Triple DES

In cryptography, Triple DES is the common name for the Triple Data Encryption Algorithm (TDEA) block cipher defined in each of:

• ANS X9.52-1998 Triple Data Encryption Algorithm Modes of Operation^[1]
• FIPS PUB 46-3 Data Encryption Standard (DES) (PDF) (withdrawn^[2])
• NIST Special Publication 800-67 Recommendation for the Triple Data Encryption Algorithm (TDEA) Block CipherPDF (483 KB)
• ISO/IEC 18033-3:2005 Information technology — Security techniques — Encryption algorithms — Part 3: Block ciphers

It is so named because it applies the Data Encryption Standard (DES) cipher algorithm three times to each data block.

Triple DES provides a relatively simple method of increasing the key size of DES to protect against brute force attacks, without requiring a completely new block cipher algorithm.

Name of the algorithm

The earliest standard that defines the algorithm (ANS X9.52, published in 1998) describes it as the "Triple Data Encryption Algorithm (TDEA)" — i.e. three operations of the Data Encryption Algorithm specified in ANSI X3.92 — and does not use the terms "Triple DES" or "DES" at all. FIPS PUB 46-3 (1999) defines the "Triple Data Encryption Algorithm (TDEA)", but also uses the terms "DES" and "Triple DES". It uses the terms "Data Encryption Algorithm" and "DES" interchangeably, including starting the specification with:

The Data Encryption Standard (DES) shall consist of the following Data Encryption Algorithm (DES) [sic] and Triple Data Encryption Algorithm (TDEA, as described in ANSI X9.52).

NIST SP 800-67(2004, 2008^[3]) primarily uses the term TDEA, but also refers to "Triple DES (TDEA)". ISO/IEC 18033-3 (2005) uses "TDEA", but mentions that:

The TDEA is commonly known as Triple DES (Data Encryption Standard).

Algorithm

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

ciphertext = E_K3(D_K2(E_K1(plaintext)))

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

Decryption is the reverse:

plaintext = D_K1(E_K2(D_K3(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 options

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 x 56 = 168 independent key bits.

Keying option 2 provides less security, with 2 x 56 = 112 key bits. This option is stronger than simply DES encrypting twice, e.g. with K₁ and K₂, because it protects against meet-in-the-middle attacks.

Keying option 3 is no better than DES, with only 56 key bits. This option provides backward compatibility with DES, because the first and second DES operations simply cancel out. It is no longer recommended by the National Institute of Standards and Technology (NIST) ^[4] and not supported by ISO/IEC 18033-3.

Other terms used to refer to the keying options

"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, but a variety of other terms have been used elsewhere — in other standards or similarly authoritative documents — to refer to those keying options. These terms include:

• For keying option 1:
  • 3TDEA, in NIST SP 800-57^[5] and SP 800-78-1^[6]

• For keying option 2:
  • 2TDEA, in NIST SP 800-57^[5] and SP 800-78-1^[6]

Encryption of more than one block

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^[7]), 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^[8] 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.

Security

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. Keying option 2, reduces the key size to 112 bits. However, this option is susceptible to certain chosen-plaintext or known-plaintext attacks^[9][10] and thus it is designated by NIST to have only 80 bits of security.^[5]

The best attack known on keying option 1 requires around 2³² known plaintexts, 2¹¹³ steps, 2⁹⁰ single DES encryptions, and 2⁸⁸ memory^[11] (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.^[5] 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.^[12]

Usage

The electronic payment industry uses Triple DES and continues to develop and promulgate standards based upon it (e.g. EMV).^[13][14]

See also

• Data Encryption Standard (DES)
• DES-X
• Advanced Encryption Standard (AES)
• Horst Feistel
• Walter Tuchman

References and notes