A method for signing a digital message, including the following steps: selecting parameters that include first and second primes, a ring of polynomials related to the primes, and at least one range-defining integer; deriving private and public keys respectively related to a random polynomial private key of the ring of polynomials, and to evaluations of roots of unity of the random polynomial to obtain a public key set of integers; storing the private key and publishing the public key; signing the digital message by: (A) generating a noise polynomial, (B) deriving a candidate signature by obtaining a hash of the digital message and the public key evaluated at the noise polynomial, and determining the candidate signature using the private key, a polynomial derived from the hash, and the noise polynomial, (C) determining whether the coefficients of the candidate signature are in a predetermined range dependent on the at least one range-defining integer, and (D) repeating steps (A) through (C) until the criterion of step (C) is satisfied, and outputting the resultant candidate signature as an encoded signed message.