TOTP: Time-based One-time Password Algorithm
draft-mraihi-totp-timebased-04.txt

Abstract

This document describes an extension of one-time password algorithm HOTP as defined in [RFC4226] (M'Raihi, D., Bellare, M., Hoornaert, F., Naccache, D., and O. Ranen, “HOTP: An HMAC-Based One-Time Password Algorithm,” December 2005.) to support time based moving factor.

Status of this Memo

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Table of Contents

1.  Introduction
    1.1.  Scope
    1.2.  Background
2.  Notation and Terminology
3.  Algorithm Requirements
4.  TOTP Algorithm
    4.1.  Notations
    4.2.  Description
5.  Security Considerations
    5.1.  General
    5.2.  Validation and Time-step Size
6.  Resynchronization
7.  IANA Considerations
8.  Acknowledgements
9.  References
    9.1.  Normative references
    9.2.  Informative References
Appendix A.  TOTP Algorithm: Reference Implementation
Appendix B.  Test Vectors
§  Authors' Addresses

1.  Introduction

1.1.  Scope

This document describes an extension of one-time password algorithm HOTP as defined in [RFC4226] (M'Raihi, D., Bellare, M., Hoornaert, F., Naccache, D., and O. Ranen, “HOTP: An HMAC-Based One-Time Password Algorithm,” December 2005.) to support time based moving factor.

1.2.  Background

As defined in [RFC4226] (M'Raihi, D., Bellare, M., Hoornaert, F., Naccache, D., and O. Ranen, “HOTP: An HMAC-Based One-Time Password Algorithm,” December 2005.) the HOTP algorithm is based on the HMAC-SHA-1 algorithm, as specified in [RFC2104] (Krawczyk, H., Bellare, M., and R. Canetti, “HMAC: Keyed-Hashing for Message Authentication,” February 1997.) applied to an increasing counter value representing the message in the HMAC computation.

Basically, the output of the HMAC-SHA-1 calculation is truncated to obtain user-friendly values:

HOTP(K,C) = Truncate(HMAC-SHA-1(K,C))

where Truncate represents the function that can convert an HMAC-SHA-1 value into an HOTP value.

TOTP is the time-based variant of this algorithm where a value T derived from a time reference and a time step replaces the counter C in the HOTP computation.

The default HMAC-SHA-1 function could be replaced by HMAC-SHA-256 or HMAC-SHA-512 to leverage HMAC implementations based on SHA-256 or SHA-512 hash functions.

2.  Notation and Terminology

The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT", "SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this document are to be interpreted as described in [RFC2119] (, “Key words for use in RFCs to Indicate Requirement Levels,” March 1997.)

3.  Algorithm Requirements

This section summarizes the requirements taken into account for designing the TOTP algorithm.

R1 - The prover (e.g. token, soft token) and verifier (authentication or validation server) MUST have access to the Unix Time

R2 - The prover and verifier MUST either share a same secret or the knowledge of a secret transformation to generate a shared secret

R3 - The algorithm MUST use HOTP [RFC4226] as a key building block.

R4 - The prover and verifier MUST use the same time step value X.

R5 - There MUST be a unique secret (key) for each prover.

R6 - The keys SHOULD be randomly generated or derived using a key derivation algorithms.

R7 - The keys MAY be stored in a tamper-resistant device and SHOULD be protected against unauthorized access and usage.

R8 - The TOTP algorithm SHOULD be used for online application.

4.  TOTP Algorithm

This variant of the HOTP algorithm specifies the calculation of a one-time password value, based on a representation of the counter as a time factor.

4.1.  Notations

- X represents the time step in seconds (default value X = 30 seconds) and is a system parameter;

- T0 is the Unix time to start counting time steps (default value is 0, Unix epoch) and is also a system parameter.

4.2.  Description

Basically, we define TOTP as TOTP = HOTP(K, T) where T is an integer and represents the number of time steps between the initial counter time T0 and the current Unix time (i.e. the number of seconds elapsed since midnight UTC of January 1, 1970).

More specifically T = (Current Unix time - T0) / X where:

- X represents the time step in seconds (default value X = 30 seconds) and is a system parameter;

- T0 is the Unix time to start counting time steps (default value is 0, Unix epoch) and is also a system parameter.

5.  Security Considerations

5.1.  General

The security and strength of this algorithm depends on the properties of the underlying building block HOTP, which is a construction based on HMAC [RFC2104] (Krawczyk, H., Bellare, M., and R. Canetti, “HMAC: Keyed-Hashing for Message Authentication,” February 1997.) using SHA-1 as the hash function.

The conclusion of the security analysis detailed in [RFC4226] (M'Raihi, D., Bellare, M., Hoornaert, F., Naccache, D., and O. Ranen, “HOTP: An HMAC-Based One-Time Password Algorithm,” December 2005.) is that, for all practical purposes, the outputs of the dynamic truncation on distinct inputs are uniformly and independently distributed strings.

The analysis demonstrates that the best possible attack against the HOTP function is the brute force attack.

As indicated in the algorithm requirement section, keys SHOULD be chosen at random or using a cryptographically strong pseudo-random generator properly seeded with a random value.

Keys SHOULD be of the length of the HMAC output to facilitate interoperability.

We RECOMMEND following the recommendations in [RFC1750] (Eastlake, D., Crocker, S., and J. Schiller, “Randomness Recommendations for Security,” December 1994.) for all pseudo-random and random generations. The pseudo-random numbers used for generating the keys SHOULD successfully pass the randomness test specified in [CN] (Coron, J. and D. Naccache, “An accurate evaluation of Maurer's universal test,” February 1999.) or a similar well-recognized test.

All the communications SHOULD take place over a secure channel e.g. SSL/TLS, IPsec connections.

We also RECOMMEND storing the keys securely in the validation system, and more specifically encrypting them using tamper-resistant hardware encryption and exposing them only when required: for example, the key is decrypted when needed to verify an OTP value, and re-encrypted immediately to limit exposure in the RAM for a short period of time.

The key store MUST be in a secure area, to avoid as much as possible direct attack on the validation system and secrets database. Particularly, access to the key material should be limited to programs and processes required by the validation system only.

5.2.  Validation and Time-step Size

An OTP generated within the same Time-step will be the same. When an OTP is received at a validation system, it doesn't know a client's exact timestamp when an OTP was generated. The validation system may typically use the timestamp when an OTP is received for OTP comparison. Due to the network latency for an OTP to transmit from a requesting application to a validation system and user's actual input time of an OTP to a receiving system, such timestamp gap between the actual OTP generation time and server's receiving time may be large. The receiving time at the validation system and the actual OTP generation may not fall within the same Time-step window that produce the same OTP. When an OTP is generated at the end of a Time-step window, the receiving time most likely falls into the next Time-step window. A validation system SHOULD typically set a policy for an acceptable OTP transmission delay window for validation. The validation system should compare OTPs not only with the receiving timestamp but also the past timesteps that are within the transmission delay. A larger acceptable delay window would introduce some OTP attack window. We RECOMMEND that at most one time step is allowed as the network delay.

The Time-step size has impact on both security and usability. A larger Time-step size means larger validity window for an OTP to be accepted by a validation system. There are the following implications with a larger Time-step size.

At first, a larger Time-step size exposes larger window for attack. When an OTP is generated and exposed to a third party before it is consumed, the third party can consume the OTP within the Time-step window.

We RECOMMEND default Time-step size for 30 seconds.

Secondly, the next different OTP must be generated in the next Time-step window. A user must wait till the clock moves to the next Time-step window from the last submission. The waiting time may not be exactly the length of Time-step depending on when the last OTP was generated. For example, if the last OTP was generated at the half way in a Time-step window, the waiting time for the next OTP is half of length of Time-step. In general, a larger Time-step window means larger waiting time for a user to get the next valid OTP after the last successfully OTP validation. A too large window, for example 10 minutes, most probably won't be suitable for typical internet login use cases; a user may not be able to get the next OTP within 10 minutes and therefore re-login back to the same site in 10 minutes. The default Time-step size 30 seconds is recommended.

6.  Resynchronization

Because of possible clock drifts between a client and a validation server, we RECOMMEND that the validator be set with a specific limit to the number of time steps a prover can be 'out of synch' before being not validated/rejected.

This limit can be set both forward and backwards from the calculated time step on receipt of the OTP value. If the time step is 30 seconds as recommended, and the validator is set to only accept 2 time step backwards then the maximum elapsed time drift would be around 89 seconds, i.e. 29 seconds in the calculated time step and 60 for two backward time steps.

This would mean the validator could perform a validation against the current time and then further two validations for each backward step (for a total of 3 validations). Upon successful validation, the validation server can record the detected clock drift for the token in terms of number of Time-step. When a new OTP is received after this step, the validator can validate the OTP with current timestamp adjusted with recorded number of Time-step clock drifts for the token.

Also, it is important to note that the longer a prover has not sent an OTP to a validation system, the longer (potentially) the accumulated clock drift between the prover and the verifier. In such cases, the default synchronization may not be proper when the drift exceeds beyond allowed threshold. Additional authentication measures SHOULD be used for the validation system to safely authenticate the prover.

7.  IANA Considerations

The OTP algorithm defined in this document can be referred by a URI defined in a separate document. There is no registration needed in this document.

8.  Acknowledgements

The authors of this draft would like to thank the following people for their contributions and support to make this a better specification: Jonathan Tuliani, David Dix, Siddharth Bajaj, Stu Veath, Shuh Chang, Oanh Hoang, John Huang, and Siddhartha Mohapatra.

9.  References

9.1. Normative references

9.2. Informative References

Appendix A.  TOTP Algorithm: Reference Implementation

import java.lang.reflect.UndeclaredThrowableException;
import java.security.GeneralSecurityException;
import java.text.DateFormat;
import java.text.SimpleDateFormat;
import java.util.Calendar;
import java.util.Date;
import javax.crypto.Mac;
import javax.crypto.spec.SecretKeySpec;
import java.math.BigInteger;
import java.util.TimeZone;

/**
 * This an example implementation of the OATH TOTP algorithm.
 * Visit www.openauthentication.org for more information.
 *
 * @author Johan Rydell, PortWise, Inc.
 */
public class TOTP {

	private TOTP() {}


	/**
	 * This method uses the JCE to provide the crypto
	 * algorithm.
	 * HMAC computes a Hashed Message Authentication Code with the
	 * crypto hash algorithm as a parameter.
	 *
	 * @param crypto     the crypto algorithm (HmacSHA1, HmacSHA256, HmacSHA512)
	 * @param keyBytes   the bytes to use for the HMAC key
	 * @param text       the message or text to be authenticated.
	 */
	private static byte[] hmac_sha1(String crypto, byte[] keyBytes, byte[] text)
	{
		try {
			Mac hmac;
			hmac = Mac.getInstance(crypto);
			SecretKeySpec macKey =
				new SecretKeySpec(keyBytes, "RAW");
			hmac.init(macKey);
			return hmac.doFinal(text);
		} catch (GeneralSecurityException gse) {
			throw new UndeclaredThrowableException(gse);
		}
	}


	/**
	 * This method converts HEX string to Byte[]
	 *
	 * @param hex   the HEX string
	 *
	 * @return      A byte array
	 */
	private static byte[] hexStr2Bytes(String hex){
		// Adding one byte to get the right conversion
		// values starting with "0" can be converted
		byte[] bArray = new BigInteger("10" + hex,16).toByteArray();

		// Copy all the REAL bytes, not the "first"
		byte[] ret = new byte[bArray.length - 1];
		for (int i = 0; i < ret.length ; i++)
			ret[i] = bArray[i+1];
		return ret;
	}


	private static final int[] DIGITS_POWER
	// 0 1  2   3    4     5      6       7        8
	= {1,10,100,1000,10000,100000,1000000,10000000,100000000 };


	/**
	 * This method generates an TOTP value for the given
	 * set of parameters.
	 *
	 * @param key   the shared secret, HEX encoded
	 * @param time 	a value that reflects a time
	 * @param returnDigits 	number of digits to return
	 * @param crypto	the crypto function to use
	 *
	 * @return      A numeric String in base 10 that includes
	 *              {@link truncationDigits} digits
	 */
	public static String generateTOTP(String key,
			String time,
			String returnDigits)
	{
		return generateTOTP(key, time, returnDigits, "HmacSHA1");
	}


	/**
	 * This method generates an TOTP value for the given
	 * set of parameters.
	 *
	 * @param key   the shared secret, HEX encoded
	 * @param time 	a value that reflects a time
	 * @param returnDigits 	number of digits to return
	 * @param crypto	the crypto function to use
	 *
	 * @return      A numeric String in base 10 that includes
	 *              {@link truncationDigits} digits
	 */
	public static String generateTOTP256(String key,
			String time,
			String returnDigits)
	{
		return generateTOTP(key, time, returnDigits, "HmacSHA256");
	}


	/**
	 * This method generates an TOTP value for the given
	 * set of parameters.
	 *
	 * @param key   the shared secret, HEX encoded
	 * @param time 	a value that reflects a time
	 * @param returnDigits 	number of digits to return
	 * @param crypto	the crypto function to use
	 *
	 * @return      A numeric String in base 10 that includes
	 *              {@link truncationDigits} digits
	 */
	public static String generateTOTP512(String key,
			String time,
			String returnDigits)
	{
		return generateTOTP(key, time, returnDigits, "HmacSHA512");
	}


	/**
	 * This method generates an TOTP value for the given
	 * set of parameters.
	 *
	 * @param key   the shared secret, HEX encoded
	 * @param time 	a value that reflects a time
	 * @param returnDigits 	number of digits to return
	 * @param crypto	the crypto function to use
	 *
	 * @return      A numeric String in base 10 that includes
	 *              {@link truncationDigits} digits
	 */
	private static String generateTOTP(String key,
			String time,
			String returnDigits,
			String crypto)
	{
		int codeDigits = Integer.decode(returnDigits).intValue();
		String result = null;
		byte[] hash;

		// Using the counter
		// First 8 bytes are for the movingFactor
		// Complaint with base RFC 4226 (HOTP)
		while(time.length() < 16 )
			time = "0" + time;

		// Get the HEX in a Byte[]
		byte[] msg = hexStr2Bytes(time);

		// Adding one byte to get the right conversion
		byte[] k = hexStr2Bytes(key);

		hash = hmac_sha1(crypto, k, msg);

		// put selected bytes into result int
		int offset = hash[hash.length - 1] & 0xf;

		int binary =
			((hash[offset] & 0x7f) << 24) | ((hash[offset + 1] & 0xff) << 16) |
			((hash[offset + 2] & 0xff) << 8) | (hash[offset + 3] & 0xff);

		int otp = binary % DIGITS_POWER[codeDigits];

		result = Integer.toString(otp);
		while (result.length() < codeDigits) {
			result = "0" + result;
		}
		return result;
	}

	public static void main(String[] args) {

		String seed = "3132333435363738393031323334353637383930";
		long testTime[] = {1111111109, 1111111111, 1234567890, 2000000000};
		String time = "0";
		Date myDate = Calendar.getInstance().getTime();
		BigInteger b = new BigInteger("0");
		DateFormat df = new SimpleDateFormat("yyyy-MM-dd HH:mm:ss");
		df.setTimeZone(TimeZone.getTimeZone("UTC"));

		try{
			System.out.println("+--------------+-----------------------+------------------+--------+--------+");
			System.out.println("|  Time(sec)   |   Time (UTC format)   | Value of T(Hex)  |  TOTP  | Mode   |");
			System.out.println("+--------------+-----------------------+------------------+--------+--------+");

			for(int i=0; i<testTime.length; i++) {
				myDate.setTime(testTime[i]*1000);

				b = new BigInteger("0" + myDate.getTime());
				b = b.divide(new BigInteger("30000"));
				time = b.toString(16).toUpperCase();
				while(time.length() < 16) time = "0" + time;
				System.out.print("|  " + testTime[i] + "  |  " + df.format(myDate) +  "  |");
				System.out.print(" " + time + " |");
				System.out.println(generateTOTP(seed, time, "8", "HmacSHA1") + "| SHA1   |");
				System.out.print("|  " + testTime[i] + "  |  " + df.format(myDate) +  "  |");
				System.out.print(" " + time + " |");
				System.out.println(generateTOTP(seed, time, "8", "HmacSHA256") + "| SHA256 |");
				System.out.print("|  " + testTime[i] + "  |  " + df.format(myDate) +  "  |");
				System.out.print(" " + time + " |");
				System.out.println(generateTOTP(seed, time, "8", "HmacSHA512") + "| SHA512 |");

				System.out.println("+--------------+-----------------------+------------------+--------+--------+");
			}
		}catch (final Exception e){
			System.out.println("Error : " + e);
		}
	}
}

Appendix B.  Test Vectors

This section provides test values that can be used for HOTP time-based variant algorithm interoperability test.

The test token shared secret uses the ASCII string value "12345678901234567890". With Time Step X = 30, and Unix epoch as initial value to count time steps where T0 = 0, the TOTP algorithm will display the following values for specified modes and timestamps.

Authors' Addresses