A method of encrypting data is provided. The method includes generating a key and encrypting data using the key. Generating the key includes determining a number of coefficients for a polynomial having a number of variables and selecting a polynomial level from the number of coefficients. Generating the key also includes selecting a first value based on the polynomial level, generating a vector (c) having coefficients based on the polynomial level, and generating a vector (t) based on the polynomial level. Furthermore, generating the key includes generating a vector (t′) based on a product of the vector (c) and the vector (t) and calculating a second value based on the first value, the vector (t), and the product. In addition, generating the key includes comparing the second value with the polynomial level and returning the coefficients of the vector (c) as the number of coefficients for the polynomial.