Efficient Algorithm for Secure Outsourcing of Modular Exponentiation with Single Server

2018 ◽  
pp. 1-1 ◽  
Author(s):  
Yanli Ren ◽  
Min Dong ◽  
Zhenxing Qian ◽  
Xinpeng Zhang ◽  
Guorui Feng
Keyword(s):  
Efficient Algorithm ◽  
Single Server ◽  
Modular Exponentiation ◽  
Secure Outsourcing

Secure Outsourcing Algorithms for Composite Modular Exponentiation Based on Single Untrusted Cloud

2020 ◽  
Vol 63 (8) ◽  
pp. 1271-1271
Author(s):  
Qianqian Su ◽  
Rui Zhang ◽  
Rui Xue
Keyword(s):  
Radio Frequency Identification ◽  
Large Scale ◽  
Low Cost ◽  
Prime Numbers ◽  
Modular Exponentiation ◽  
Public Key Cryptosystems ◽  
Rsa Algorithm ◽  
Secure Outsourcing ◽  
Frequency Identification ◽  
Identity Based

Abstract Modular exponentiation, as a fundamental operation used in many public-key cryptosystems, has always be considered to be very time-consuming. It is difficult for some devices with limited computation capability, such as mobile devices and low-cost radio frequency identification (RFID) tags, to perform large-scale modular exponentiations. In cryptosystems, one typical case of modular exponentiation is that the modulus is a composite number. For instance, in RSA algorithm, the modulus is the product of two distinct prime numbers. In this paper, we investigate how to securely and efficiently outsource composite modular exponentiations and put forward two secure outsourcing algorithms for composite modular exponentiations based on single untrusted cloud. The first algorithm, named MCExp, is designed for outsourcing single composite modular exponentiation, i.e. $u^a$ mod $N$. The second algorithm, named SMCExp, is designed for outsourcing simultaneous composite modular exponentiation, i.e. $\prod ^{n}_{i=1}u^{a_i}_{i}$ mod $N$. Different from algorithms based on two untrusted servers, the proposed algorithms are very practical because they avoid the strong assumption that there must exist two servers without collusion. The proposed algorithms not only protect the privacy of the exponent and the base simultaneously, but also enable users to verify the correctness of the result returned by the cloud with high probability. Compared with using the square-and-multiply algorithm, the user can achieve higher efficiency by using the proposed algorithms. Besides, we prove the security of our algorithms and conduct several experiments to demonstrate the efficiency of the proposed algorithms. Finally, we show that the proposed algorithms can be used to construct the secure outsourcing algorithms for Shamir’s identity-based signature and identity-based multi-signature.

scholarly journals Blockchain-Based Secure Outsourcing of Polynomial Multiplication and Its Application in Fully Homomorphic Encryption

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Mingyang Song ◽  
Yingpeng Sang ◽  
Yuying Zeng ◽  
Shunchao Luo
Keyword(s):  
Homomorphic Encryption ◽  
Security Analysis ◽  
Secure Computation ◽  
Modular Exponentiation ◽  
Local Computation ◽  
Fully Homomorphic Encryption ◽  
Polynomial Multiplication ◽  
Secure Outsourcing ◽  
Cheating Detection ◽  
Constrained Devices

The efficiency of fully homomorphic encryption has always affected its practicality. With the dawn of Internet of things, the demand for computation and encryption on resource-constrained devices is increasing. Complex cryptographic computing is a major burden for those devices, while outsourcing can provide great convenience for them. In this paper, we firstly propose a generic blockchain-based framework for secure computation outsourcing and then propose an algorithm for secure outsourcing of polynomial multiplication into the blockchain. Our algorithm for polynomial multiplication can reduce the local computation cost to O n . Previous work based on Fast Fourier Transform can only achieve O n log n for the local cost. Finally, we integrate the two secure outsourcing schemes for polynomial multiplication and modular exponentiation into the fully homomorphic encryption using hidden ideal lattice and get an outsourcing scheme of fully homomorphic encryption. Through security analysis, our schemes achieve the goals of privacy protection against passive attackers and cheating detection against active attackers. Experiments also demonstrate our schemes are more efficient in comparisons with the corresponding nonoutsourcing schemes.

Optimal Control Policies for Stochastic Inventory Systems with Endogenous Supply

1993 ◽  
Vol 7 (2) ◽  
pp. 257-272 ◽  
Author(s):  
A. Federgruen ◽  
Y.-S. Zheng
Keyword(s):  
Optimal Control ◽  
Efficient Algorithm ◽  
Critical Level ◽  
Inventory Systems ◽  
Inventory Level ◽  
Single Server ◽  
Compound Poisson ◽  
Stochastic Inventory ◽  
General Distributions ◽  
Poisson Demands

We consider an inventory system with compound Poisson demands replenished by discrete production of units on a single-server facility. This facility may start a vacation at any production completion epoch; at the completion of a vacation the inventory level is inspected to decide whether or not to resume production. Unit production and vacation times are independent and identically distributed with general distributions. Under an (s, S) policy, production is terminated when the inventory level reaches a critical level S, and production is resumed when the inventory level, upon completion of a vacation, is at or below a prespecified value s. In this paper we prove that an (s, S) policy is optimal among all possible policies. We also derive a highly efficient algorithm for the determination and evaluation of an optimal (s, S) policy.

Sign in / Sign up

Export Citation Format

Share Document