--- Log opened Fri Sep 18 00:00:22 2020
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05:10 < roconnor> In particular, why can't we instead decompose a scalar value into k = k0 + k1 * lambda + k2 * lambda^2 where k0,k1,k2 are all 85 bit numbers?
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06:31 < roconnor> Anyone know how to run a lattice reduction?
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08:17 < roconnor> okay I see that this plan won't work because 1 + lambda + lambda^2 = 0 (mod n).
08:17 < roconnor> suppose there where 85 bit values k0, k1 and k2 such that k = k0 + k1 * lambda + k2 * lambda^2
08:17 < roconnor> since lambda^2 = -1 - lambda we can substutute and we have
08:17 < roconnor> k = (k0 - k2) + (k1 - k2)*lambda.
08:19 < roconnor> which implies we have 86ish bit coefficents k0' = (k0 - k2), k1' = (k1 - k2) such that k = k0' + k1' * lambda.
08:19 < roconnor> But there are not enough bits to cover the entropy of k.
08:20 < roconnor> My mistake was thinking that lambda was the root of a cubic because it is a cube root.
08:21 < roconnor> but really lambda is generated by a quadratic, once we factor x^3-1.
08:36 < roconnor> gap> LLLReducedBasis(http://en.wikipedia.org/wiki/Special:Search?go=Go&search=1,0,115792089237316195423570985008687907852837564279074904382605163141518161494337],[0,1,37718080363155996902926221483475020450927657555482586988616620542887997980018).basis;
08:36 < roconnor> [ [ 21011179226632705335158493575954588082, -64502973549206556628585045361533709077, 367917413016453100223835821029139468248 ], [ -98834128363575826231712400374302886273, 303414439467246543595250775667605759171,
08:36 < roconnor>       64502973549206556628585045361533709077 ] ]
08:37 < roconnor> god damn Konversation.
08:37 < roconnor> gap> LLLReducedBasis([[1,0,115792089237316195423570985008687907852837564279074904382605163141518161494337],[0,1,37718080363155996902926221483475020450927657555482586988616620542887997980018]]).basis;
08:37 < roconnor> [ [ 21011179226632705335158493575954588082, -64502973549206556628585045361533709077, 367917413016453100223835821029139468248 ], [ -98834128363575826231712400374302886273, 303414439467246543595250775667605759171,
08:37 < roconnor>       64502973549206556628585045361533709077 ] ]
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--- Log closed Sat Sep 19 00:00:22 2020