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a(x) = a<sub>0</sub> + a<sub>1</sub>x + a<sub>2</sub>x<sup>2</sup> + ... + a<sub>n-3</sub>x<sup>n-3</sup> + a<sub>n-2</sub>x<sup>n-2</sup> + a<sub>n-1</sub>x<sup>n-1</sup>
The coefficients of this polynomial, the a<sub>i</sub>'s, are integers mod q. The polynomial
The RLWE-KEX uses polynomials which are considered "small" with respect to a measure called the "[[infinity norm]]." The infinity norm for a polynomial is simply the value of the largest coefficient of the polynomial when the coefficients are considered as integers in Z rather than <math>Zq</math>(i.e.from the set {-(q-1)/2,..., 0, ... (q-1)/2} ). The algorithm's security depends on an ability to generate random polynomials which are small with respect to the infinity norm. This is done simply by randomly generating the coefficients for a polynomial (s<sub>n-1</sub>, ..., s<sub>0</sub>) which are guaranteed or very likely to be small. There are two common ways to do this:
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