bugfix(prob) handle sigma > q

[bencrts]

Leaving in draft for now, will try to come up with a better condition than sigma > q as it's not the one we want.

[malb]

I don't think this is the correct fix. IIRC the KF analysis of BKW on Binary LWE uses sigma > q. The advantage is small, but not zero, e.g.

sage: q=2^13; sigma=2^15; log(float(exp(-float(pi) * (float(sigma / q) ** 2))), 2.)
-72.5177622692351

[bencrts]

Indeed I agree -- I've left the PR as draft for now. I'll take a look at the advantage formula and edit to someting more reasonable asap.

[bencrts]

Alternatively we could just use some larger arbitrary bound, the problem was that the optimization was getting to:

sage: sigma = 2.32635228499049e947
sage: q = 16369619120181469452283419146795337838756316829754574698247620392195385261672706601332322013852753
....: 903223620612005347547568443576301324009744462831784432007180117250379339731260566921104165956679636026
....: 071068887222235733068105836856857083444590817350909528504074694291691092139548999928924484582086252478
....: 977633818457376405409231086116246168367047039176965052754559121441305592658834773042270186227068683230
....: 815767812692570326671423805343812399828024592832603292760006139062134619510217374480970637509621909629
....: 132424341126237483954993915411214076712692111051902940729020471900580101114968926454825939983166452660
....: 569882221948169114307695627932888903160524898910557246807652042223153662188221235158821666169210876076
....: 693138615217053841090670627933973595298962019709647311664185065483481987899214266368
sage: sigma/q
1.42114014254762e154

[malb]

Yeah, the advantage log base 2 is RR(-pi*gap^2)/log(2.,e), so e.g. sigma/q > 16 should cover us

[bencrts]

ah nice, thanks! Made the change and looks like all tests pass -- will take the PR out of draft.