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refactor(CramerShoup): replace projection chains in Scheme, Reductions, and CramerShoup (#1764) #1985

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SamuelSchlesinger merged 2 commits into from
Nov 1, 2026
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refactor(CramerShoup): replace projection chains in Scheme, Reductions, and CramerShoup (#1764) #1985

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3bc58fc
refactor(CramerShoup): replace projection chains in Scheme, Reduction…
SamuelSchlesinger Oct 31, 2026
c217ab1
Address PR #1985 review: add named Cramer-Shoup accessors and documen…
SamuelSchlesinger Oct 31, 2026
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30 changes: 18 additions & 12 deletions Complexity/Crypto/Computational/CramerShoup.lean
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Original file line number Diff line number Diff line change
Expand Up @@ -189,14 +189,15 @@ noncomputable def cramerShoupMsgCCA2Game
(F.cramerShoupPhase1Oracle hasAD H isElem d sk))
(adversary.choose n pk)).run ())
let choice := choiceOut.1
let m₀ := encodeMsg (d, choice.1.1.1)
let m₁ := encodeMsg (d, choice.1.1.2)
let ad := encodeAD (d, choice.1.2)
let m₀ := encodeMsg (d, csChoiceMsg₀ choice)
let m₁ := encodeMsg (d, csChoiceMsg₁ choice)
let ad := encodeAD (d, csChoiceAD choice)
if isElem (d, m₀) && isElem (d, m₁) then
let m := if bit then m₁ else m₀
let β ← PMF.uniformOfFintype (ZMod (F.order d))
let ct := F.encodeCramerShoupEncrypt H d
(F.encode d pkVal.1, F.encode d pkVal.2.1, F.encode d pkVal.2.2.1, F.encode d pkVal.2.2.2)
(F.encode d (csPkU pkVal), F.encode d (csPkH pkVal),
F.encode d (csPkH₁ pkVal), F.encode d (csPkH₂ pkVal))
m ad β.val
let guessOut ← ProbComp.eval ((OracleComp.interpret
(ProbOracleComp.handler (fun m => StateT.lift (ProbComp.unifFin m))
Expand Down Expand Up @@ -316,9 +317,9 @@ noncomputable def cramerShoupGame1
(F.cramerShoupPhase1Oracle hasAD H isElem d sk))
(adversary.choose n pk)).run ())
let choice := choiceOut.1
let m₀ := encodeMsg (d, choice.1.1.1)
let m₁ := encodeMsg (d, choice.1.1.2)
let ad := encodeAD (d, choice.1.2)
let m₀ := encodeMsg (d, csChoiceMsg₀ choice)
let m₁ := encodeMsg (d, csChoiceMsg₁ choice)
let ad := encodeAD (d, csChoiceAD choice)
if isElem (d, m₀) && isElem (d, m₁) then
let m := if bit then m₁ else m₀
let ct := F.encodeCramerShoupChallenge H d sk v w m ad
Expand All @@ -342,6 +343,7 @@ theorem cramerShoupMsgCCA2Game_eq_game1
F.cramerShoupGame1 hasAD encodeMsg encodeAD setup H isElem adversary bit n := by
simp only [cramerShoupMsgCCA2Game, cramerShoupGame1, PMF.monad_bind_eq_bind,
PMF.monad_pure_eq_pure, encodeCramerShoupPublicKey_encode, skNatOfZMod,
csSkS, csSkT, csSkS₁, csSkT₁, csSkS₂, csSkT₂, csChoiceMsg₀, csChoiceMsg₁, csChoiceAD,
ZMod.natCast_zmod_val, encodeCramerShoupEncrypt_publicKey_eq_challenge]
refine congrArg _ (funext fun d => congrArg _ (funext fun α => ?_))
conv_rhs => rw [PMF.bind_comm (PMF.uniformOfFintype (ZMod (F.order d)))]
Expand Down Expand Up @@ -392,9 +394,9 @@ noncomputable def cramerShoupGame2
(F.cramerShoupPhase1Oracle hasAD H isElem d sk))
(adversary.choose n pk)).run ())
let choice := choiceOut.1
let m₀ := encodeMsg (d, choice.1.1.1)
let m₁ := encodeMsg (d, choice.1.1.2)
let ad := encodeAD (d, choice.1.2)
let m₀ := encodeMsg (d, csChoiceMsg₀ choice)
let m₁ := encodeMsg (d, csChoiceMsg₁ choice)
let ad := encodeAD (d, csChoiceAD choice)
if isElem (d, m₀) && isElem (d, m₁) then
let m := if bit then m₁ else m₀
let ct := F.encodeCramerShoupChallenge H d sk v w m ad
Expand Down Expand Up @@ -1521,7 +1523,9 @@ theorem advantage_cca2ADGameOn_cramerShoupADGroupCCA2Game_le
congrArg _ (funext fun τ₁ => congrArg _ (funext fun σ₂ =>
congrArg _ (funext fun τ₂ => ?_)))))))
simp only [cramerShoupCCA2InnerSK, cramerShoupCCA2InnerB, ↓reduceIte,
encodeCramerShoupPublicKey_encode, skNatOfZMod, ZMod.natCast_zmod_val]
encodeCramerShoupPublicKey_encode, skNatOfZMod,
csPkU, csPkH, csPkH₁, csPkH₂, csSkS, csSkT, csSkS₁, csSkT₁, csSkS₂, csSkT₂,
csChoiceMsg₀, csChoiceMsg₁, csChoiceAD, ZMod.natCast_zmod_val]
rw [hgame0, hgame1]
exact F.advantage_cramerShoupCCA2InnerSK_le true (fun p => encAD p.2) H isElem (d n)
adversary bit n
Expand Down Expand Up @@ -1665,7 +1669,9 @@ theorem advantage_cca2GameOn_cramerShoupGroupCCA2Game_le
congrArg _ (funext fun τ₁ => congrArg _ (funext fun σ₂ =>
congrArg _ (funext fun τ₂ => ?_)))))))
simp only [cramerShoupCCA2InnerSK, cramerShoupCCA2InnerB, ↓reduceIte,
encodeCramerShoupPublicKey_encode, skNatOfZMod, ZMod.natCast_zmod_val]
encodeCramerShoupPublicKey_encode, skNatOfZMod,
csPkU, csPkH, csPkH₁, csPkH₂, csSkS, csSkT, csSkS₁, csSkT₁, csSkS₂, csSkT₂,
csChoiceMsg₀, csChoiceMsg₁, ZMod.natCast_zmod_val]
rw [hgame0, hgame1]
exact F.advantage_cramerShoupCCA2InnerSK_le false (fun _ => []) H isElem (d n)
adversary.toADUnit bit n
Expand Down
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