Abstract:In order to protect data privacy whilst allowing efficient access to data in multi-nodes cloud environments, a parallel homomorphic encryption (PHE) scheme is proposed based on the additive homomorphism of the Paillier encryption algorithm. In this paper we propose a PHE algorithm, in which plaintext is divided into several blocks and blocks are encrypted with a parallel mode. Experiment results demonstrate that the encryption algorithm can reach a speed-up ratio at about 7.1 in the MapReduce environment with 16 cores and 4 nodes.
The issue of the privacy-preserving of information has become more prominent, especially regarding the privacy-preserving problem in a cloud environment. Homomorphic encryption can be operated directly on the ciphertext; this encryption provides a new method for privacy-preserving. However, we face a challenge in understanding how to construct a practical fully homomorphic encryption on non-integer data types. This paper proposes a revised floating-point fully homomorphic encryption scheme (FFHE) that achieves the goal of floating-point numbers operation without privacy leakage to unauthorized parties. We encrypt a matrix of plaintext bits as a single ciphertext to reduce the ciphertext expansion ratio and reduce the public key size by encrypting with a quadratic form in three types of public key elements and pseudo-random number generators. Additionally, we make the FFHE scheme more applicable by generalizing the homomorphism of addition and multiplication of floating-point numbers to analytic functions using the Taylor formula. We prove that the FFHE scheme for ciphertext operation may limit an additional loss of accuracy. Specifically, the precision of the ciphertext operation's result is similar to unencrypted floating-point number computation. Compared to other schemes, our FFHE scheme is more practical for privacy-preserving in the cloud environment with its low ciphertext expansion ratio and public key size, supporting multiple operation types and high precision.
In this paper, a rough Heston model with variable volatility of volatility (vol-of-vol) is derived by modifying the generalized nonlinear Hawkes process and extending the scaling techniques. Then the nonlinear fractional Riccati equation for the characteristic function of the asset log-price is derived. The existence, uniqueness and regularity of the solution to the nonlinear fractional Riccati equation are proved and the equation is solved by the Adams methods. Finally the Fourier-cosine methods are combined with the Adams methods to price the options.
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