diff --git a/src/libraries/Common/tests/System/Security/Cryptography/AlgorithmImplementations/RSA/RSAFactory.cs b/src/libraries/Common/tests/System/Security/Cryptography/AlgorithmImplementations/RSA/RSAFactory.cs
index 56d4978f756d6c..9a4b27348ab4a0 100644
--- a/src/libraries/Common/tests/System/Security/Cryptography/AlgorithmImplementations/RSA/RSAFactory.cs
+++ b/src/libraries/Common/tests/System/Security/Cryptography/AlgorithmImplementations/RSA/RSAFactory.cs
@@ -11,6 +11,7 @@ public interface IRSAProvider
         bool SupportsLargeExponent { get; }
         bool SupportsSha2Oaep { get; }
         bool SupportsPss { get; }
+        bool SupportsSha1Signatures { get; }
     }
 
     public static partial class RSAFactory
@@ -39,5 +40,7 @@ public static RSA Create(RSAParameters rsaParameters)
         public static bool SupportsSha2Oaep => s_provider.SupportsSha2Oaep;
 
         public static bool SupportsPss => s_provider.SupportsPss;
+
+        public static bool SupportsSha1Signatures => s_provider.SupportsSha1Signatures;
     }
 }
diff --git a/src/libraries/Common/tests/System/Security/Cryptography/AlgorithmImplementations/RSA/RSASignatureFormatter.cs b/src/libraries/Common/tests/System/Security/Cryptography/AlgorithmImplementations/RSA/RSASignatureFormatter.cs
index d58ac86a4cbebe..c1ce8e1754b87a 100644
--- a/src/libraries/Common/tests/System/Security/Cryptography/AlgorithmImplementations/RSA/RSASignatureFormatter.cs
+++ b/src/libraries/Common/tests/System/Security/Cryptography/AlgorithmImplementations/RSA/RSASignatureFormatter.cs
@@ -10,7 +10,7 @@ namespace System.Security.Cryptography.Rsa.Tests
     [SkipOnPlatform(TestPlatforms.Browser, "Not supported on Browser")]
     public partial class RSASignatureFormatterTests : AsymmetricSignatureFormatterTests
     {
-        [Fact]
+        [ConditionalFact(typeof(RSAFactory), nameof(RSAFactory.SupportsSha1Signatures))]
         public static void VerifySignature_SHA1()
         {
             using (RSA rsa = RSAFactory.Create())
@@ -66,7 +66,7 @@ public static void InvalidHashAlgorithm()
             }
         }
 
-        [Fact]
+        [ConditionalFact(typeof(RSAFactory), nameof(RSAFactory.SupportsSha1Signatures))]
         public static void VerifyKnownSignature()
         {
             byte[] hash = "012d161304fa0c6321221516415813022320620c".HexToByteArray();
diff --git a/src/libraries/Common/tests/System/Security/Cryptography/AlgorithmImplementations/RSA/SignVerify.cs b/src/libraries/Common/tests/System/Security/Cryptography/AlgorithmImplementations/RSA/SignVerify.cs
index e78cea374bac53..0bbdd7db7372da 100644
--- a/src/libraries/Common/tests/System/Security/Cryptography/AlgorithmImplementations/RSA/SignVerify.cs
+++ b/src/libraries/Common/tests/System/Security/Cryptography/AlgorithmImplementations/RSA/SignVerify.cs
@@ -3,6 +3,7 @@
 
 using System.Collections.Generic;
 using System.IO;
+using Microsoft.DotNet.XUnitExtensions;
 using Test.Cryptography;
 using Test.IO.Streams;
 using Xunit;
@@ -26,14 +27,14 @@ public void NullArray_Throws()
         {
             using (RSA rsa = RSAFactory.Create())
             {
-                AssertExtensions.Throws<ArgumentNullException>("data", () => SignData(rsa, null, HashAlgorithmName.SHA1, RSASignaturePadding.Pkcs1));
-                AssertExtensions.Throws<ArgumentNullException>("hash", () => SignHash(rsa, null, HashAlgorithmName.SHA1, RSASignaturePadding.Pkcs1));
+                AssertExtensions.Throws<ArgumentNullException>("data", () => SignData(rsa, null, HashAlgorithmName.SHA256, RSASignaturePadding.Pkcs1));
+                AssertExtensions.Throws<ArgumentNullException>("hash", () => SignHash(rsa, null, HashAlgorithmName.SHA256, RSASignaturePadding.Pkcs1));
 
-                AssertExtensions.Throws<ArgumentNullException>("data", () => VerifyData(rsa, null, new byte[1], HashAlgorithmName.SHA1, RSASignaturePadding.Pkcs1));
-                AssertExtensions.Throws<ArgumentNullException>("hash", () => VerifyHash(rsa, null, new byte[1], HashAlgorithmName.SHA1, RSASignaturePadding.Pkcs1));
+                AssertExtensions.Throws<ArgumentNullException>("data", () => VerifyData(rsa, null, new byte[1], HashAlgorithmName.SHA256, RSASignaturePadding.Pkcs1));
+                AssertExtensions.Throws<ArgumentNullException>("hash", () => VerifyHash(rsa, null, new byte[1], HashAlgorithmName.SHA256, RSASignaturePadding.Pkcs1));
 
-                AssertExtensions.Throws<ArgumentNullException>("signature", () => VerifyData(rsa, new byte[1], null, HashAlgorithmName.SHA1, RSASignaturePadding.Pkcs1));
-                AssertExtensions.Throws<ArgumentNullException>("signature", () => VerifyHash(rsa, new byte[1], null, HashAlgorithmName.SHA1, RSASignaturePadding.Pkcs1));
+                AssertExtensions.Throws<ArgumentNullException>("signature", () => VerifyData(rsa, new byte[1], null, HashAlgorithmName.SHA256, RSASignaturePadding.Pkcs1));
+                AssertExtensions.Throws<ArgumentNullException>("signature", () => VerifyHash(rsa, new byte[1], null, HashAlgorithmName.SHA256, RSASignaturePadding.Pkcs1));
             }
         }
     }
@@ -72,10 +73,10 @@ public void NullPadding_Throws()
         {
             using (RSA rsa = RSAFactory.Create())
             {
-                AssertExtensions.Throws<ArgumentNullException>("padding", () => SignData(rsa, new byte[1], HashAlgorithmName.SHA1, null));
-                AssertExtensions.Throws<ArgumentNullException>("padding", () => SignHash(rsa, new byte[1], HashAlgorithmName.SHA1, null));
-                AssertExtensions.Throws<ArgumentNullException>("padding", () => VerifyData(rsa, new byte[1], new byte[1], HashAlgorithmName.SHA1, null));
-                AssertExtensions.Throws<ArgumentNullException>("padding", () => VerifyHash(rsa, new byte[1], new byte[1], HashAlgorithmName.SHA1, null));
+                AssertExtensions.Throws<ArgumentNullException>("padding", () => SignData(rsa, new byte[1], HashAlgorithmName.SHA256, null));
+                AssertExtensions.Throws<ArgumentNullException>("padding", () => SignHash(rsa, new byte[1], HashAlgorithmName.SHA256, null));
+                AssertExtensions.Throws<ArgumentNullException>("padding", () => VerifyData(rsa, new byte[1], new byte[1], HashAlgorithmName.SHA256, null));
+                AssertExtensions.Throws<ArgumentNullException>("padding", () => VerifyHash(rsa, new byte[1], new byte[1], HashAlgorithmName.SHA256, null));
             }
         }
 
@@ -87,7 +88,7 @@ public void UseAfterDispose(bool importKey)
             RSA rsa = importKey ? RSAFactory.Create(TestData.RSA2048Params) : RSAFactory.Create(1024);
             byte[] data = TestData.HelloBytes;
             byte[] sig;
-            HashAlgorithmName alg = HashAlgorithmName.SHA1;
+            HashAlgorithmName alg = HashAlgorithmName.SHA256;
             RSASignaturePadding padding = RSASignaturePadding.Pkcs1;
 
             using (rsa)
@@ -115,12 +116,12 @@ public void InvalidKeySize_DoesNotInvalidateKey()
         {
             using (RSA rsa = RSAFactory.Create())
             {
-                byte[] signature = SignData(rsa, TestData.HelloBytes, HashAlgorithmName.SHA1, RSASignaturePadding.Pkcs1);
+                byte[] signature = SignData(rsa, TestData.HelloBytes, HashAlgorithmName.SHA256, RSASignaturePadding.Pkcs1);
 
                 // A 2049-bit key is hard to describe, none of the providers support it.
                 Assert.ThrowsAny<CryptographicException>(() => rsa.KeySize = 2049);
 
-                Assert.True(VerifyData(rsa, TestData.HelloBytes, signature, HashAlgorithmName.SHA1, RSASignaturePadding.Pkcs1));
+                Assert.True(VerifyData(rsa, TestData.HelloBytes, signature, HashAlgorithmName.SHA256, RSASignaturePadding.Pkcs1));
             }
         }
 
@@ -143,11 +144,11 @@ public void SignEmptyHash()
             using (RSA rsa = RSAFactory.Create())
             {
                 Assert.ThrowsAny<CryptographicException>(
-                    () => SignHash(rsa, Array.Empty<byte>(), HashAlgorithmName.SHA1, RSASignaturePadding.Pkcs1));
+                    () => SignHash(rsa, Array.Empty<byte>(), HashAlgorithmName.SHA256, RSASignaturePadding.Pkcs1));
             }
         }
 
-        [Fact]
+        [ConditionalFact(typeof(RSAFactory), nameof(RSAFactory.SupportsSha1Signatures))]
         public void ExpectedSignature_SHA1_384()
         {
             byte[] expectedSignature =
@@ -178,7 +179,7 @@ public void ExpectedSignature_SHA1_384()
             }
         }
 
-        [Fact]
+        [ConditionalFact(typeof(RSAFactory), nameof(RSAFactory.SupportsSha1Signatures))]
         public void ExpectedSignature_SHA1_1032()
         {
             byte[] expectedSignature =
@@ -205,7 +206,7 @@ public void ExpectedSignature_SHA1_1032()
             ExpectSignature(expectedSignature, TestData.HelloBytes, "SHA1", TestData.RSA1032Parameters);
         }
 
-        [Fact]
+        [ConditionalFact(typeof(RSAFactory), nameof(RSAFactory.SupportsSha1Signatures))]
         public void ExpectedSignature_SHA1_2048()
         {
             byte[] expectedSignature = new byte[]
@@ -350,7 +351,7 @@ public void ExpectSignature_SHA256_1024_Stream()
             Assert.Equal(expectedSignature, signature);
         }
 
-        [Fact]
+        [ConditionalFact(typeof(RSAFactory), nameof(RSAFactory.SupportsSha1Signatures))]
         public void VerifySignature_SHA1_384()
         {
             byte[] signature =
@@ -366,7 +367,7 @@ public void VerifySignature_SHA1_384()
             VerifySignature(signature, TestData.HelloBytes, "SHA1", TestData.RSA384Parameters);
         }
 
-        [Fact]
+        [ConditionalFact(typeof(RSAFactory), nameof(RSAFactory.SupportsSha1Signatures))]
         public void VerifySignature_SHA1_1032()
         {
             byte[] signature =
@@ -393,7 +394,7 @@ public void VerifySignature_SHA1_1032()
             VerifySignature(signature, TestData.HelloBytes, "SHA1", TestData.RSA1032Parameters);
         }
 
-        [Fact]
+        [ConditionalFact(typeof(RSAFactory), nameof(RSAFactory.SupportsSha1Signatures))]
         public void VerifySignature_SHA1_2048()
         {
             byte[] signature = new byte[]
@@ -516,8 +517,12 @@ public static IEnumerable<object[]> RoundTripTheories
             {
                 foreach (RSAParameters rsaParameters in new[] { TestData.RSA1024Params, TestData.RSA2048Params })
                 {
+                    if (RSAFactory.SupportsSha1Signatures)
+                    {
+                        yield return new object[] { nameof(HashAlgorithmName.SHA1), rsaParameters };
+                    }
+
                     yield return new object[] { nameof(HashAlgorithmName.MD5), rsaParameters };
-                    yield return new object[] { nameof(HashAlgorithmName.SHA1), rsaParameters };
                     yield return new object[] { nameof(HashAlgorithmName.SHA256), rsaParameters };
                 }
 
@@ -532,8 +537,8 @@ public void NegativeVerify_WrongAlgorithm()
             using (RSA rsa = RSAFactory.Create())
             {
                 rsa.ImportParameters(TestData.RSA2048Params);
-                byte[] signature = SignData(rsa, TestData.HelloBytes, HashAlgorithmName.SHA1, RSASignaturePadding.Pkcs1);
-                bool signatureMatched = VerifyData(rsa, TestData.HelloBytes, signature, HashAlgorithmName.SHA256, RSASignaturePadding.Pkcs1);
+                byte[] signature = SignData(rsa, TestData.HelloBytes, HashAlgorithmName.SHA256, RSASignaturePadding.Pkcs1);
+                bool signatureMatched = VerifyData(rsa, TestData.HelloBytes, signature, HashAlgorithmName.SHA384, RSASignaturePadding.Pkcs1);
 
                 Assert.False(signatureMatched);
             }
@@ -545,12 +550,12 @@ public void NegativeVerify_WrongSignature()
             using (RSA rsa = RSAFactory.Create())
             {
                 rsa.ImportParameters(TestData.RSA2048Params);
-                byte[] signature = SignData(rsa, TestData.HelloBytes, HashAlgorithmName.SHA1, RSASignaturePadding.Pkcs1);
+                byte[] signature = SignData(rsa, TestData.HelloBytes, HashAlgorithmName.SHA256, RSASignaturePadding.Pkcs1);
 
                 // Invalidate the signature.
                 signature[0] = unchecked((byte)~signature[0]);
 
-                bool signatureMatched = VerifyData(rsa, TestData.HelloBytes, signature, HashAlgorithmName.SHA1, RSASignaturePadding.Pkcs1);
+                bool signatureMatched = VerifyData(rsa, TestData.HelloBytes, signature, HashAlgorithmName.SHA256, RSASignaturePadding.Pkcs1);
                 Assert.False(signatureMatched);
             }
         }
@@ -561,8 +566,8 @@ public void NegativeVerify_TamperedData()
             using (RSA rsa = RSAFactory.Create())
             {
                 rsa.ImportParameters(TestData.RSA2048Params);
-                byte[] signature = SignData(rsa, TestData.HelloBytes, HashAlgorithmName.SHA1, RSASignaturePadding.Pkcs1);
-                bool signatureMatched = VerifyData(rsa, Array.Empty<byte>(), signature, HashAlgorithmName.SHA1, RSASignaturePadding.Pkcs1);
+                byte[] signature = SignData(rsa, TestData.HelloBytes, HashAlgorithmName.SHA256, RSASignaturePadding.Pkcs1);
+                bool signatureMatched = VerifyData(rsa, Array.Empty<byte>(), signature, HashAlgorithmName.SHA256, RSASignaturePadding.Pkcs1);
                 Assert.False(signatureMatched);
             }
         }
@@ -575,13 +580,13 @@ public void NegativeVerify_BadKeysize()
             using (RSA rsa = RSAFactory.Create())
             {
                 rsa.ImportParameters(TestData.RSA2048Params);
-                signature = SignData(rsa, TestData.HelloBytes, HashAlgorithmName.SHA1, RSASignaturePadding.Pkcs1);
+                signature = SignData(rsa, TestData.HelloBytes, HashAlgorithmName.SHA256, RSASignaturePadding.Pkcs1);
             }
 
             using (RSA rsa = RSAFactory.Create())
             {
                 rsa.ImportParameters(TestData.RSA1024Params);
-                bool signatureMatched = VerifyData(rsa, TestData.HelloBytes, signature, HashAlgorithmName.SHA1, RSASignaturePadding.Pkcs1);
+                bool signatureMatched = VerifyData(rsa, TestData.HelloBytes, signature, HashAlgorithmName.SHA256, RSASignaturePadding.Pkcs1);
 
                 Assert.False(signatureMatched);
             }
@@ -610,7 +615,7 @@ public void PkcsSignHash_MismatchedHashSize()
             }
         }
 
-        [Fact]
+        [ConditionalFact(typeof(RSAFactory), nameof(RSAFactory.SupportsSha1Signatures))]
         public void ExpectedHashSignature_SHA1_2048()
         {
             byte[] expectedHashSignature = new byte[]
@@ -741,7 +746,7 @@ public void ExpectedHashSignature_SHA256_2048()
             ExpectHashSignature(expectedHashSignature, dataHash, "SHA256", TestData.RSA2048Params);
         }
 
-        [Fact]
+        [ConditionalFact(typeof(RSAFactory), nameof(RSAFactory.SupportsSha1Signatures))]
         public void VerifyHashSignature_SHA1_2048()
         {
             byte[] hashSignature = new byte[]
@@ -872,7 +877,7 @@ public void VerifyHashSignature_SHA256_2048()
             VerifyHashSignature(hashSignature, dataHash, "SHA256", TestData.RSA2048Params);
         }
 
-        [Theory]
+        [ConditionalTheory]
         [InlineData("SHA256")]
         [InlineData("SHA384")]
         [InlineData("SHA512")]
@@ -880,6 +885,11 @@ public void VerifyHashSignature_SHA256_2048()
         [InlineData("SHA1")]
         public void PssRoundtrip(string hashAlgorithmName)
         {
+            if (!RSAFactory.SupportsSha1Signatures && hashAlgorithmName == "SHA1")
+            {
+                throw new SkipTestException("Platform does not support RSA with SHA1 signatures.");
+            }
+
             RSAParameters privateParameters = TestData.RSA2048Params;
             RSAParameters publicParameters = new RSAParameters
             {
diff --git a/src/libraries/Common/tests/System/Security/Cryptography/AlgorithmImplementations/RSA/SignVerify.netcoreapp.cs b/src/libraries/Common/tests/System/Security/Cryptography/AlgorithmImplementations/RSA/SignVerify.netcoreapp.cs
index e79beb71246b95..fcb06908e91620 100644
--- a/src/libraries/Common/tests/System/Security/Cryptography/AlgorithmImplementations/RSA/SignVerify.netcoreapp.cs
+++ b/src/libraries/Common/tests/System/Security/Cryptography/AlgorithmImplementations/RSA/SignVerify.netcoreapp.cs
@@ -56,7 +56,7 @@ public static void VerifyDefaultSpanHash()
                 byte[] signature = new byte[2048 / 8];
 
                 Assert.False(
-                    rsa.VerifyHash(ReadOnlySpan<byte>.Empty, signature, HashAlgorithmName.SHA1, RSASignaturePadding.Pkcs1));
+                    rsa.VerifyHash(ReadOnlySpan<byte>.Empty, signature, HashAlgorithmName.SHA256, RSASignaturePadding.Pkcs1));
 
                 if (RSAFactory.SupportsPss)
                 {
diff --git a/src/libraries/Common/tests/System/Security/Cryptography/SignatureSupport.cs b/src/libraries/Common/tests/System/Security/Cryptography/SignatureSupport.cs
new file mode 100644
index 00000000000000..abdbabb14b8433
--- /dev/null
+++ b/src/libraries/Common/tests/System/Security/Cryptography/SignatureSupport.cs
@@ -0,0 +1,51 @@
+// Licensed to the .NET Foundation under one or more agreements.
+// The .NET Foundation licenses this file to you under the MIT license.
+
+namespace System.Security.Cryptography.Tests
+{
+    internal static class SignatureSupport
+    {
+        internal static bool CanProduceSha1Signature(AsymmetricAlgorithm algorithm)
+        {
+            // We expect all non-Linux platforms to support SHA1 signatures, currently.
+            if (!OperatingSystem.IsLinux())
+            {
+                return true;
+            }
+
+            switch (algorithm)
+            {
+                case ECDsa ecdsa:
+                    try
+                    {
+                        ecdsa.SignData(Array.Empty<byte>(), HashAlgorithmName.SHA1);
+                        return true;
+                    }
+                    catch (CryptographicException)
+                    {
+                        return false;
+                    }
+                    finally
+                    {
+                        algorithm.Dispose();
+                    }
+                case RSA rsa:
+                    try
+                    {
+                        rsa.SignData(Array.Empty<byte>(), HashAlgorithmName.SHA1, RSASignaturePadding.Pkcs1);
+                        return true;
+                    }
+                    catch (CryptographicException)
+                    {
+                        return false;
+                    }
+                    finally
+                    {
+                        algorithm.Dispose();
+                    }
+                default:
+                    throw new NotSupportedException($"Algorithm type {algorithm.GetType()} is not supported.");
+            }
+        }
+    }
+}
diff --git a/src/libraries/System.Security.Cryptography.Cng/tests/RSACngProvider.cs b/src/libraries/System.Security.Cryptography.Cng/tests/RSACngProvider.cs
index 76854a55f07b64..963bd925d800c7 100644
--- a/src/libraries/System.Security.Cryptography.Cng/tests/RSACngProvider.cs
+++ b/src/libraries/System.Security.Cryptography.Cng/tests/RSACngProvider.cs
@@ -34,6 +34,8 @@ public bool Supports384PrivateKey
         public bool SupportsSha2Oaep => true;
 
         public bool SupportsPss => true;
+
+        public bool SupportsSha1Signatures => true;
     }
 
     public partial class RSAFactory
diff --git a/src/libraries/System.Security.Cryptography.Cng/tests/System.Security.Cryptography.Cng.Tests.csproj b/src/libraries/System.Security.Cryptography.Cng/tests/System.Security.Cryptography.Cng.Tests.csproj
index b2c8ebf7aab8a9..aaec2eb1c432cb 100644
--- a/src/libraries/System.Security.Cryptography.Cng/tests/System.Security.Cryptography.Cng.Tests.csproj
+++ b/src/libraries/System.Security.Cryptography.Cng/tests/System.Security.Cryptography.Cng.Tests.csproj
@@ -15,6 +15,8 @@
     <Compile Include="TestData.cs" />
   </ItemGroup>
   <ItemGroup Condition="'$(TargetPlatformIdentifier)' == 'windows'">
+    <Compile Include="$(CommonTestPath)System\Security\Cryptography\SignatureSupport.cs"
+             Link="CommonTest\System\Security\Cryptography\SignatureSupport.cs" />
     <Compile Include="$(CommonTestPath)System\Security\Cryptography\AlgorithmImplementations\AES\AesCipherTests.Data.cs"
              Link="CommonTest\AlgorithmImplementations\AES\AesCipherTests.Data.cs" />
     <Compile Include="$(CommonTestPath)System\Security\Cryptography\AlgorithmImplementations\AES\AesCornerTests.cs"
diff --git a/src/libraries/System.Security.Cryptography.Csp/tests/RSACryptoServiceProviderBackCompat.cs b/src/libraries/System.Security.Cryptography.Csp/tests/RSACryptoServiceProviderBackCompat.cs
index 35741b83f18a1f..887bdc3d983e2e 100644
--- a/src/libraries/System.Security.Cryptography.Csp/tests/RSACryptoServiceProviderBackCompat.cs
+++ b/src/libraries/System.Security.Cryptography.Csp/tests/RSACryptoServiceProviderBackCompat.cs
@@ -156,24 +156,26 @@ public static void VerifyLegacySignVerifyHash(bool useLegacySign, bool useLegacy
 
         public static IEnumerable<object[]> AlgorithmIdentifiers()
         {
-            return new[]
+            yield return new object[] { "MD5", MD5.Create() };
+            yield return new object[] { "MD5", typeof(MD5) };
+            yield return new object[] { "MD5", "1.2.840.113549.2.5" };
+
+            if (RSAFactory.SupportsSha1Signatures)
             {
-                new object[] { "MD5", MD5.Create() },
-                new object[] { "MD5", typeof(MD5) },
-                new object[] { "MD5", "1.2.840.113549.2.5" },
-                new object[] { "SHA1", SHA1.Create() },
-                new object[] { "SHA1", typeof(SHA1) },
-                new object[] { "SHA1", "1.3.14.3.2.26" },
-                new object[] { "SHA256", SHA256.Create() },
-                new object[] { "SHA256", typeof(SHA256) },
-                new object[] { "SHA256", "2.16.840.1.101.3.4.2.1" },
-                new object[] { "SHA384", SHA384.Create() },
-                new object[] { "SHA384", typeof(SHA384) },
-                new object[] { "SHA384", "2.16.840.1.101.3.4.2.2" },
-                new object[] { "SHA512", SHA512.Create() },
-                new object[] { "SHA512", typeof(SHA512) },
-                new object[] { "SHA512", "2.16.840.1.101.3.4.2.3" },
-            };
+                yield return new object[] { "SHA1", SHA1.Create() };
+                yield return new object[] { "SHA1", typeof(SHA1) };
+                yield return new object[] { "SHA1", "1.3.14.3.2.26" };
+            }
+
+            yield return new object[] { "SHA256", SHA256.Create() };
+            yield return new object[] { "SHA256", typeof(SHA256) };
+            yield return new object[] { "SHA256", "2.16.840.1.101.3.4.2.1" };
+            yield return new object[] { "SHA384", SHA384.Create() };
+            yield return new object[] { "SHA384", typeof(SHA384) };
+            yield return new object[] { "SHA384", "2.16.840.1.101.3.4.2.2" };
+            yield return new object[] { "SHA512", SHA512.Create() };
+            yield return new object[] { "SHA512", typeof(SHA512) };
+            yield return new object[] { "SHA512", "2.16.840.1.101.3.4.2.3" };
         }
     }
 }
diff --git a/src/libraries/System.Security.Cryptography.Csp/tests/RSACryptoServiceProviderProvider.cs b/src/libraries/System.Security.Cryptography.Csp/tests/RSACryptoServiceProviderProvider.cs
index 763925168a3933..7f4f3eb5b7d462 100644
--- a/src/libraries/System.Security.Cryptography.Csp/tests/RSACryptoServiceProviderProvider.cs
+++ b/src/libraries/System.Security.Cryptography.Csp/tests/RSACryptoServiceProviderProvider.cs
@@ -2,11 +2,14 @@
 // The .NET Foundation licenses this file to you under the MIT license.
 
 using System.Runtime.InteropServices;
+using System.Security.Cryptography.Tests;
 
 namespace System.Security.Cryptography.Rsa.Tests
 {
     public class RSACryptoServiceProviderProvider : IRSAProvider
     {
+        private bool? _supportsSha1Signatures;
+
         public RSA Create() => new RSACryptoServiceProvider();
 
         public RSA Create(int keySize) => new RSACryptoServiceProvider(keySize);
@@ -18,6 +21,8 @@ public class RSACryptoServiceProviderProvider : IRSAProvider
         public bool SupportsSha2Oaep => false;
 
         public bool SupportsPss => false;
+
+        public bool SupportsSha1Signatures => _supportsSha1Signatures ??= SignatureSupport.CanProduceSha1Signature(Create());
     }
 
     public partial class RSAFactory
diff --git a/src/libraries/System.Security.Cryptography.Csp/tests/RSACryptoServiceProviderTests.cs b/src/libraries/System.Security.Cryptography.Csp/tests/RSACryptoServiceProviderTests.cs
index b16d5e66d39eef..89c9405d84b4d8 100644
--- a/src/libraries/System.Security.Cryptography.Csp/tests/RSACryptoServiceProviderTests.cs
+++ b/src/libraries/System.Security.Cryptography.Csp/tests/RSACryptoServiceProviderTests.cs
@@ -1,6 +1,7 @@
 // Licensed to the .NET Foundation under one or more agreements.
 // The .NET Foundation licenses this file to you under the MIT license.
 
+using System.Security.Cryptography.Tests;
 using System.Security.Cryptography.Rsa.Tests;
 using Xunit;
 
@@ -305,7 +306,7 @@ public static void ImportParameters_ExponentTooBig_Throws()
             }
         }
 
-        [Fact]
+        [ConditionalFact(typeof(RSAFactory), nameof(RSAFactory.SupportsSha1Signatures))]
         public static void SignHash_DefaultAlgorithm_Success()
         {
             byte[] hashVal = SHA1.HashData(TestData.HelloBytes);
@@ -317,7 +318,7 @@ public static void SignHash_DefaultAlgorithm_Success()
             }
         }
 
-        [Fact]
+        [ConditionalFact(typeof(RSAFactory), nameof(RSAFactory.SupportsSha1Signatures))]
         public static void VerifyHash_DefaultAlgorithm_Success()
         {
             byte[] hashVal = SHA1.HashData(TestData.HelloBytes);
@@ -352,7 +353,7 @@ public static void Sign_InvalidPaddingMode_Throws()
         {
             using (var rsa = new RSACryptoServiceProvider())
             {
-                Assert.Throws<CryptographicException>(() => rsa.SignData(TestData.HelloBytes, HashAlgorithmName.SHA1, RSASignaturePadding.Pss));
+                Assert.Throws<CryptographicException>(() => rsa.SignData(TestData.HelloBytes, HashAlgorithmName.SHA256, RSASignaturePadding.Pss));
             }
         }
 
@@ -361,8 +362,8 @@ public static void Verify_InvalidPaddingMode_Throws()
         {
             using (var rsa = new RSACryptoServiceProvider())
             {
-                byte[] sig = rsa.SignData(TestData.HelloBytes, "SHA1");
-                Assert.Throws<CryptographicException>(() => rsa.VerifyData(TestData.HelloBytes, sig, HashAlgorithmName.SHA1, RSASignaturePadding.Pss));
+                byte[] sig = rsa.SignData(TestData.HelloBytes, "SHA256");
+                Assert.Throws<CryptographicException>(() => rsa.VerifyData(TestData.HelloBytes, sig, HashAlgorithmName.SHA256, RSASignaturePadding.Pss));
             }
         }
 
@@ -378,15 +379,15 @@ public static void SignatureAlgorithm_Success()
         [Fact]
         public static void SignData_VerifyHash_CaseInsensitive_Success()
         {
-            byte[] hashVal = SHA1.HashData(TestData.HelloBytes);
+            byte[] hashVal = SHA256.HashData(TestData.HelloBytes);
 
             using (var rsa = new RSACryptoServiceProvider())
             {
-                byte[] signVal = rsa.SignData(TestData.HelloBytes, "SHA1");
-                Assert.True(rsa.VerifyHash(hashVal, "SHA1", signVal));
+                byte[] signVal = rsa.SignData(TestData.HelloBytes, "SHA256");
+                Assert.True(rsa.VerifyHash(hashVal, "SHA256", signVal));
 
-                signVal = rsa.SignData(TestData.HelloBytes, "sha1");
-                Assert.True(rsa.VerifyHash(hashVal, "sha1", signVal));
+                signVal = rsa.SignData(TestData.HelloBytes, "sha256");
+                Assert.True(rsa.VerifyHash(hashVal, "sha256", signVal));
             }
         }
 
diff --git a/src/libraries/System.Security.Cryptography.Csp/tests/System.Security.Cryptography.Csp.Tests.csproj b/src/libraries/System.Security.Cryptography.Csp/tests/System.Security.Cryptography.Csp.Tests.csproj
index 2343260ca112b0..ca7460db9b2d76 100644
--- a/src/libraries/System.Security.Cryptography.Csp/tests/System.Security.Cryptography.Csp.Tests.csproj
+++ b/src/libraries/System.Security.Cryptography.Csp/tests/System.Security.Cryptography.Csp.Tests.csproj
@@ -12,6 +12,8 @@
     <Compile Include="RSACryptoServiceProviderProvider.cs" />
     <Compile Include="RSACryptoServiceProviderTests.cs" />
     <Compile Include="ShimHelpers.cs" />
+    <Compile Include="$(CommonTestPath)System\Security\Cryptography\SignatureSupport.cs"
+             Link="CommonTest\System\Security\Cryptography\SignatureSupport.cs" />
     <Compile Include="$(CommonTestPath)System\Security\Cryptography\ByteUtils.cs"
              Link="CommonTest\System\Security\Cryptography\ByteUtils.cs" />
     <Compile Include="$(CommonTestPath)System\Security\Cryptography\CryptoUtils.cs"
diff --git a/src/libraries/System.Security.Cryptography.OpenSsl/tests/RSAOpenSslProvider.cs b/src/libraries/System.Security.Cryptography.OpenSsl/tests/RSAOpenSslProvider.cs
index 8244f389e63cd5..deeecbe7cb18bd 100644
--- a/src/libraries/System.Security.Cryptography.OpenSsl/tests/RSAOpenSslProvider.cs
+++ b/src/libraries/System.Security.Cryptography.OpenSsl/tests/RSAOpenSslProvider.cs
@@ -1,10 +1,14 @@
 // Licensed to the .NET Foundation under one or more agreements.
 // The .NET Foundation licenses this file to you under the MIT license.
 
+using System.Security.Cryptography.Tests;
+
 namespace System.Security.Cryptography.Rsa.Tests
 {
     public class RSAOpenSslProvider : IRSAProvider
     {
+        private bool? _supportsSha1Signatures;
+
         public RSA Create() => new RSAOpenSsl();
 
         public RSA Create(int keySize) => new RSAOpenSsl(keySize);
@@ -16,6 +20,8 @@ public class RSAOpenSslProvider : IRSAProvider
         public bool SupportsSha2Oaep => true;
 
         public bool SupportsPss => true;
+
+        public bool SupportsSha1Signatures => _supportsSha1Signatures ??= SignatureSupport.CanProduceSha1Signature(Create());
     }
 
     public partial class RSAFactory
diff --git a/src/libraries/System.Security.Cryptography.OpenSsl/tests/System.Security.Cryptography.OpenSsl.Tests.csproj b/src/libraries/System.Security.Cryptography.OpenSsl/tests/System.Security.Cryptography.OpenSsl.Tests.csproj
index 676580f1349553..b9ca6fa4508f1a 100644
--- a/src/libraries/System.Security.Cryptography.OpenSsl/tests/System.Security.Cryptography.OpenSsl.Tests.csproj
+++ b/src/libraries/System.Security.Cryptography.OpenSsl/tests/System.Security.Cryptography.OpenSsl.Tests.csproj
@@ -18,6 +18,8 @@
              Link="CommonTest\System\Security\Cryptography\ByteUtils.cs" />
     <Compile Include="$(CommonTestPath)System\Security\Cryptography\PlatformSupport.cs"
              Link="CommonTest\System\Security\Cryptography\PlatformSupport.cs" />
+    <Compile Include="$(CommonTestPath)System\Security\Cryptography\SignatureSupport.cs"
+             Link="CommonTest\System\Security\Cryptography\SignatureSupport.cs" />
     <Compile Include="$(CommonTestPath)System\Security\Cryptography\AlgorithmImplementations\RC2\RC2Factory.cs"
              Link="CommonTest\System\Security\Cryptography\AlgorithmImplementations\RC2\RC2Factory.cs" />
     <Compile Include="$(CommonTestPath)System\Security\Cryptography\AlgorithmImplementations\EC\CurveDef.cs"
diff --git a/src/libraries/System.Security.Cryptography.X509Certificates/tests/CtorTests.cs b/src/libraries/System.Security.Cryptography.X509Certificates/tests/CtorTests.cs
index 4da9a049088b66..254eef6c5b057e 100644
--- a/src/libraries/System.Security.Cryptography.X509Certificates/tests/CtorTests.cs
+++ b/src/libraries/System.Security.Cryptography.X509Certificates/tests/CtorTests.cs
@@ -189,9 +189,9 @@ public static void TestCopyConstructor_Lifetime_Independent()
             using (var c2 = new X509Certificate2(TestData.PfxData, TestData.PfxDataPassword))
             {
                 RSA rsa = c2.GetRSAPrivateKey();
-                byte[] hash = new byte[20];
-                byte[] sig = rsa.SignHash(hash, HashAlgorithmName.SHA1, RSASignaturePadding.Pkcs1);
-                Assert.Equal(TestData.PfxSha1Empty_ExpectedSig, sig);
+                byte[] hash = new byte[SHA256.HashSizeInBytes];
+                byte[] sig = rsa.SignHash(hash, HashAlgorithmName.SHA256, RSASignaturePadding.Pkcs1);
+                Assert.Equal(TestData.PfxSha256Empty_ExpectedSig, sig);
 
                 c1.Dispose();
                 rsa.Dispose();
@@ -202,9 +202,9 @@ public static void TestCopyConstructor_Lifetime_Independent()
                 // Verify other cert and previous key do not affect cert
                 using (rsa = c2.GetRSAPrivateKey())
                 {
-                    hash = new byte[20];
-                    sig = rsa.SignHash(hash, HashAlgorithmName.SHA1, RSASignaturePadding.Pkcs1);
-                    Assert.Equal(TestData.PfxSha1Empty_ExpectedSig, sig);
+                    hash = new byte[SHA256.HashSizeInBytes];
+                    sig = rsa.SignHash(hash, HashAlgorithmName.SHA256, RSASignaturePadding.Pkcs1);
+                    Assert.Equal(TestData.PfxSha256Empty_ExpectedSig, sig);
                 }
             }
         }
@@ -259,9 +259,9 @@ private static void TestPrivateKey(X509Certificate2 c, bool expectSuccess)
             {
                 using (RSA rsa = c.GetRSAPrivateKey())
                 {
-                    byte[] hash = new byte[20];
-                    byte[] sig = rsa.SignHash(hash, HashAlgorithmName.SHA1, RSASignaturePadding.Pkcs1);
-                    Assert.Equal(TestData.PfxSha1Empty_ExpectedSig, sig);
+                    byte[] hash = new byte[SHA256.HashSizeInBytes];
+                    byte[] sig = rsa.SignHash(hash, HashAlgorithmName.SHA256, RSASignaturePadding.Pkcs1);
+                    Assert.Equal(TestData.PfxSha256Empty_ExpectedSig, sig);
                 }
             }
             else
diff --git a/src/libraries/System.Security.Cryptography.X509Certificates/tests/PfxTests.cs b/src/libraries/System.Security.Cryptography.X509Certificates/tests/PfxTests.cs
index 1132d8d85a406b..b7d8b6de5116ac 100644
--- a/src/libraries/System.Security.Cryptography.X509Certificates/tests/PfxTests.cs
+++ b/src/libraries/System.Security.Cryptography.X509Certificates/tests/PfxTests.cs
@@ -134,9 +134,9 @@ public static void TestPrivateKeyProperty()
 
         private static void VerifyPrivateKey(RSA rsa)
         {
-            byte[] hash = new byte[20];
-            byte[] sig = rsa.SignHash(hash, HashAlgorithmName.SHA1, RSASignaturePadding.Pkcs1);
-            Assert.Equal(TestData.PfxSha1Empty_ExpectedSig, sig);
+            byte[] hash = new byte[SHA256.HashSizeInBytes];
+            byte[] sig = rsa.SignHash(hash, HashAlgorithmName.SHA256, RSASignaturePadding.Pkcs1);
+            Assert.Equal(TestData.PfxSha256Empty_ExpectedSig, sig);
         }
 
         [Theory]
diff --git a/src/libraries/System.Security.Cryptography.X509Certificates/tests/TestData.cs b/src/libraries/System.Security.Cryptography.X509Certificates/tests/TestData.cs
index 8673bf5fca616b..a0151384fe999a 100644
--- a/src/libraries/System.Security.Cryptography.X509Certificates/tests/TestData.cs
+++ b/src/libraries/System.Security.Cryptography.X509Certificates/tests/TestData.cs
@@ -173,11 +173,11 @@ public static SecureString CreatePfxDataPasswordSecureString()
             return s;
         }
 
-        public static readonly byte[] PfxSha1Empty_ExpectedSig = (
-            "44b15120b8c7de19b4968d761600ffb8c54e5d0c1bcaba0880a20ab48912c8fd" +
-            "fa81b28134eabf58f3211a0d1eefdaae115e7872d5a67045c3b62a5da4393940" +
-            "e5a496413a6d55ea6309d0013e90657c83c6e40aa8fafeee66acbb6661c14190" +
-            "11e1fde6f4fcc328bd7e537e4aa2dbe216d8f1f3aa7e5ec60eb9cfdca7a41d74").HexToByteArray();
+        public static readonly byte[] PfxSha256Empty_ExpectedSig = (
+            "35306b63fbfe8eaf8e32937432e366d255461b02fb9e77368df319b99a8273cc" +
+            "dad52a21e8ae9c5df97ffa877d6c3ef6eb8a27ac7bbc93efdddd5dda9cf8d30e" +
+            "c52a76c7b2f9e478efe272d6e6f474033fb854e5685c44898367af860d5c893c" +
+            "56f89a69b84cd53434457de3296f80fbbe4eb938b4066b51638e35bce1e1c308").HexToByteArray();
 
         private static readonly byte[] PfxData_RC2ContentEncryption = (
             "3082063A020103308205F606092A864886F70D010701A08205E7048205E33082" +
diff --git a/src/libraries/System.Security.Cryptography/tests/DefaultRSAProvider.cs b/src/libraries/System.Security.Cryptography/tests/DefaultRSAProvider.cs
index 36e3efad794ae6..e39bc782bc04a4 100644
--- a/src/libraries/System.Security.Cryptography/tests/DefaultRSAProvider.cs
+++ b/src/libraries/System.Security.Cryptography/tests/DefaultRSAProvider.cs
@@ -2,12 +2,14 @@
 // The .NET Foundation licenses this file to you under the MIT license.
 
 using System.Runtime.InteropServices;
+using System.Security.Cryptography.Tests;
 
 namespace System.Security.Cryptography.Rsa.Tests
 {
     public class DefaultRSAProvider : IRSAProvider
     {
         private bool? _supports384PrivateKey;
+        private bool? _supportsSha1Signatures;
 
         public RSA Create() => RSA.Create();
 
@@ -38,6 +40,8 @@ public bool Supports384PrivateKey
             }
         }
 
+        public bool SupportsSha1Signatures => _supportsSha1Signatures ??= SignatureSupport.CanProduceSha1Signature(Create());
+
         public bool SupportsLargeExponent => true;
 
         public bool SupportsSha2Oaep { get; } = true;
diff --git a/src/libraries/System.Security.Cryptography/tests/System.Security.Cryptography.Tests.csproj b/src/libraries/System.Security.Cryptography/tests/System.Security.Cryptography.Tests.csproj
index b672db1d9ecd1f..6fa63793c4d82b 100644
--- a/src/libraries/System.Security.Cryptography/tests/System.Security.Cryptography.Tests.csproj
+++ b/src/libraries/System.Security.Cryptography/tests/System.Security.Cryptography.Tests.csproj
@@ -28,6 +28,8 @@
              Link="ProductionCode\Common\System\Net\MultiArrayBuffer.cs" />
     <Compile Include="$(CommonPath)System\Net\StreamBuffer.cs"
              Link="ProductionCode\Common\System\Net\StreamBuffer.cs" />
+    <Compile Include="$(CommonTestPath)System\Security\Cryptography\SignatureSupport.cs"
+             Link="CommonTest\System\Security\Cryptography\SignatureSupport.cs" />
     <Compile Include="$(CommonTestPath)System\Security\Cryptography\AlgorithmImplementations\AES\AesCipherTests.Data.cs"
              Link="CommonTest\System\Security\Cryptography\AlgorithmImplementations\AES\AesCipherTests.Data.cs" />
     <Compile Include="$(CommonTestPath)System\Security\Cryptography\AlgorithmImplementations\AES\AesCipherTests.cs"