Formalization for SMC protocols #136
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* port to MC2 (affeldt-aist#116) --------- Co-authored-by: Reynald Affeldt <[email protected]> Co-authored-by: Takafumi Saikawa <[email protected]> * changelog * fix * lemma 3.1 * cleaning * Lemma 3.2 * Lemma 3.3 in a new file probability/smc.v * WIP: try to prove Lemma 3.4 * WIP: lemma 3.4 * WIP: try prob + uniform dist * pXY_unif * comments * mc2 --------- Co-authored-by: Enrico Tassi <[email protected]> Co-authored-by: Reynald Affeldt <[email protected]> Co-authored-by: Greg Weng <[email protected]> Co-authored-by: weng-chenghui <[email protected]>
Based on the relation between restricted distribution and conditional probability, re-use lemma 3.4 as much as possible.
* clean up lemma_3_5 * prove Z_X_indep * remove more dead code
…+ mixed types RV2
…e about RV2_inde_reduce
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For these two lemmas, I think the graphoid axioms suffice. |
garrigue
reviewed
Jan 14, 2025
| Lemma RV2_indeC : | ||
| P |= [% X, X] _|_ [% Y, Z] -> | ||
| P |= [% X, Y] _|_ [% X, Z]. | ||
| Proof. |
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Certainly not provable: assuming P |= X _|_ Y we can derive P |= [%X, X] _|_ [% Y, Y], but P |= [% X, Y] _|_ [% X, Y] definitely looks impossible.
smc/smc_proba.v
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| Lemma RV2_inde_reduce : | ||
| P |= X _|_ Y -> | ||
| P |= [% X, X] _|_ Y. |
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Just use index_rv_comp with f = fun x => (x, x) and g' = idfun.
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This is the pull-request contains all formalization work in: "Toward a Formalization of Secure-Multiparty Computation Stack".