diff --git a/src/client.ts b/src/client.ts
index 32874e2e1..b89594ab5 100644
--- a/src/client.ts
+++ b/src/client.ts
@@ -47,7 +47,7 @@ import {
     PREFIX_UNSTABLE,
     retryNetworkOperation,
 } from "./http-api";
-import { Crypto, fixBackupKey, IBootstrapCrossSigningOpts, isCryptoAvailable } from './crypto';
+import { Crypto, fixBackupKey, IBootstrapCrossSigningOpts, IMegolmSessionData, isCryptoAvailable } from './crypto';
 import { DeviceInfo, IDevice } from "./crypto/deviceinfo";
 import { decodeRecoveryKey } from './crypto/recoverykey';
 import { keyFromAuthData } from './crypto/key_passphrase';
@@ -2096,7 +2096,7 @@ export class MatrixClient extends EventEmitter {
      * @return {Promise} a promise which resolves when the keys
      *    have been imported
      */
-    public importRoomKeys(keys: any[], opts: IImportRoomKeysOpts): Promise<void> {
+    public importRoomKeys(keys: IMegolmSessionData[], opts: IImportRoomKeysOpts): Promise<void> {
         if (!this.crypto) {
             throw new Error("End-to-end encryption disabled");
         }
diff --git a/src/crypto/algorithms/base.js b/src/crypto/algorithms/base.ts
similarity index 63%
rename from src/crypto/algorithms/base.js
rename to src/crypto/algorithms/base.ts
index 87b8a82c0..256a499de 100644
--- a/src/crypto/algorithms/base.js
+++ b/src/crypto/algorithms/base.ts
@@ -1,5 +1,5 @@
 /*
-Copyright 2016 OpenMarket Ltd
+Copyright 2016 - 2021 The Matrix.org Foundation C.I.C.
 
 Licensed under the Apache License, Version 2.0 (the "License");
 you may not use this file except in compliance with the License.
@@ -20,13 +20,20 @@ limitations under the License.
  * @module
  */
 
+import { MatrixClient } from "../../client";
+import { Room } from "../../models/room";
+import { OlmDevice } from "../OlmDevice";
+import { MatrixEvent, RoomMember } from "../..";
+import { IEventDecryptionResult, IMegolmSessionData, IncomingRoomKeyRequest } from "..";
+import { DeviceInfo } from "../deviceinfo";
+
 /**
  * map of registered encryption algorithm classes. A map from string to {@link
  * module:crypto/algorithms/base.EncryptionAlgorithm|EncryptionAlgorithm} class
  *
  * @type {Object.<string, function(new: module:crypto/algorithms/base.EncryptionAlgorithm)>}
  */
-export const ENCRYPTION_CLASSES = {};
+export const ENCRYPTION_CLASSES: Record<string, EncryptionAlgorithm> = {};
 
 /**
  * map of registered encryption algorithm classes. Map from string to {@link
@@ -34,7 +41,16 @@ export const ENCRYPTION_CLASSES = {};
  *
  * @type {Object.<string, function(new: module:crypto/algorithms/base.DecryptionAlgorithm)>}
  */
-export const DECRYPTION_CLASSES = {};
+export const DECRYPTION_CLASSES: Record<string, DecryptionAlgorithm> = {};
+
+interface IParams {
+    userId: string;
+    deviceId: string;
+    crypto: Crypto;
+    olmDevice: OlmDevice;
+    baseApis: MatrixClient;
+    roomId: string;
+}
 
 /**
  * base type for encryption implementations
@@ -50,14 +66,21 @@ export const DECRYPTION_CLASSES = {};
  * @param {string} params.roomId  The ID of the room we will be sending to
  * @param {object} params.config  The body of the m.room.encryption event
  */
-export class EncryptionAlgorithm {
-    constructor(params) {
-        this._userId = params.userId;
-        this._deviceId = params.deviceId;
-        this._crypto = params.crypto;
-        this._olmDevice = params.olmDevice;
-        this._baseApis = params.baseApis;
-        this._roomId = params.roomId;
+export abstract class EncryptionAlgorithm {
+    protected readonly userId: string;
+    protected readonly deviceId: string;
+    protected readonly crypto: Crypto;
+    protected readonly olmDevice: OlmDevice;
+    protected readonly baseApis: MatrixClient;
+    protected readonly roomId: string;
+
+    constructor(params: IParams) {
+        this.userId = params.userId;
+        this.deviceId = params.deviceId;
+        this.crypto = params.crypto;
+        this.olmDevice = params.olmDevice;
+        this.baseApis = params.baseApis;
+        this.roomId = params.roomId;
     }
 
     /**
@@ -66,21 +89,22 @@ export class EncryptionAlgorithm {
      *
      * @param {module:models/room} room the room the event is in
      */
-    prepareToEncrypt(room) {
-    }
+    public abstract prepareToEncrypt(room: Room): void;
 
     /**
      * Encrypt a message event
      *
      * @method module:crypto/algorithms/base.EncryptionAlgorithm.encryptMessage
+     * @public
      * @abstract
      *
      * @param {module:models/room} room
      * @param {string} eventType
-     * @param {object} plaintext event content
+     * @param {object} content event content
      *
      * @return {Promise} Promise which resolves to the new event body
      */
+    public abstract encryptMessage(room: Room, eventType: string, content: object): Promise<object>;
 
     /**
      * Called when the membership of a member of the room changes.
@@ -89,9 +113,18 @@ export class EncryptionAlgorithm {
      * @param {module:models/room-member} member  user whose membership changed
      * @param {string=} oldMembership  previous membership
      * @public
+     * @abstract
      */
-     onRoomMembership(event, member, oldMembership) {
-     }
+    public abstract onRoomMembership(event: MatrixEvent, member: RoomMember, oldMembership?: string);
+
+    public abstract reshareKeyWithDevice(
+        senderKey: string,
+        sessionId: string,
+        userId: string,
+        device: DeviceInfo,
+    ): Promise<void>;
+
+    public forceDiscardSession?: () => void;
 }
 
 /**
@@ -106,13 +139,19 @@ export class EncryptionAlgorithm {
  * @param {string=} params.roomId The ID of the room we will be receiving
  *     from. Null for to-device events.
  */
-export class DecryptionAlgorithm {
-    constructor(params) {
-        this._userId = params.userId;
-        this._crypto = params.crypto;
-        this._olmDevice = params.olmDevice;
-        this._baseApis = params.baseApis;
-        this._roomId = params.roomId;
+export abstract class DecryptionAlgorithm {
+    private readonly userId: string;
+    private readonly crypto: Crypto;
+    private readonly olmDevice: OlmDevice;
+    private readonly baseApis: MatrixClient;
+    private readonly roomId: string;
+
+    constructor(params: Omit<IParams, "deviceId">) {
+        this.userId = params.userId;
+        this.crypto = params.crypto;
+        this.olmDevice = params.olmDevice;
+        this.baseApis = params.baseApis;
+        this.roomId = params.roomId;
     }
 
     /**
@@ -127,6 +166,7 @@ export class DecryptionAlgorithm {
      * resolves once we have finished decrypting. Rejects with an
      * `algorithms.DecryptionError` if there is a problem decrypting the event.
      */
+    public abstract decryptEvent(event: MatrixEvent): Promise<IEventDecryptionResult>;
 
     /**
      * Handle a key event
@@ -135,7 +175,7 @@ export class DecryptionAlgorithm {
      *
      * @param {module:models/event.MatrixEvent} params event key event
      */
-    onRoomKeyEvent(params) {
+    public onRoomKeyEvent(params: MatrixEvent): void {
         // ignore by default
     }
 
@@ -143,8 +183,9 @@ export class DecryptionAlgorithm {
      * Import a room key
      *
      * @param {module:crypto/OlmDevice.MegolmSessionData} session
+     * @param {object} opts object
      */
-    importRoomKey(session) {
+    public async importRoomKey(session: IMegolmSessionData, opts: object): Promise<void> {
         // ignore by default
     }
 
@@ -155,7 +196,7 @@ export class DecryptionAlgorithm {
      * @return {Promise<boolean>} true if we have the keys and could (theoretically) share
      *  them; else false.
      */
-    hasKeysForKeyRequest(keyRequest) {
+    public hasKeysForKeyRequest(keyRequest: IncomingRoomKeyRequest): Promise<boolean> {
         return Promise.resolve(false);
     }
 
@@ -164,7 +205,7 @@ export class DecryptionAlgorithm {
      *
      * @param {module:crypto~IncomingRoomKeyRequest} keyRequest
      */
-    shareKeysWithDevice(keyRequest) {
+    public shareKeysWithDevice(keyRequest: IncomingRoomKeyRequest) {
         throw new Error("shareKeysWithDevice not supported for this DecryptionAlgorithm");
     }
 
@@ -174,9 +215,12 @@ export class DecryptionAlgorithm {
      *
      * @param {string} senderKey the sender's key
      */
-    async retryDecryptionFromSender(senderKey) {
+    public async retryDecryptionFromSender(senderKey: string): Promise<void> {
         // ignore by default
     }
+
+    public onRoomKeyWithheldEvent?: (event: MatrixEvent) => Promise<void>;
+    public sendSharedHistoryInboundSessions?: (devicesByUser: Record<string, DeviceInfo[]>) => Promise<void>;
 }
 
 /**
@@ -191,22 +235,21 @@ export class DecryptionAlgorithm {
  * @extends Error
  */
 export class DecryptionError extends Error {
-    constructor(code, msg, details) {
+    public readonly detailedString: string;
+
+    constructor(public readonly code: string, msg: string, details: Record<string, string>) {
         super(msg);
         this.code = code;
         this.name = 'DecryptionError';
-        this.detailedString = _detailedStringForDecryptionError(this, details);
+        this.detailedString = detailedStringForDecryptionError(this, details);
     }
 }
 
-function _detailedStringForDecryptionError(err, details) {
+function detailedStringForDecryptionError(err: DecryptionError, details: Record<string, string>): string {
     let result = err.name + '[msg: ' + err.message;
 
     if (details) {
-        result += ', ' +
-            Object.keys(details).map(
-                (k) => k + ': ' + details[k],
-            ).join(', ');
+        result += ', ' + Object.keys(details).map((k) => k + ': ' + details[k]).join(', ');
     }
 
     result += ']';
@@ -224,7 +267,7 @@ function _detailedStringForDecryptionError(err, details) {
  * @extends Error
  */
 export class UnknownDeviceError extends Error {
-    constructor(msg, devices) {
+    constructor(msg: string, public readonly devices: Record<string, Record<string, object>>) {
         super(msg);
         this.name = "UnknownDeviceError";
         this.devices = devices;
@@ -244,7 +287,11 @@ export class UnknownDeviceError extends Error {
  *     module:crypto/algorithms/base.DecryptionAlgorithm|DecryptionAlgorithm}
  *     implementation
  */
-export function registerAlgorithm(algorithm, encryptor, decryptor) {
+export function registerAlgorithm(
+    algorithm: string,
+    encryptor: EncryptionAlgorithm,
+    decryptor: DecryptionAlgorithm,
+): void {
     ENCRYPTION_CLASSES[algorithm] = encryptor;
     DECRYPTION_CLASSES[algorithm] = decryptor;
 }
diff --git a/src/crypto/index.ts b/src/crypto/index.ts
index 9d60276e3..132821219 100644
--- a/src/crypto/index.ts
+++ b/src/crypto/index.ts
@@ -117,13 +117,14 @@ export interface IRoomKeyRequestBody extends IRoomKey {
     sender_key: string
 }
 
-interface IMegolmSessionData {
+export interface IMegolmSessionData {
     sender_key: string;
     forwarding_curve25519_key_chain: string[];
     sender_claimed_keys: Record<string, string>;
     room_id: string;
     session_id: string;
     session_key: string;
+    algorithm: string;
 }
 /* eslint-enable camelcase */
 
@@ -168,7 +169,7 @@ interface ISignableObject {
     unsigned?: object
 }
 
-interface IEventDecryptionResult {
+export interface IEventDecryptionResult {
     clearEvent: object;
     senderCurve25519Key?: string;
     claimedEd25519Key?: string;
@@ -193,7 +194,7 @@ export class Crypto extends EventEmitter {
 
     private readonly reEmitter: ReEmitter;
     private readonly verificationMethods: any; // TODO types
-    private readonly supportedAlgorithms: DecryptionAlgorithm[];
+    private readonly supportedAlgorithms: string[];
     private readonly outgoingRoomKeyRequestManager: OutgoingRoomKeyRequestManager;
     private readonly toDeviceVerificationRequests: ToDeviceRequests;
     private readonly inRoomVerificationRequests: InRoomRequests;
@@ -2630,7 +2631,7 @@ export class Crypto extends EventEmitter {
      * @param {Function} opts.progressCallback called with an object which has a stage param
      * @return {Promise} a promise which resolves once the keys have been imported
      */
-    public importRoomKeys(keys: IRoomKey[], opts: any = {}): Promise<any> { // TODO types
+    public importRoomKeys(keys: IMegolmSessionData[], opts: any = {}): Promise<any> { // TODO types
         let successes = 0;
         let failures = 0;
         const total = keys.length;
@@ -3430,9 +3431,7 @@ export class Crypto extends EventEmitter {
             }
 
             try {
-                await encryptor.reshareKeyWithDevice(
-                    body.sender_key, body.session_id, userId, device,
-                );
+                await encryptor.reshareKeyWithDevice(body.sender_key, body.session_id, userId, device);
             } catch (e) {
                 logger.warn(
                     "Failed to re-share keys for session " + body.session_id +
@@ -3643,7 +3642,7 @@ export function fixBackupKey(key: string): string | null {
  *    the relevant crypto algorithm implementation to share the keys for
  *    this request.
  */
-class IncomingRoomKeyRequest {
+export class IncomingRoomKeyRequest {
     public readonly userId: string;
     public readonly deviceId: string;
     public readonly requestId: string;