Ring learning with errors signature: Difference between revisions

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clarifying k a bit more.
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=== Other Parameters ===
Following GLP and as noted above, the maximum degree of the polynomials will be n-1 and therefore have n coefficients.<ref name=":0" /> Typical values for n are 512, and 1024.<ref name=":0" /> The coefficients of these polynomials will be from the field F<sub>q</sub> where q is an odd prime congruent to 1 mod 4. For n =512 the authors of GLP set q to be a 22 bit prime and the corresponding b value to be 2<sup>14</sup>. For n=1024, GLP sets q to be a 23-bit prime and b to be 2<sup>15</sup>.<ref name=":0" /> The number k of non-zero coefficients k produced by the hash function is equal to 32 for both cases.<ref name=":0" /> The security of the signature scheme is closely tied to the relative sizes of n, q, b, and k. Details on setting these parameters can be found in references 5 and 6 below.<ref name=":1" /><ref name=":0" />
 
As noted above, the polynomial Φ(x) which defines the ring of polynomials used will be x<sup>n</sup> + 1. Finally, a(x) will be a randomly chosen and fixed polynomial with coefficients from the set { -(q-1)/2 to (q-1)/2 }. All signers and verifiers of signatures will know n, q, b, k, Φ(x), a(x) and '''β''' = b-k