Abstract:Secure multiparty computation is valuable for studying data privacy protection issues due to its decentralization, input privacy, fairness, etc. One of the most fundamental problems is to confidentially compute the maximum and the minimum of multiple data. In this paper, an efficient secure multipart computation scheme that can compute the maximum and the minimum simultaneously without a trusted third party was proposed to address the problems of existing secure multi-party computation protocols, such as inability of computing the maximum and the minimum at one time, low efficiency, and security risks caused by unique designated decryption key holder. In the scheme, an encoding method that can simultaneously compute the maximum and the minimum was first provided, whose basic idea was to give a complete set of ordinal numbers with potential l (l ≥ the number of participants n), and each participant encodes its data into an array with length l where the location of the data in the complete set was coded as a random number and the other positions were coded as 1. The positions of the leftmost and rightmost non-1 values in the product array were the positions of the maximum and minimum in the whole set. Based on the proposed encoding method, the ElGamal homomorphic encryption algorithm was used to guarantee the confidentiality of all participants’ data, and the maximum threshold decryption was used to make each participant hold part of the decryption key, which avoids the security threats caused by centralized decryption of calculation result by designated key holder. The proposed scheme was proven to be resistant to collusive attacks by any participant under a semi-honest model based on an ideal-realistic simulation paradigm. Finally, the efficiency analysis and performance comparison with related maximum (minimum) computing schemes were given, which showed that the proposed protocol has advantages over existing schemes in terms of computational complexity and communication complexity under the premise of higher security.