Open main menu

Wikipedia β

In cryptography, Triple DES (3DES), officially the Triple Data Encryption Algorithm (TDEA or Triple DEA), is a symmetric-key block cipher, which applies the Data Encryption Standard (DES) cipher algorithm three times to each data block.

Triple Data Encryption Algorithm
First published 1998 (ANS X9.52)
Derived from DES
Cipher detail
Key sizes 168, 112 or 56 bits (keying option 1, 2, 3 respectively)
Block sizes 64 bits
Structure Feistel network
Rounds 48 DES-equivalent rounds
Best public cryptanalysis
Lucks: 232 known plaintexts, 2113 operations including 290 DES encryptions, 288 memory; Biham: find one of 228 target keys with a handful of chosen plaintexts per key and 284 encryptions

The original DES cipher's key size of 56 bits was generally sufficient when that algorithm was designed, but the availability of increasing computational power made brute-force attacks feasible. Triple DES provides a relatively simple method of increasing the key size of DES to protect against such attacks, without the need to design a completely new block cipher algorithm.



The Triple Data Encryption Algorithm is variously defined in several standards documents:

  • RFC 1851, The ESP Triple DES Transform[1] (approved in 1995)
  • ANSI ANS X9.52-1998 Triple Data Encryption Algorithm Modes of Operation[2] (approved in 1998, withdrawn in 2008[3])
  • FIPS PUB 46-3 Data Encryption Standard (DES)[4] (approved in 1999, withdrawn in 2005[5])
  • NIST Special Publication 800-67 Revision 1 Recommendation for the Triple Data Encryption Algorithm (TDEA) Block Cipher[6] (approved in 2012[7])
  • ISO/IEC 18033-3:2010: Part 3: Block ciphers[8] (approved in 2005)

Name of the algorithmEdit

While the government and industry standards abbreviate the algorithm as TDES (Triple DES) and TDEA (Triple Data Encryption Algorithm), RFC 1851 called it 3DES from the time it first promulgated the idea, and 3DES has since come into wide use by most vendors, users, and cryptographers.[9][10][11][12]


A naive approach to increase strength of a block encryption algorithm with short key length (like DES) would be to use two keys (K1, K2) instead of one, and encrypt each block twice: EK2(EK1(plaintext)). If the original key length is n bits, one would hope this scheme provides security equivalent to using key 2n bits long. Unfortunately, this approach is vulnerable to meet-in-the-middle attack: given a known plaintext pair (x, y), such that y = EK2(EK1(x)), one can recover the key pair (K1, K2) in ~2n steps, instead of ~22n steps one would expect from algorithm with 2n bits of key.

Therefore, Triple DES uses a "key bundle" that comprises three DES keys, K1, K2 and K3, each of 56 bits (excluding parity bits). The encryption algorithm is:

ciphertext = EK3(DK2(EK1(plaintext)))

I.e., DES encrypt with K1, DES decrypt with K2, then DES encrypt with K3.

Decryption is the reverse:

plaintext = DK1(EK2(DK3(ciphertext)))

I.e., decrypt with K3, encrypt with K2, then decrypt with K1.

Each triple encryption encrypts one block of 64 bits of data.

In each case the middle operation is the reverse of the first and last. This improves the strength of the algorithm when using keying option 2, and provides backward compatibility with DES with keying option 3.

Keying optionsEdit

The standards define three keying options:

Keying option 1
All three keys are independent.
Keying option 2
K1 and K2 are independent, and K3 = K1.
Keying option 3
All three keys are identical, i.e. K1 = K2 = K3.

Keying option 1 is the strongest, with 3 × 56 = 168 independent key bits. It is still vulnerable to meet-in-the-middle attack, but the attack requires 22 × 56 steps, instead of 256 steps required for attacking "double DES" scheme where one encrypts twice.

Keying option 2 provides shorter key length with 2 × 56 = 112 key bits. While the key length is shorter than in option 1, the meet-in-the-middle attack still requires 22 × 56 steps, which is not any faster than brute force attack. There are no known attacks on option 2, if attacker only knows a small number of plaintexts, so option 2 is reasonable choice in practice, if the key length of 112 bits is satisfactory.[13]

Keying option 3 is equivalent to DES, with only 56 key bits. It provides backward compatibility with DES, because the first and second DES operations cancel out. It is no longer recommended by the National Institute of Standards and Technology (NIST),[6] and is not supported by ISO/IEC 18033-3.

Each DES key is nominally stored or transmitted as 8 bytes, each of odd parity,[14] so a key bundle requires 24 bytes for option 1, 16 for option 2, or 8 for option 3.

Other termsEdit

"Keying option n" is the term used by the standards (X9.52, FIPS PUB 46-3, SP 800-67, ISO/IEC 18033-3) that define the TDEA. However, other terms are used in other standards and related recommendations, and general usage.

  • For keying option 1:
    • 3TDEA, in NIST SP 800-57[15] and SP 800-78-4[16]
    • Triple-length keys, in general usage[17][18]
  • For keying option 2:
    • 2TDEA, in NIST SP 800-57[15] and SP 800-78-4[16]
    • Double-length keys, in general usage[17][18]

Encryption of more than one blockEdit

As with all block ciphers, encryption and decryption of multiple blocks of data may be performed using a variety of modes of operation, which can generally be defined independently of the block cipher algorithm. However, ANS X9.52 specifies directly, and NIST SP 800-67 specifies via SP 800-38A[19] that some modes shall only be used with certain constraints on them that do not necessarily apply to general specifications of those modes. For example, ANS X9.52 specifies that for cipher block chaining, the initialization vector shall be different each time, whereas ISO/IEC 10116[20] does not. FIPS PUB 46-3 and ISO/IEC 18033-3 define only the single block algorithm, and do not place any restrictions on the modes of operation for multiple blocks.


In general, Triple DES with three independent keys (keying option 1) has a key length of 168 bits (three 56-bit DES keys), but due to the meet-in-the-middle attack, the effective security it provides is only 112 bits.[15] Keying option 2 reduces the effective key size to 112 bits (because the third key is the same as the first). However, this option is susceptible to certain chosen-plaintext or known-plaintext attacks,[21][22] and thus, it is designated by NIST to have only 80 bits of security.[15] This can be considered broken, as the whole 3des keyspace can be searched through by affordable consumer hardware today (2017).

The best attack known on keying option 1 requires around 232 known plaintexts, 2113 steps, 290 single DES encryptions, and 288 memory[23] (the paper presents other tradeoffs between time and memory). This is not currently practical and NIST considers keying option 1 to be appropriate through 2030.[15] If the attacker seeks to discover any one of many cryptographic keys, there is a memory-efficient attack which will discover one of 228 keys, given a handful of chosen plaintexts per key and around 284 encryption operations.[24]


The electronic payment industry uses Triple DES and continues to develop and promulgate standards based upon it (e.g. EMV).[25]

Microsoft OneNote,[26] Microsoft Outlook 2007[27] and Microsoft System Center Configuration Manager 2012[28] use Triple DES to password protect user content and system data.

See alsoEdit

References and notesEdit

  1. ^ Karn, P.; Metzger, P.; Simpson, W. (September 1995). The ESP Triple DES Transform. RFC 1851. 
  2. ^ "ANSI X9.52-1998 Triple Data Encryption Algorithm Modes of Operation". Retrieved 2017-05-01.  Extends ANSI X3.92-1981 Data Encryption Algorithm.
  3. ^ "ANSI Standards Action" (PDF). Vol. 39 no. 46. ANSI. Nov 14, 2008. Retrieved 2017-05-01. 
  4. ^ "FIPS PUB 46-3: Data Encryption Standard (DES)" (PDF). United States Department of Commerce. Oct 25, 1999. Retrieved 2017-05-01. 
  5. ^ "Announcing Approval of the Withdrawal of Federal Information Processing Standard (FIPS) 46–3...." (PDF). Federal Register. 70 (96). May 19, 2005. Retrieved 2017-05-01. 
  6. ^ a b Barker, William C.; Barker, Elaine (January 2012). "NIST Special Publication 800-67 Revision 1: Recommendation for the Triple Data Encryption Algorithm (TDEA) Block Cipher". NIST. Retrieved 2017-05-01. 
  7. ^ Barker, William C. (January 2012). "Recommendation for the Triple Data Encryption Algorithm (TDEA) Block Cipher". Retrieved 2017-06-19. 
  8. ^ "ISO/IEC 18033-3:2010. Information technology -- Security techniques -- Encryption algorithms -- Part 3: Block ciphers". ISO. December 2010. Retrieved 2017-05-01. 
  9. ^ "New Comparative Study Between DES, 3DES and AES within Nine Factors" (PDF). Journal of Computing. 2 (3). March 2010. ISSN 2151-9617. Retrieved 2017-05-01. 
  10. ^ "Obtaining a DES License or a 3DES-AES License" (PDF). Cisco. Retrieved 2017-05-01. 
  11. ^ "3DES Update: Most Banks Are Done, But...". ATM & Debit News. March 29, 2007. Retrieved 2017-05-01. 
  12. ^ RFC 2828 and RFC 4949
  13. ^ Katz, Jonathan; Lindell, Yehuda (2015). Introduction to Modern Cryptography. Chapman and Hall/CRC. p. 223. ISBN 978-1466570269. 
  14. ^ According to ANSI X3.92-1981 (one of the standards that defines the DES algorithm), section 3.5: "One bit in each 8-bit byte of the KEY may be utilized for error detection in key generation, distribution, and storage. Bits 8, 16,..., 64 are for use in ensuring that each byte is of odd parity."
  15. ^ a b c d e Barker, Elaine (January 2016). "NIST Special Publication 800-57 Recommendation for Key Management, Part 1: General (Revised)" (PDF). NIST. Retrieved 2017-05-01. 
  16. ^ a b "NIST Special Publication 800-78-4 Cryptographic Algorithms and Key Sizes for Personal Identity Verification" (PDF). NIST. May 2015. Retrieved 2017-05-01. 
  17. ^ a b "The Cryptography Guide: Triple DES". Cryptography World. Retrieved 2015-07-12. 
  18. ^ a b "Triple DES Encryption". IBM. Retrieved 2010-05-17. 
  19. ^ NIST Special Publication 800-38A, Recommendation for Block Cipher Modes of Operation, Methods and Techniques, 2001 Edition (PDF)
  20. ^ ISO/IEC 10116:2006 Information technology — Security techniques — Modes of operation for an n-bit block cipher
  21. ^ Merkle, Ralph; Hellman, Martin (July 1981). "On the Security of Multiple Encryption" (PDF). Communications of the ACM. 24 (7): 465–467. doi:10.1145/358699.358718. 
  22. ^ van Oorschot, Paul; Wiener, Michael J. (1990). A known-plaintext attack on two-key triple encryption. EUROCRYPT'90, LNCS 473. pp. 318–325. CiteSeerX . 
  23. ^ Stefan Lucks: Attacking Triple Encryption (PDF), Fast Software Encryption 1998, pp 239–253.
  24. ^ Eli Biham: How to Forge DES-Encrypted Messages in 228 Steps (PostScript), 1996.
  25. ^ "Annex B Approved Cryptographic Algorithms – B1.1 Data Encryption Standard (DES)". EMV 4.2: Book 2 - Security and Key Management (4.2 ed.). EMVCo. June 2008. p. 137. Retrieved 16 August 2013. The double-length key triple DES encipherment algorithm (see ISO/IEC 18033-3) is the approved cryptographic algorithm to be used in the encipherment and MAC mechanisms specified in Annex A1. The algorithm is based on the (single) DES algorithm standardised in ISO 16609. 
  26. ^ Daniel Escapa's OneNote Blog - Encryption for Password Protected Sections, November 2006
  27. ^ Microsoft - Encrypt E-mail Messages, Outlook 2007
  28. ^ Microsoft TechNet product documentation - Technical Reference for Cryptographic Controls Used in Configuration Manager, October 2012

External linksEdit