practice, the preprocessing prepares a secure 64-bit multiplication for 3 players in about 13 ms. In this paper we introduce a new tool for controlling the knowledge transfer process in cryptographic protocol design. It is applied to solve a general class of problems which include most of the two-party cryptographic problems in the literature. Specifically, we show how two parties A and B can interactively generate a random integer N = p?q such that its secret, i.e., the prime factors (p, q), is hidden from either party individually but is recoverable jointly if desired. This can be utilized to give a protocol for two parties with private values i and j to compute any polynomially computable functions f(i,j) and g(i,j) with minimal knowledge transfer and a strong fairness property. As a special case, A and B can exchange a pair of secrets sA, sB, e.g. the factorization of an integer and a Hamiltonian circuit in a graph, in such a way that sA becomes computable by B when and only when sB becomes computable by A. All these results are proved assuming only that the problem of factoring large intergers is computationally intractable. In this paper we introduce a new tool for controlling the knowl­ edge transfer process in cryptographic protocol design. It is applied to solve a general class of problems which include most of the two-party cryptographic problems in the literature. -- -_.Specifically, we show how two parties A and B can interactively generate a random integer N =p' q such that its secret, i.e., the prime factors (p, q), is hidden from either party individually but is recoverab jointly if desired. This can be utilized to give a protocol for two parties with private values i and j to compute any polynomially computable functions f(i,j) and g(i,j) with minimal knowledge transfer and a strong fairness property. As a special case, A and B can exchange a pair of secrets SA, SB, e.g. the factorizatio of an integer and a Hamiltonian circuit in a graph, in such a way that SA becomes computable by Bwhen and only when SB becomes computable by A. All these results are proved assuming only that the problem of factoring large intergers is computationally intractable. Polar codes, as the first provable capacity-achieving error-correcting codes, have received much attention in recent years. However, the decoding performance of polar codes with traditional successive-cancellation (SC) algorithm cannot match that of the low-density parity-check or Turbo codes. Because SC list (SCL) decoding algorithm can significantly improve the error-correcting performance of polar codes, design of SCL decoders is important for polar codes to be deployed in practical applications. However, because the prior latency reduction approaches for SC decoders are not applicable for SCL decoders, these list decoders suffer from the long-latency bottleneck. In this paper, we propose a multibit-decision approach that can significantly reduce latency of SCL decoders. First, we present a reformulated SCL algorithm that can perform intermediate decoding of 2 b together. The proposed approach, referred as 2-bit reformulated SCL ( 2b-rSCL ) algorithm , can reduce the latency of SCL decoder from ( @math ) to ( @math ) clock cycles without any performance loss. Then, we extend the idea of 2-b-decision to general case, and propose a general decoding scheme that can perform intermediate decoding of any @math bits simultaneously. This general approach, referred as @math -bit reformulated SCL ( @math b-rSCL ) algorithm , can reduce the overall decoding latency to as short as @math cycles. Furthermore, on the basis of the proposed algorithms, very large-scale integration architectures for 2b-rSCL and 4b-rSCL decoders are synthesized. Compared with a prior SCL decoder, the proposed (1024, 512) 2b-rSCL and 4b-rSCL decoders can achieve 21 and 60 reduction in latency, 1.66 and 2.77 times increase in coded throughput with list size 2, and 2.11 and 3.23 times increase in coded throughput with list size 4, respectively.