diff --git a/CHANGELOG.md b/CHANGELOG.md
index 5ce1afa..7f7a5ad 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -1,5 +1,12 @@
 # Changelog
 
+# 2.2.0 (Jul 10, 2026)
+- `generateByTime` and `generateByTimeWindow` now reject a non-positive `$window` (previously an uncaught `DivisionByZeroError`) and a negative `$timestamp` (previously a silent, unintended counter), throwing `InvalidArgumentException` instead.
+- `generateByCounter`, `generateByTime` and `generateByTimeWindow` accept an optional `$algorithm` parameter (defaults to `sha1`), enabling HMAC-SHA-256 and HMAC-SHA-512 TOTP per RFC 6238.
+- Fixed dynamic truncation in `HOTPResult` to derive the RFC 4226 offset from the digest's actual final byte, so wider SHA-256/512 digests truncate correctly (no change for SHA-1).
+- The time-based methods accept an optional `$startTime` parameter (RFC 6238 "T0", defaults to `0`) to set the Unix time from which time steps are counted. A `$startTime` later than `$timestamp` is rejected with `InvalidArgumentException`, as it would yield a negative time step.
+- All new behavior is validated against the RFC 6238 Appendix B SHA-1, SHA-256 and SHA-512 test vectors. These additions are backwards compatible.
+
 # 2.1.0 (Apr 13, 2026)
 - Adopts PSR-12 syntax everywhere (:heart: [jrzepa](https://github.com/jrzepa) [#12](https://github.com/thecodedrift/hotp-php/commit/7578eb618f2bca4f6a7121aaa75ee2b4c6fe6a94))
 - Expands version range for PHPUnit to ensure tests run against PHP 7.2 [#16](https://github.com/jakobo/hotp-php/pull/16)
diff --git a/src/HOTP.php b/src/HOTP.php
index b461c15..a7f9878 100644
--- a/src/HOTP.php
+++ b/src/HOTP.php
@@ -18,10 +18,15 @@ class HOTP
      * Generate a HOTP key based on a counter value (event based HOTP)
      * @param string $key the key to use for hashing
      * @param int $counter the number of attempts represented in this hashing
+     * @param string $algorithm the HMAC hash algorithm to use, defaults to sha1
      * @return HOTPResult a HOTP Result which can be truncated or output
      */
-    public static function generateByCounter(string $key, int $counter): HOTPResult
+    public static function generateByCounter(string $key, int $counter, string $algorithm = 'sha1'): HOTPResult
     {
+        if (!in_array($algorithm, hash_hmac_algos(), true)) {
+            throw new \InvalidArgumentException("Unsupported HMAC algorithm: {$algorithm}");
+        }
+
         // The counter value can be more than one byte long,
         // so we need to pack it down properly.
         $curCounter = [ 0, 0, 0, 0, 0, 0, 0, 0 ];
@@ -34,7 +39,7 @@ public static function generateByCounter(string $key, int $counter): HOTPResult
         $binCounter = str_pad(implode("", $curCounter), 8, chr(0), STR_PAD_LEFT);
 
         // HMAC
-        $hash = hash_hmac('sha1', $binCounter, $key);
+        $hash = hash_hmac($algorithm, $binCounter, $key);
 
         return new HOTPResult($hash);
     }
@@ -44,19 +49,33 @@ public static function generateByCounter(string $key, int $counter): HOTPResult
      * @param string $key the key to use for hashing
      * @param int $window the size of the window a key is valid for in seconds
      * @param int|false $timestamp a timestamp to calculate for, defaults to time()
+     * @param string $algorithm the HMAC hash algorithm to use, defaults to sha1
+     * @param int $startTime the Unix time to start counting time steps from (RFC 6238 "T0"), defaults to 0
      * @return HOTPResult a HOTP Result which can be truncated or output
      */
-    public static function generateByTime(string $key, int $window, int|false $timestamp = false): HOTPResult
+    public static function generateByTime(string $key, int $window, int|false $timestamp = false, string $algorithm = 'sha1', int $startTime = 0): HOTPResult
     {
+        if ($window <= 0) {
+            throw new \InvalidArgumentException('$window must be a positive integer');
+        }
+
         if (!$timestamp && $timestamp !== 0) {
             // @codeCoverageIgnoreStart
             $timestamp = self::getTime();
             // @codeCoverageIgnoreEnd
         }
 
-        $counter = intval($timestamp / $window) ;
+        if ($timestamp < 0) {
+            throw new \InvalidArgumentException('$timestamp must not be negative');
+        }
+
+        if ($timestamp - $startTime < 0) {
+            throw new \InvalidArgumentException('$timestamp must not be earlier than $startTime');
+        }
+
+        $counter = intval(($timestamp - $startTime) / $window) ;
 
-        return self::generateByCounter($key, $counter);
+        return self::generateByCounter($key, $counter, $algorithm);
     }
 
     /**
@@ -68,23 +87,37 @@ public static function generateByTime(string $key, int $window, int|false $times
      * @param int $min the minimum window to accept before $timestamp
      * @param int $max the maximum window to accept after $timestamp
      * @param int|false $timestamp a timestamp to calculate for, defaults to time()
+     * @param string $algorithm the HMAC hash algorithm to use, defaults to sha1
+     * @param int $startTime the Unix time to start counting time steps from (RFC 6238 "T0"), defaults to 0
      * @return HOTPResult[]
      */
-    public static function generateByTimeWindow(string $key, int $window, int $min = -1, int $max = 1, int|false $timestamp = false): array
+    public static function generateByTimeWindow(string $key, int $window, int $min = -1, int $max = 1, int|false $timestamp = false, string $algorithm = 'sha1', int $startTime = 0): array
     {
+        if ($window <= 0) {
+            throw new \InvalidArgumentException('$window must be a positive integer');
+        }
+
         if (!$timestamp && $timestamp !== 0) {
             // @codeCoverageIgnoreStart
             $timestamp = self::getTime();
             // @codeCoverageIgnoreEnd
         }
 
-        $counter = intval($timestamp / $window);
+        if ($timestamp < 0) {
+            throw new \InvalidArgumentException('$timestamp must not be negative');
+        }
+
+        if ($timestamp - $startTime < 0) {
+            throw new \InvalidArgumentException('$timestamp must not be earlier than $startTime');
+        }
+
+        $counter = intval(($timestamp - $startTime) / $window);
         $window = range($min, $max);
 
         $out = [];
         foreach ($window as $value) {
             $shiftCounter = $counter + $value;
-            $out[$shiftCounter] = self::generateByCounter($key, $shiftCounter);
+            $out[$shiftCounter] = self::generateByCounter($key, $shiftCounter, $algorithm);
         }
 
         return $out;
diff --git a/src/HOTPResult.php b/src/HOTPResult.php
index b9e39af..f5d695c 100644
--- a/src/HOTPResult.php
+++ b/src/HOTPResult.php
@@ -54,7 +54,10 @@ public function toDec(): int
                 $hmacResult[] = hexdec($hex);
             }
 
-            $offset = $hmacResult[19] & 0xf;
+            // RFC 4226 dynamic truncation uses the low nibble of the digest's
+            // final byte as the offset. SHA-1 digests are 20 bytes (index 19),
+            // but wider digests (SHA-256/512) place that byte at a higher index.
+            $offset = $hmacResult[array_key_last($hmacResult)] & 0xf;
 
             $this->decimal = (
                 (($hmacResult[$offset + 0] & 0x7f) << 24) |
diff --git a/tests/HOTPTest.php b/tests/HOTPTest.php
index 8016171..ab51340 100644
--- a/tests/HOTPTest.php
+++ b/tests/HOTPTest.php
@@ -150,6 +150,75 @@ public function testTOTP(string $seed, string $result): void
         );
     }
 
+    public function provideTOTPAlgorithms(): array
+    {
+        // Expected TOTP values from RFC 6238 Appendix B; the per-algorithm keys
+        // (20/32/64-byte ASCII seeds) come from the Appendix A reference code.
+        return [
+            // [algorithm, key, timestamp, expected 8-digit TOTP]
+            ['sha1', '12345678901234567890', '59', '94287082'],
+            ['sha1', '12345678901234567890', '1234567890', '89005924'],
+            ['sha256', '12345678901234567890123456789012', '59', '46119246'],
+            ['sha256', '12345678901234567890123456789012', '1234567890', '91819424'],
+            ['sha512', '1234567890123456789012345678901234567890123456789012345678901234', '59', '90693936'],
+            ['sha512', '1234567890123456789012345678901234567890123456789012345678901234', '1234567890', '93441116'],
+        ];
+    }
+
+    /** @dataProvider provideTOTPAlgorithms */
+    public function testTOTPWithAlgorithm(string $algorithm, string $key, string $seed, string $result): void
+    {
+        $totp = HOTP::generateByTime($key, 30, $seed, $algorithm);
+
+        $this->assertEquals(
+            $result,
+            $totp->toHOTP(8)
+        );
+    }
+
+    public function testGenerateByCounterRejectsUnsupportedAlgorithm(): void
+    {
+        $this->expectException(\InvalidArgumentException::class);
+        HOTP::generateByCounter(self::KEY, 0, 'not-a-real-algo');
+    }
+
+    public function testGenerateByTimeHonorsStartTime(): void
+    {
+        // With a start time of 29 and timestamp of 88, the effective time step
+        // is (88 - 29) / 30 = counter 1, matching the RFC 6238 T=59 vector.
+        $withStartTime = HOTP::generateByTime(self::KEY, 30, 88, 'sha1', 29);
+        $baseline = HOTP::generateByTime(self::KEY, 30, 59, 'sha1', 0);
+
+        $this->assertEquals('94287082', $withStartTime->toHOTP(8));
+        $this->assertEquals($baseline->toHOTP(8), $withStartTime->toHOTP(8));
+    }
+
+    public function testGenerateByTimeRejectsStartTimeLaterThanTimestamp(): void
+    {
+        // A start time after $timestamp would yield a negative effective step.
+        $this->expectException(\InvalidArgumentException::class);
+        HOTP::generateByTime(self::KEY, 30, 30, 'sha1', 60);
+    }
+
+    public function testGenerateByTimeWindowRejectsStartTimeLaterThanTimestamp(): void
+    {
+        $this->expectException(\InvalidArgumentException::class);
+        HOTP::generateByTimeWindow(self::KEY, 30, -1, 1, 30, 'sha1', 60);
+    }
+
+    public function testGenerateByTimeWindowHonorsStartTime(): void
+    {
+        $withStartTime = HOTP::generateByTimeWindow(self::KEY, 30, -1, 1, 88, 'sha1', 29);
+        $baseline = HOTP::generateByTimeWindow(self::KEY, 30, -1, 1, 59, 'sha1', 0);
+
+        $reduce = static fn (array $results): array => array_map(
+            static fn ($r) => $r->toHOTP(6),
+            array_values($results)
+        );
+
+        $this->assertEquals($reduce($baseline), $reduce($withStartTime));
+    }
+
     public function provideGenerateByTimeWindow(): array
     {
         return [
@@ -168,6 +237,29 @@ public function provideGenerateByTimeWindow(): array
         ];
     }
 
+    public function provideInvalidTimeArguments(): array
+    {
+        return [
+            'zero window'         => [0, 59],
+            'negative window'     => [-30, 59],
+            'negative timestamp'  => [30, -59],
+        ];
+    }
+
+    /** @dataProvider provideInvalidTimeArguments */
+    public function testGenerateByTimeRejectsInvalidArguments(int $window, int $timestamp): void
+    {
+        $this->expectException(\InvalidArgumentException::class);
+        HOTP::generateByTime(self::KEY, $window, $timestamp);
+    }
+
+    /** @dataProvider provideInvalidTimeArguments */
+    public function testGenerateByTimeWindowRejectsInvalidArguments(int $window, int $timestamp): void
+    {
+        $this->expectException(\InvalidArgumentException::class);
+        HOTP::generateByTimeWindow(self::KEY, $window, -1, 1, $timestamp);
+    }
+
     /** @dataProvider provideGenerateByTimeWindow */
     public function testGenerateByTimeWindow(string $seed, array $result): void
     {