The invention is directed to a system that enables an authentication process that involves secure multi-party computation. The authentication process can be performed between a user device operated by a user and an access device. The user device and the access device may conduct the authentication process such that enrollment information and authentication information input by the user is not transmitted between the devices. Instead, the user device may determine and utilize obfuscated values associated with the authentication information. The user device may also determine an obfuscated authentication function that can be utilized to determine an authentication result without revealing enrollment information and authentication information associated with the user. The user can be authenticated based on the authentication result.