diff --git a/FEDERATION.md b/FEDERATION.md
index 75f2bd4..62afea7 100644
--- a/FEDERATION.md
+++ b/FEDERATION.md
@@ -8,6 +8,7 @@ PrivaPub is an ActivityPub server written in C#. This document follows
 - [ActivityPub](https://www.w3.org/TR/activitypub/) (server-to-server)
 - [WebFinger](https://webfinger.net/)
 - [HTTP Signatures](https://datatracker.ietf.org/doc/html/draft-cavage-http-signatures), `rsa-sha256` / `hs2019` with RSA keys
+  (`hs2019` hashed with SHA-256, or SHA-512 as some sign it; a `SHA-256=` or `SHA-512=` digest)
 - [HTTP Message Signatures](https://www.rfc-editor.org/rfc/rfc9421) (RFC 9421) and Content-Digest (RFC 9530), verified on
   deliveries and signed fetches: `rsa-v1_5-sha256` and `rsa-pss-sha512` with RSA keys
 - [NodeInfo](https://nodeinfo.diaspora.software/) 2.0 and 2.1
diff --git a/PrivaPub.Tests/Federation/HttpSignaturesTests.cs b/PrivaPub.Tests/Federation/HttpSignaturesTests.cs
index 55b769d..6579a91 100644
--- a/PrivaPub.Tests/Federation/HttpSignaturesTests.cs
+++ b/PrivaPub.Tests/Federation/HttpSignaturesTests.cs
@@ -101,6 +101,33 @@ namespace PrivaPub.Tests.Federation
 			Assert.Equal("the signature has expired",
 				Check(MastodonRequest(extra: $",expires=\"{Now.AddMinutes(-20).ToUnixTimeSeconds()}\"")));
 
+		// hs2019 leaves the hash to the key: some sign RSA with SHA-512, which rsa-sha256 does not allow; and a SHA-512 digest
+		[Fact]
+		public void Accepts_hs2019_hashed_with_sha512_and_a_sha512_digest()
+		{
+			var context = new DefaultHttpContext();
+			context.Request.Method = "POST";
+			context.Request.Host = new HostString(Host);
+			context.Request.Path = "/peasants/bob/mouth";
+			context.Features.Get<IHttpRequestFeature>().RawTarget = "/peasants/bob/mouth";
+			var date = Now.ToString("r", CultureInfo.InvariantCulture);
+			var digest = "SHA-512=" + Convert.ToBase64String(SHA512.HashData(Body));
+			context.Request.Headers["Date"] = date;
+			context.Request.Headers["Digest"] = digest;
+			var signingString = $"(request-target): post /peasants/bob/mouth\nhost: {Host}\ndate: {date}\ndigest: {digest}";
+			var signature = Convert.ToBase64String(_key.SignData(Encoding.UTF8.GetBytes(signingString), HashAlgorithmName.SHA512, RSASignaturePadding.Pkcs1));
+			string Signed(string algorithm) => $"keyId=\"{KeyId}\",algorithm=\"{algorithm}\",headers=\"(request-target) host date digest\",signature=\"{signature}\"";
+
+			context.Request.Headers["Signature"] = Signed("hs2019");
+			var parameters = HttpSignatures.Parse(context.Request.Headers["Signature"].ToString());
+			Assert.Null(HttpSignatures.CheckRequest(context.Request, parameters, Body, Now));
+			Assert.True(HttpSignatures.Verify(PublicKey, HttpSignatures.SigningString(context.Request, parameters), parameters.Signature, parameters.Algorithm));
+
+			context.Request.Headers["Signature"] = Signed("rsa-sha256");
+			parameters = HttpSignatures.Parse(context.Request.Headers["Signature"].ToString());
+			Assert.False(HttpSignatures.Verify(PublicKey, HttpSignatures.SigningString(context.Request, parameters), parameters.Signature, parameters.Algorithm));
+		}
+
 		[Fact]
 		public void Signs_with_the_raw_request_target()
 		{
diff --git a/PrivaPub/Federation/Signing/HttpSignatures.cs b/PrivaPub/Federation/Signing/HttpSignatures.cs
index 1442f02..95cca1f 100644
--- a/PrivaPub/Federation/Signing/HttpSignatures.cs
+++ b/PrivaPub/Federation/Signing/HttpSignatures.cs
@@ -152,9 +152,11 @@ namespace PrivaPub.Federation.Signing
 			{
 				if (!parameters.Headers.Contains("digest"))
 					return "the digest is not signed";
-				var expectedHash = Convert.ToBase64String(SHA256.HashData(body));
+				var sha256 = Convert.ToBase64String(SHA256.HashData(body));
+				var sha512 = Convert.ToBase64String(SHA512.HashData(body));
 				var matches = request.Headers["Digest"].ToString().Split(',').Select(d => d.Trim())
-					.Any(d => d.StartsWith("SHA-256=", StringComparison.OrdinalIgnoreCase) && d[8..] == expectedHash);
+					.Any(d => d.StartsWith("SHA-256=", StringComparison.OrdinalIgnoreCase) && d[8..] == sha256
+						|| d.StartsWith("SHA-512=", StringComparison.OrdinalIgnoreCase) && d[8..] == sha512);
 				if (!matches)
 					return "the digest does not match the body";
 			}
@@ -213,7 +215,8 @@ namespace PrivaPub.Federation.Signing
 			return string.IsNullOrEmpty(raw) || raw[0] != '/' ? $"{request.PathBase}{request.Path}{request.QueryString}" : raw;
 		}
 
-		public static bool Verify(string publicKeyPem, string signingString, byte[] signature)
+		// hs2019 leaves the hash to the key: RSA with SHA-256, as nearly everyone signs, else with SHA-512, as some do
+		public static bool Verify(string publicKeyPem, string signingString, byte[] signature, string algorithm = "rsa-sha256")
 		{
 			if (string.IsNullOrEmpty(publicKeyPem) || signingString == null)
 				return false;
@@ -221,8 +224,9 @@ namespace PrivaPub.Federation.Signing
 			{
 				using var rsa = RSA.Create();
 				rsa.ImportFromPem(publicKeyPem);
-				return rsa.VerifyData(Encoding.UTF8.GetBytes(signingString), signature,
-					HashAlgorithmName.SHA256, RSASignaturePadding.Pkcs1);
+				var data = Encoding.UTF8.GetBytes(signingString);
+				return rsa.VerifyData(data, signature, HashAlgorithmName.SHA256, RSASignaturePadding.Pkcs1)
+					|| algorithm == "hs2019" && rsa.VerifyData(data, signature, HashAlgorithmName.SHA512, RSASignaturePadding.Pkcs1);
 			}
 			catch (CryptographicException)
 			{
diff --git a/PrivaPub/Federation/Signing/RequestSignature.cs b/PrivaPub/Federation/Signing/RequestSignature.cs
index 6612f31..a072110 100644
--- a/PrivaPub/Federation/Signing/RequestSignature.cs
+++ b/PrivaPub/Federation/Signing/RequestSignature.cs
@@ -40,6 +40,6 @@ namespace PrivaPub.Federation.Signing
 			_message != default ? MessageSignatures.Base(request, _message, baseAddress) : HttpSignatures.SigningString(request, _cavage);
 
 		public bool VerifiedBy(string publicKeyPem, string signed) =>
-			_message != default ? MessageSignatures.Verify(publicKeyPem, _message, signed) : HttpSignatures.Verify(publicKeyPem, signed, _cavage.Signature);
+			_message != default ? MessageSignatures.Verify(publicKeyPem, _message, signed) : HttpSignatures.Verify(publicKeyPem, signed, _cavage.Signature, _cavage.Algorithm);
 	}
 }
diff --git a/docs/ROADMAP.md b/docs/ROADMAP.md
index 37d8752..81f23ad 100644
--- a/docs/ROADMAP.md
+++ b/docs/ROADMAP.md
@@ -692,7 +692,7 @@ it, raw where it doesn't.
     Mitra refuses a proof by a key it has not read and does not read the actor again; a forwarded activity with a
     proof its actor's key verifies is taken without reading it again; Mastodon accepts PrivaPub's, so Activity-Relay's
     forwards reach it);
-  - `hs2019` with SHA-512.
+  - `hs2019` with SHA-512: **done 2026-10-06** (and `SHA-512=` digests).
 - **Discovery:**
   - a relay client for both relay styles: **done 2026-10-05/06** (`Federation:Relays`; forwarded posts read again
     from their origin, announces unwrapped; personas' public posts sent to them, owner decision; checked live against