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Two-factor authentication (2FA) provides improved protection, since users are prompted to provide something they know and something they have. This method delivers a higher-level of authentication assurance, which is essential for online banking security. Many banking systems have satisfied the2FA requirements by sending a One Time Password (OTP), something possessed, through an SMS to the user's phone device. Unfortunately, international roaming and SMS costs and delays put restrictions on this system reliability. This paper presents a novel two-factor authentication scheme whereby a user's device produces multiples OTPs from an initial seed using the proposed production scheme. The initial seed is produced by the communications partners' unique parameters. Applying the many from one function to a certain seed removes the requirement of sending SMS-based OTPs to users, and reduces the restrictions caused by the SMS system.