diff --git a/Sources/HomomorphicEncryption/HeScheme.swift b/Sources/HomomorphicEncryption/HeScheme.swift
index e9564f03..19307461 100644
--- a/Sources/HomomorphicEncryption/HeScheme.swift
+++ b/Sources/HomomorphicEncryption/HeScheme.swift
@@ -17,7 +17,7 @@ import ModularArithmetic
 /// Polynomial format.
 ///
 /// - Warning: There should be no other conformances to ``PolyFormat`` beyond ``Coeff`` and ``Eval``.
-public protocol PolyFormat {
+public protocol PolyFormat: Sendable {
     /// A textual representation of the format.
     static var description: String { get }
 }
diff --git a/Sources/PrivateInformationRetrieval/IndexPir/MulPir.swift b/Sources/PrivateInformationRetrieval/IndexPir/MulPir.swift
index 65053764..9d7f2f77 100644
--- a/Sources/PrivateInformationRetrieval/IndexPir/MulPir.swift
+++ b/Sources/PrivateInformationRetrieval/IndexPir/MulPir.swift
@@ -416,7 +416,7 @@ extension MulPirServer {
 
             try await responseCiphertexts
                 .append(.init(stride(from: 0, to: database.count, by: perChunkPlaintextCount).async
-                        .map { startIndex in
+                        .map { [queryCiphertexts, firstDimensionQueries] startIndex in
                             try await self.computeResponseForOneChunk(
                                 expandedDim0Query: firstDimensionQueries,
                                 expandedRemainingQuery: queryCiphertexts,
diff --git a/Sources/PrivateInformationRetrieval/IndexPir/PirUtil.swift b/Sources/PrivateInformationRetrieval/IndexPir/PirUtil.swift
index f285ea8d..4c7460ea 100644
--- a/Sources/PrivateInformationRetrieval/IndexPir/PirUtil.swift
+++ b/Sources/PrivateInformationRetrieval/IndexPir/PirUtil.swift
@@ -17,7 +17,7 @@ import HomomorphicEncryption
 import ModularArithmetic
 
 /// A protocol  outlining the auxiliary functionalities used in PIR.
-public protocol PirUtilProtocol {
+public protocol PirUtilProtocol: Sendable {
     /// The underlying HE scheme.
     associatedtype Scheme: HeScheme
     /// The Scalar type used by the HE scheme.
@@ -169,15 +169,16 @@ extension PirUtilProtocol {
             remainingOutputs -= outputToGenerate
             return outputToGenerate
         }
-        let expanded: [[CanonicalCiphertext]] = try await .init((0..<ciphertexts.count).async.map { ciphertextIndex in
-            let outputToGenerate = lengths[ciphertextIndex]
-            return try await expandCiphertext(
-                ciphertexts[ciphertextIndex],
-                outputCount: outputToGenerate,
-                logStep: 1,
-                expectedHeight: outputToGenerate.ceilLog2,
-                using: evaluationKey)
-        })
+        let expanded: [[CanonicalCiphertext]] = try await .init((0..<ciphertexts.count).async
+            .map { [ciphertexts] ciphertextIndex in
+                let outputToGenerate = lengths[ciphertextIndex]
+                return try await expandCiphertext(
+                    ciphertexts[ciphertextIndex],
+                    outputCount: outputToGenerate,
+                    logStep: 1,
+                    expectedHeight: outputToGenerate.ceilLog2,
+                    using: evaluationKey)
+            })
         return expanded.flatMap(\.self)
     }