This paper introduces an efficient algorithm to develop a privacy-preserving voice verification based on iVector and linear discriminant analysis techniques. This research considers a scenario in which users enrol their voice biometric to access different services (i.e., banking). Once enrolment is completed, users can verify themselves using their voice print instead of alphanumeric passwords. Since a voice print is unique for everyone, storing it with a third-party server raises several privacy concerns. To address this challenge, this paper proposes a novel technique based on randomization to carry out voice authentication, which allows the user to enrol and verify their voice in the randomized domain. To achieve this, the iVector-based voice verification technique has been redesigned to work on the randomized domain. The proposed algorithm is validated using a well-known speech dataset. The proposed algorithm neither compromises the authentication accuracy nor adds additional complexity due to the randomization operations.