Attainable Index Mappings Sample Clauses
Attainable Index Mappings. In the real world, each tuple (xi, yi) ∈ τ corresponds to an evaluation of the function EDMp1 ,p−2 1 and thus to a one call to p and one to p : x ›→ p (x ) and yi ›→ p2(yi), such that p1(xi) ⊕ p2(yi) = xi. Indeed, p1 and p2 xor to xi in the middle of the function EDMp1 ,p−2 1 . Writing P := p (x ) and P := p (y ), the ai 1 i transcript τ defines q equations on the unknowns: Pa1 ⊕ Pb1 = x1 , Pa2 ⊕ Pb2 = x2 , Paq ⊕ Pbq = xq . bi 2
Attainable Index Mappings. In the real world, each tuple (νi, mi, ti) ∈ τcq corresponds to an evaluation of 2 the function EWCDMh,p1 ,p2−1 and thus evaluations ν '→ p (ν ) and t p (t ), ⊕ ⊕ such that p1(νi) p2(ti) = νi h(mi) (note the fundamental difference with respect to the analysis of EDMp1 ,p−2 1 of Sect. 4, namely the addition of h(m )). Writing Pai := p1(νi) and Pbi := p2(ti), the transcript τcq defines q equations on the unknowns: Pa1 ⊕ Pb1 = ν1 ⊕ h(m1) , Pa2 ⊕ Pb2 = ν2 ⊕ h(m2) , . Paq ⊕ Pbq = νq ⊕ h(mq) .
Attainable Index Mappings. 0 ∈ F and satisfies