Twisted Edwards MSM: setNeutral instead of zeroMem (#406)

* fix: initialization of buckets in MSM and equality check with zero points for Twisted Edwards * fix: twistedEdwards zero affine point conversion to projective * enabled optimized MSM for Verkle IPA
mratsim · Jun 27, 2024 · 29def11 · 29def11
1 parent da3a68a
commit 29def11
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Showing 8 changed files with 58 additions and 34 deletions.
diff --git a/config.nims b/config.nims
@@ -1,2 +1,2 @@
-# Absolute imports from porject root
+# Absolute imports from project root
 --path:"."
diff --git a/constantine/commitments/eth_verkle_ipa.nim b/constantine/commitments/eth_verkle_ipa.nim
@@ -422,7 +422,7 @@ func ipa_verify*[N, logN: static int, EcAff, F](
 
   # ∑ᵢ[uᵢ]Lᵢ + ∑ᵢ[uᵢ⁻¹]Rᵢ + [⟨ā,b̄⟩.w]G - [a₀]G₀ - [a₀.b₀.w]G
   var t {.noInit.}: EC
-  t.multiScalarMul_reference_vartime(fs.toOpenArray(), ecs.toOpenArray())
+  t.multiScalarMul_vartime(fs.toOpenArray(), ecs.toOpenArray())
 
   # ∑ᵢ[uᵢ]Lᵢ + ∑ᵢ[uᵢ⁻¹]Rᵢ + [⟨ā,b̄⟩.w]G - [a₀]G₀ - [a₀.b₀.w]G = -⟨ā,Ḡ⟩
   var C {.noInit.}: EC
@@ -949,7 +949,7 @@ func ipa_multi_verify*[N, logN: static int, EcAff, F](
   # E = ∑rⁱ.Cᵢ/(t-zᵢ)
   var E {.noInit.}: EC
   var Eaff {.noInit.}: EcAff
-  E.multiScalarMul_reference_vartime(invTminusChallenges, comms_by_challenges, num_distinct_challenges)
+  E.multiScalarMul_vartime(invTminusChallenges, comms_by_challenges, num_distinct_challenges)
   Eaff.affine(E)
   transcript.absorb("E", Eaff)
   freeHeapAligned(invTminusChallenges)

diff --git a/constantine/commitments/pedersen_commitments.nim b/constantine/commitments/pedersen_commitments.nim
@@ -33,7 +33,7 @@ func pedersen_commit[EC, ECaff](
   ##
   ## Output:
   ##   Commit(m) := ∑[mᵢ]Gᵢ
-  r.multiScalarMul_reference_vartime(messages, public_generators)
+  r.multiScalarMul_vartime(messages, public_generators)
 
 func pedersen_commit*[N: static int, EC, ECaff, F](
       crs: PolynomialEval[N, EcAff],
@@ -49,7 +49,7 @@ func pedersen_commit*[N: static int, EC, ECaff, F](
   ##
   ## Output:
   ##   Commit(m) := ∑[mᵢ]Gᵢ
-  r.multiScalarMul_reference_vartime(messages.evals, crs.evals)
+  r.multiScalarMul_vartime(messages.evals, crs.evals)
 
 func pedersen_commit*[EC, ECaff, F](
       public_generators: View[ECaff],

diff --git a/constantine/math/elliptic/ec_multi_scalar_mul.nim b/constantine/math/elliptic/ec_multi_scalar_mul.nim
@@ -264,7 +264,8 @@ func multiScalarMul_vartime*[bits: static int, EC, ECaff](
   const numBuckets = 1 shl (c-1)
 
   let buckets = allocHeapArray(EC, numBuckets)
-  zeroMem(buckets[0].addr, sizeof(EC) * numBuckets)
+  for i in 0 ..< numBuckets:
+    buckets[i].setNeutral()
 
   # Algorithm
   # ---------
@@ -366,7 +367,8 @@ func multiScalarMulAffine_vartime[bits: static int, EC, ECaff](
   when top != 0:      # Prologue
     when excess != 0:
       # The top might use only a few bits, the affine scheduler would likely have significant collisions
-      zeroMem(sched.buckets.pt.addr, buckets.pt.sizeof())
+      for i in 0 ..< numBuckets:
+        sched.buckets.pt[i].setNeutral()
       r.miniMSM(sched.buckets.pt.asUnchecked(), w, kTopWindow, c, coefs, points, N)
       w -= c
     else:

diff --git a/constantine/math/elliptic/ec_multi_scalar_mul_parallel.nim b/constantine/math/elliptic/ec_multi_scalar_mul_parallel.nim
@@ -134,14 +134,15 @@ export bestBucketBitSize
 # Parallel MSM non-affine
 # ------------------------------
 
-proc bucketAccumReduce_zeroMem[bits: static int, EC, ECaff](
+proc bucketAccumReduce_withInit[bits: static int, EC, ECaff](
        windowSum: ptr EC,
        buckets: ptr EC or ptr UncheckedArray[EC],
        bitIndex: int, miniMsmKind: static MiniMsmKind, c: static int,
        coefs: ptr UncheckedArray[BigInt[bits]], points: ptr UncheckedArray[ECaff], N: int) =
   const numBuckets = 1 shl (c-1)
   let buckets = cast[ptr UncheckedArray[EC]](buckets)
-  zeroMem(buckets, sizeof(EC) * numBuckets)
+  for i in 0 ..< numBuckets:
+    buckets[i].setNeutral()
   bucketAccumReduce(windowSum[], buckets, bitIndex, miniMsmKind, c, coefs, points, N)
 
 proc msm_vartime_parallel[bits: static int, EC, ECaff](
@@ -168,14 +169,14 @@ proc msm_vartime_parallel[bits: static int, EC, ECaff](
   # ---------
 
   block: # 1. Bucket accumulation and reduction
-    miniMSMsReady[0] = tp.spawnAwaitable bucketAccumReduce_zeroMem(
+    miniMSMsReady[0] = tp.spawnAwaitable bucketAccumReduce_withInit(
                                   miniMSMsResults[0].addr,
                                   bucketsMatrix[0].addr,
                                   bitIndex = 0, kBottomWindow, c,
                                   coefs, points, N)
 
   for w in 1 ..< numFullWindows:
-    miniMSMsReady[w] = tp.spawnAwaitable bucketAccumReduce_zeroMem(
+    miniMSMsReady[w] = tp.spawnAwaitable bucketAccumReduce_withInit(
                                   miniMSMsResults[w].addr,
                                   bucketsMatrix[w*numBuckets].addr,
                                   bitIndex = w*c, kFullWindow, c,
@@ -187,7 +188,7 @@ proc msm_vartime_parallel[bits: static int, EC, ECaff](
 
   when top != 0:
     when excess != 0:
-      bucketAccumReduce_zeroMem(
+      bucketAccumReduce_withInit(
         r,
         bucketsMatrix[numFullWindows*numBuckets].addr,
         bitIndex = top, kTopWindow, c,
@@ -374,7 +375,8 @@ proc msmAffine_vartime_parallel[bits: static int, EC, ECaff](
   when top != 0:
     when excess != 0:
       let buckets = allocHeapArray(EC, numBuckets)
-      zeroMem(buckets[0].addr, sizeof(EC) * numBuckets)
+      for i in 0 ..< numBuckets:
+        buckets[i].setNeutral()
       r[].bucketAccumReduce(buckets, bitIndex = top, kTopWindow, c,
                                 coefs, points, N)
       buckets.freeHeap()

diff --git a/constantine/math/elliptic/ec_twistededwards_projective.nim b/constantine/math/elliptic/ec_twistededwards_projective.nim
@@ -36,6 +36,22 @@ type EC_TwEdw_Prj*[F] = object
 template getScalarField*(EC: type EC_TwEdw_Prj): untyped =
   Fr[EC.F.Name]
 
+func isNeutral*(P: EC_TwEdw_Prj): SecretBool {.inline.} =
+  ## Returns true if P is the neutral element / identity element
+  ## and false otherwise, i.e. ∀Q, P+Q == Q
+  ## Contrary to Short Weierstrass curve, the neutral element is on the curve
+  # Isogeny-based constructions to create
+  # prime order curves overload this generic identity check.
+  result = P.x.isZero() and (P.y == P.z)
+
+func setNeutral*(P: var EC_TwEdw_Prj) {.inline.} =
+  ## Set P to the neutral element / identity element
+  ## i.e. ∀Q, P+Q == Q.
+  ## Contrary to Short Weierstrass curve, the neutral element is on the curve
+  P.x.setZero()
+  P.y.setOne()
+  P.z.setOne()
+
 func `==`*(P, Q: EC_TwEdw_Prj): SecretBool =
   ## Constant-time equality check
   ## This is a costly operation
@@ -52,21 +68,8 @@ func `==`*(P, Q: EC_TwEdw_Prj): SecretBool =
   b.prod(Q.y, P.z)
   result = result and a == b
 
-func isNeutral*(P: EC_TwEdw_Prj): SecretBool {.inline.} =
-  ## Returns true if P is the neutral element / identity element
-  ## and false otherwise, i.e. ∀Q, P+Q == Q
-  ## Contrary to Short Weierstrass curve, the neutral element is on the curve
-  # Isogeny-based constructions to create
-  # prime order curves overload this generic identity check.
-  result = P.x.isZero() and (P.y == P.z)
-
-func setNeutral*(P: var EC_TwEdw_Prj) {.inline.} =
-  ## Set P to the neutral element / identity element
-  ## i.e. ∀Q, P+Q == Q.
-  ## Contrary to Short Weierstrass curve, the neutral element is on the curve
-  P.x.setZero()
-  P.y.setOne()
-  P.z.setOne()
+  # Ensure a zero-init point doesn't propagate 0s and match any
+  result = result and not(P.isNeutral() xor Q.isNeutral())
 
 func ccopy*(P: var EC_TwEdw_Prj, Q: EC_TwEdw_Prj, ctl: SecretBool) {.inline.} =
   ## Constant-time conditional copy
@@ -458,6 +461,11 @@ func fromAffine*[F](
   proj.y = aff.y
   proj.z.setOne()
 
+  let inf = aff.isNeutral()
+  proj.x.csetZero(inf)
+  proj.y.csetOne(inf)
+  proj.z.csetOne(inf)
+
 # Vartime overloading
 # ------------------------------------------------------------
 # For generic vartime operations on both ShortWeierstrass curves and Twisted Edwards

diff --git a/constantine/named/README.md b/constantine/named/README.md
@@ -1,3 +1,13 @@
 # Named Algebraic Objects
 
 This folder holds named fields and named curves configuration and precomputed constants.
+
+
+⚠️ For Twisted Edwards curves
+  The formula are complete only if d is not a square, otherwise
+  they must be modified to handle the identity/neutral element with conditional moves.
+
+Sage script to check with Bandersnatch constants for example
+  r = Integer('0x1cfb69d4ca675f520cce760202687600ff8f87007419047174fd06b52876e7e1')
+  d = Integer('0x6389c12633c267cbc66e3bf86be3b6d8cb66677177e54f92b369f2f5188d58e7')
+  GF(r)(d).nth_root(2, all=True)
diff --git a/constantine/named/config_fields_and_curves.nim b/constantine/named/config_fields_and_curves.nim
@@ -33,12 +33,14 @@ export CurveFamily, SexticTwist
 # Barbulescu, R. and S. Duquesne, "Updating Key Size Estimations for Pairings",
 # Journal of Cryptology, DOI 10.1007/s00145-018-9280-5, January 2018.
 
-# Generates public:
-# - type Curve* = enum
-# - proc Mod*(curve: static Curve): auto
-#   which returns the field modulus of the curve
-# - proc family*(curve: static Curve): CurveFamily
-#   which returns the curve family
+# ⚠️ For Twisted Edwards curves
+#   The formula are complete only if d is not a square, otherwise
+#   they must be modified to handle the identity/neutral element with conditional moves.
+#
+# Sage script to check with Bandersnatch constants for example
+#   r = Integer('0x1cfb69d4ca675f520cce760202687600ff8f87007419047174fd06b52876e7e1')
+#   d = Integer('0x6389c12633c267cbc66e3bf86be3b6d8cb66677177e54f92b369f2f5188d58e7')
+#   GF(r)(d).nth_root(2, all=True)
 
 declareCurves:
   # -----------------------------------------------------------------------------