### Triple-DES

General | |
---|---|

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: 2^{32} known plaintexts, 2^{113} operations including 2^{90} DES encryptions, 2^{88} memory; Biham: find one of 2^{28} target keys with a handful of chosen plaintexts per key and 2^{84} encryptions |

In cryptography, **Triple DES** is the common name for the **Triple Data Encryption Algorithm** (**TDEA** or **Triple DEA**) block cipher, which applies the Data Encryption Standard (DES) cipher algorithm three times to each data block.

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.

## Contents

## Definitive standards

The Triple Data Encryption Algorithm (TDEA) is defined in each of:

- ANS
^{[1]}X9.52-1998*Triple Data Encryption Algorithm Modes of Operation*^{[2]}(withdrawn) - )

## 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, 2012) 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).

While none of the standards that define the algorithm use the term "3DES", this term is used by some vendors, users, and cryptographers.^{[5]}^{[6]}^{[7]}^{[8]}

## Algorithm

Triple DES uses a "key bundle" which comprises three DES keys, K_{1}, K_{2} and K_{3}, each of 56 bits (excluding parity bits). The encryption algorithm is:

- ciphertext = E
_{K3}(D_{K2}(E_{K1}(plaintext)))

I.e., DES encrypt with K_{1}, DES *decrypt* with K_{2}, then DES encrypt with K_{3}.

Decryption is the reverse:

- plaintext = D
_{K1}(E_{K2}(D_{K3}(ciphertext)))

I.e., decrypt with K_{3}, *encrypt* with K_{2}, then decrypt with K_{1}.

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: K
_{1}and K_{2}are independent, and K_{3}= K_{1}. - Keying option 3: All three keys are identical, i.e. K
_{1}= K_{2}= K_{3}.

Keying option 1 is the strongest, with 3 × 56 = 168 independent key bits.

Keying option 2 provides less security, with 2 × 56 = 112 key bits. This option is stronger than simply DES encrypting twice, e.g. with K_{1} and K_{2}, because it protects against meet-in-the-middle attacks.

Keying option 3 is equivalent to DES, with only 56 key bits. This option 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),^{[4]} and is not supported by ISO/IEC 18033-3.

Each DES key is nominally stored or transmitted as 8 bytes, each of odd parity,^{[9]}
so a key bundle requires 24, 16 or 8 bytes, for keying option 1, 2 or 3 respectively.

### 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. However, other terms are used in other standards and related recommendations, and general usage.

- For keying option 1:
- 3TDEA, in NIST SP 800-57
^{[10]}and SP 800-78-3^{[11]} - Triple-length keys, in general usage
^{[12]}^{[13]}

- 3TDEA, in NIST SP 800-57

- For keying option 2:
- 2TDEA, in NIST SP 800-57
^{[10]}and SP 800-78-3^{[11]} - Double-length keys, in general usage
^{[12]}^{[13]}

- 2TDEA, in NIST SP 800-57

## 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^{[14]} 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^{[15]} 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,^{[16]}^{[17]} and thus, it is designated by NIST to have only 80 bits of security.^{[10]}

The best attack known on keying option 1 requires around 2^{32} known plaintexts, 2^{113} steps, 2^{90} single DES encryptions, and 2^{88} memory^{[18]} (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.^{[10]} If the attacker seeks to discover any one of many cryptographic keys, there is a memory-efficient attack which will discover one of 2^{28} keys, given a handful of chosen plaintexts per key and around 2^{84} encryption operations.^{[19]}

## Usage

The electronic payment industry uses Triple DES and continues to develop and promulgate standards based upon it (e.g. EMV).^{[20]}

Adobe Systems, Microsoft OneNote, Microsoft Outlook 2007 and Microsoft System Center Configuration Manager 2012 use Triple DES to password protect user content and system data.^{[21]}^{[22]}^{[23]}

## See also

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