Systems and methods for cryptography based on 128 bit integers include: receiving a complex input, the input including a 128-bit number; encrypting by: setting an imaginary part of the input to a predetermined value; encrypting the input using a Fourier transform and a scaling factor; adding a first noise and a second noise to the encrypted input, wherein the second noise obfuscates the first noise; and decrypting by: receiving the encrypted input with added first noise and second noise; estimating a standard deviation of the first noise based on an imaginary part of the received encrypted complex input; computing a standard deviation of the second noise based on the standard deviation of the first noise and a predetermined parameter; and decrypting the encrypted message using an inverse Fourier transform, the first noise, and the second noise.