diff --git a/package.json b/package.json
index 25b0f9353..fbef0c861 100644
--- a/package.json
+++ b/package.json
@@ -78,7 +78,7 @@
     "@babel/preset-env": "^7.12.11",
     "@babel/preset-typescript": "^7.12.7",
     "@babel/register": "^7.12.10",
-    "@matrix-org/olm": "https://gitlab.matrix.org/api/v4/projects/27/packages/npm/@matrix-org/olm/-/@matrix-org/olm-3.2.8.tgz",
+    "@matrix-org/olm": "https://gitlab.matrix.org/api/v4/projects/27/packages/npm/@matrix-org/olm/-/@matrix-org/olm-3.2.12.tgz",
     "@types/bs58": "^4.0.1",
     "@types/content-type": "^1.1.5",
     "@types/jest": "^28.0.0",
diff --git a/spec/unit/crypto/verification/sas.spec.js b/spec/unit/crypto/verification/sas.spec.js
index 0a57e55a3..7344c0379 100644
--- a/spec/unit/crypto/verification/sas.spec.js
+++ b/spec/unit/crypto/verification/sas.spec.js
@@ -218,7 +218,7 @@ describe("SAS verification", function() {
             ]);
 
             // make sure that it uses the preferred method
-            expect(macMethod).toBe("hkdf-hmac-sha256");
+            expect(macMethod).toBe("org.matrix.msc3783.hkdf-hmac-sha256");
             expect(keyAgreement).toBe("curve25519-hkdf-sha256");
 
             // make sure Alice and Bob verified each other
@@ -230,6 +230,62 @@ describe("SAS verification", function() {
             expect(aliceDevice.isVerified()).toBeTruthy();
         });
 
+        it("should be able to verify using the old base64", async () => {
+            // pretend that Alice can only understand the old (incorrect) base64
+            // encoding, and make sure that she can still verify with Bob
+            let macMethod;
+            const aliceOrigSendToDevice = alice.client.sendToDevice.bind(alice.client);
+            alice.client.sendToDevice = (type, map) => {
+                if (type === "m.key.verification.start") {
+                    // Note: this modifies not only the message that Bob
+                    // receives, but also the copy of the message that Alice
+                    // has, since it is the same object.  If this does not
+                    // happen, the verification will fail due to a hash
+                    // commitment mismatch.
+                    map[bob.client.getUserId()][bob.client.deviceId]
+                        .message_authentication_codes = ['hkdf-hmac-sha256'];
+                }
+                return aliceOrigSendToDevice(type, map);
+            };
+            const bobOrigSendToDevice = bob.client.sendToDevice.bind(bob.client);
+            bob.client.sendToDevice = (type, map) => {
+                if (type === "m.key.verification.accept") {
+                    macMethod = map[alice.client.getUserId()][alice.client.deviceId]
+                        .message_authentication_code;
+                }
+                return bobOrigSendToDevice(type, map);
+            };
+
+            alice.httpBackend.when('POST', '/keys/query').respond(200, {
+                failures: {},
+                device_keys: {
+                    "@bob:example.com": BOB_DEVICES,
+                },
+            });
+            bob.httpBackend.when('POST', '/keys/query').respond(200, {
+                failures: {},
+                device_keys: {
+                    "@alice:example.com": ALICE_DEVICES,
+                },
+            });
+
+            await Promise.all([
+                aliceVerifier.verify(),
+                bobPromise.then((verifier) => verifier.verify()),
+                alice.httpBackend.flush(),
+                bob.httpBackend.flush(),
+            ]);
+
+            expect(macMethod).toBe("hkdf-hmac-sha256");
+
+            const bobDevice
+                  = await alice.client.getStoredDevice("@bob:example.com", "Dynabook");
+            expect(bobDevice.isVerified()).toBeTruthy();
+            const aliceDevice
+                  = await bob.client.getStoredDevice("@alice:example.com", "Osborne2");
+            expect(aliceDevice.isVerified()).toBeTruthy();
+        });
+
         it("should be able to verify using the old MAC", async () => {
             // pretend that Alice can only understand the old (incorrect) MAC,
             // and make sure that she can still verify with Bob
diff --git a/src/crypto/verification/SAS.ts b/src/crypto/verification/SAS.ts
index a909ce742..9e68e70ca 100644
--- a/src/crypto/verification/SAS.ts
+++ b/src/crypto/verification/SAS.ts
@@ -180,6 +180,7 @@ function generateSas(sasBytes: number[], methods: string[]): IGeneratedSas {
 
 const macMethods = {
     "hkdf-hmac-sha256": "calculate_mac",
+    "org.matrix.msc3783.hkdf-hmac-sha256": "calculate_mac_fixed_base64",
     "hmac-sha256": "calculate_mac_long_kdf",
 };
 
@@ -221,7 +222,7 @@ const calculateKeyAgreement = {
  */
 const KEY_AGREEMENT_LIST = ["curve25519-hkdf-sha256", "curve25519"];
 const HASHES_LIST = ["sha256"];
-const MAC_LIST = ["hkdf-hmac-sha256", "hmac-sha256"];
+const MAC_LIST = ["org.matrix.msc3783.hkdf-hmac-sha256", "hkdf-hmac-sha256", "hmac-sha256"];
 const SAS_LIST = Object.keys(sasGenerators);
 
 const KEY_AGREEMENT_SET = new Set(KEY_AGREEMENT_LIST);
diff --git a/yarn.lock b/yarn.lock
index 44451b0e6..286ec2699 100644
--- a/yarn.lock
+++ b/yarn.lock
@@ -1307,10 +1307,9 @@
     "@jridgewell/resolve-uri" "^3.0.3"
     "@jridgewell/sourcemap-codec" "^1.4.10"
 
-"@matrix-org/olm@https://gitlab.matrix.org/api/v4/projects/27/packages/npm/@matrix-org/olm/-/@matrix-org/olm-3.2.8.tgz":
-  version "3.2.8"
-  uid "8d53636d045e1776e2a2ec6613e57330dd9ce856"
-  resolved "https://gitlab.matrix.org/api/v4/projects/27/packages/npm/@matrix-org/olm/-/@matrix-org/olm-3.2.8.tgz#8d53636d045e1776e2a2ec6613e57330dd9ce856"
+"@matrix-org/olm@https://gitlab.matrix.org/api/v4/projects/27/packages/npm/@matrix-org/olm/-/@matrix-org/olm-3.2.12.tgz":
+  version "3.2.12"
+  resolved "https://gitlab.matrix.org/api/v4/projects/27/packages/npm/@matrix-org/olm/-/@matrix-org/olm-3.2.12.tgz#0bce3c86f9d36a4984d3c3e07df1c3fb4c679bd9"
 
 "@nicolo-ribaudo/chokidar-2@2.1.8-no-fsevents.3":
   version "2.1.8-no-fsevents.3"