Abstract: The techniques and/or systems described herein are directed to improvements in homomorphic encryption to improve processing speed and storage requirements. For example, the techniques and/or systems can be used on a client device to encode data to be sent to a remote server, to be operated on while maintaining confidentiality of data. For example, data including a real number can be encoded as a polynomial, with the fractional part of the real number encoded as high-order coefficients in the polynomial. Further, real numbers can be approximated and encoded in a polynomial using a fractional base, and/or the encoding can include slot encoding. Thus, the optimized encodings disclosed herein provide an optimized homomorphic encryption scheme.