a rlwe signature uses polynomials which are considered "small" with respect to a measure called the "infinity norm". the infinity norm for a polynomial is simply the largest absolute value of the coefficients of the polynomial when those coefficients are viewed as integers in z rather than z . the signature algorithm will create random polynomials which are small with respect to a particular infinity norm bound. this is easily done by randomly generating all of the coefficients of the polynomial (a, ..., a) in a manner which is guaranteed or very likely to be less than or equal to this bound. in the literature on ring learning with errors, there are two common ways to do this: