Triple DES

In

While the US government and industry standards abbreviate the algorithm's name as TDES (Triple DES) and TDEA (Triple Data Encryption Algorithm),[2] RFC 1851 referred to it as 3DES from the time it first promulgated the idea, and this namesake has since come into wide use by most vendors, users, and cryptographers.^[3][4][5][6]

History

In 1978, a triple encryption method using DES with two 56-bit keys was proposed by Walter Tuchman; in 1981 Merkle and Hellman proposed a more secure triple key version of 3DES with 112 bits of security.^[7]

Standards

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

• RFC 1851, The ESP Triple DES Transform^[8] (approved in 1995)
• ANSI ANS X9.52-1998 Triple Data Encryption Algorithm Modes of Operation^[9] (approved in 1998, withdrawn in 2008^[10]
  )
• FIPS PUB 46-3 Data Encryption Standard (DES)^[11] (approved in 1999, withdrawn in 2005^[12])
• NIST Special Publication 800-67 Revision 2 Recommendation for the Triple Data Encryption Algorithm (TDEA) Block Cipher^[13] (approved in 2017, withdrawn Jan 1st 2024 ^[14]
  )
• ISO/IEC 18033-3:2010: Part 3: Block ciphers^[15]
  (approved in 2005)

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.

A naive approach to increase strength of a block encryption algorithm with short key length (like DES) would be to use two keys ${\displaystyle (K1,K2)}$ instead of one, and encrypt each block twice: ${\displaystyle E_{K2}(E_{K1}({\textrm {plaintext}}))}$. If the original key length is ${\displaystyle n}$ bits, one would hope this scheme provides security equivalent to using key ${\displaystyle 2n}$ bits long. Unfortunately, this approach is vulnerable to meet-in-the-middle attack: given a known plaintext pair ${\displaystyle (x,y)}$, such that ${\displaystyle y=E_{K2}(E_{K1}(x))}$, one can recover the key pair ${\displaystyle (K1,K2)}$ in ${\displaystyle 2^{n+1}}$ steps, instead of the ${\displaystyle 2^{2n}}$ steps one would expect from an ideally secure algorithm with ${\displaystyle 2n}$ bits of key.

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

${\displaystyle {\textrm {ciphertext}}=E_{K3}(D_{K2}(E_{K1}({\textrm {plaintext}}))).}$

That is, DES encrypt with ${\displaystyle K1}$, DES decrypt with ${\displaystyle K2}$, then DES encrypt with ${\displaystyle K3}$.

Decryption is the reverse:

${\displaystyle {\textrm {plaintext}}=D_{K1}(E_{K2}(D_{K3}({\textrm {ciphertext}}))).}$

That is, decrypt with ${\displaystyle K3}$, encrypt with ${\displaystyle K2}$, then decrypt with ${\displaystyle K1}$.

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. Sometimes known as 3TDEA^[16] or triple-length keys.^[17]

This is the strongest, with 3 × 56 = 168 independent key bits. It is still vulnerable to meet-in-the-middle attack, but the attack requires 2^{2 × 56} steps.

Keying option 2

K₁ and K₂ are independent, and K₃ = K₁. Sometimes known as 2TDEA^[16] or double-length keys.^[17]

This provides a shorter key length of 56*2 or 112 bits and a reasonable compromise between DES and Keying option 1, with the same caveat as above.^[18] This is an improvement over "double DES" which only requires 2⁵⁶ steps to attack. NIST has deprecated this option.^[16]

Keying option 3

All three keys are identical, i.e. K₁ = K₂ = K₃.

This is backward compatible with DES, since two operations cancel out. ISO/IEC 18033-3 never allowed this option, and NIST no longer allows K₁ = K₂ or K₂ = K₃.^[16][13]

Each DES key is 8 odd-parity bytes, with 56 bits of key and 8 bits of error-detection.^[9] A key bundle requires 24 bytes for option 1, 16 for option 2, or 8 for option 3.

NIST (and the current TCG specifications version 2.0 of approved algorithms for Trusted Platform Module) also disallows using any one of the 64 following 64-bit values in any keys (note that 32 of them are the binary complement of the 32 others; and that 32 of these keys are also the reverse permutation of bytes of the 32 others), listed here in hexadecimal (in each byte, the least significant bit is an odd-parity generated bit, it is discarded when forming the effective 56-bit keys):

01.01.01.01.01.01.01.01, FE.FE.FE.FE.FE.FE.FE.FE, E0.FE.FE.E0.F1.FE.FE.F1, 1F.01.01.1F.0E.01.01.0E,
01.01.FE.FE.01.01.FE.FE, FE.FE.01.01.FE.FE.01.01, E0.FE.01.1F.F1.FE.01.0E, 1F.01.FE.E0.0E.01.FE.F1,
01.01.E0.E0.01.01.F1.F1, FE.FE.1F.1F.FE.FE.0E.0E, E0.FE.1F.01.F1.FE.0E.01, 1F.01.E0.FE.0E.01.F1.FE,
01.01.1F.1F.01.01.0E.0E, FE.FE.E0.E0.FE.FE.F1.F1, E0.FE.E0.FE.F1.FE.F1.FE, 1F.01.1F.01.0E.01.0E.01,
01.FE.01.FE.01.FE.01.FE, FE.01.FE.01.FE.01.FE.01, E0.01.FE.1F.F1.01.FE.0E, 1F.FE.01.E0.0E.FE.01.F1,
01.FE.FE.01.01.FE.FE.01, FE.01.01.FE.FE.01.01.FE, E0.01.01.E0.F1.01.01.F1, 1F.FE.FE.1F.0E.FE.FE.0E,
01.FE.E0.1F.01.FE.F1.0E, FE.01.1F.E0.FE.01.0E.F1, E0.01.1F.FE.F1.01.0E.FE, 1F.FE.E0.01.0E.FE.F1.01,
01.FE.1F.E0.01.FE.0E.F1, FE.01.E0.1F.FE.01.F1.0E, E0.01.E0.01.F1.01.F1.01, 1F.FE.1F.FE.0E.FE.0E.FE,
01.E0.01.E0.01.F1.01.F1, FE.1F.FE.1F.FE.0E.FE.0E, E0.1F.FE.01.F1.0E.FE.01, 1F.E0.01.FE.0E.F1.01.FE,
01.E0.FE.1F.01.F1.FE.0E, FE.1F.01.E0.FE.0E.01.F1, E0.1F.01.FE.F1.0E.01.FE, 1F.E0.FE.01.0E.F1.FE.01,
01.E0.E0.01.01.F1.F1.01, FE.1F.1F.FE.FE.0E.0E.FE, E0.1F.1F.E0.F1.0E.0E.F1, 1F.E0.E0.1F.0E.F1.F1.0E,
01.E0.1F.FE.01.F1.0E.FE, FE.1F.E0.01.FE.0E.F1.01, E0.1F.E0.1F.F1.0E.F1.0E, 1F.E0.1F.E0.0E.F1.0E.F1,
01.1F.01.1F.01.0E.01.0E, FE.E0.FE.E0.FE.F1.FE.F1, E0.E0.FE.FE.F1.F1.FE.FE, 1F.1F.01.01.0E.0E.01.01,
01.1F.FE.E0.01.0E.FE.F1, FE.E0.01.1F.FE.F1.01.0E, E0.E0.01.01.F1.F1.01.01, 1F.1F.FE.FE.0E.0E.FE.FE,
01.1F.E0.FE.01.0E.F1.FE, FE.E0.1F.01.FE.F1.0E.01, E0.E0.1F.1F.F1.F1.0E.0E, 1F.1F.E0.E0.0E.0E.F1.F1,
01.1F.1F.01.01.0E.0E.01, FE.E0.E0.FE.FE.F1.F1.FE, E0.E0.E0.E0.F1.F1.F1.F1, 1F.1F.1F.1F.0E.0E.0E.0E,

With these restrictions on allowed keys, Triple DES has been reapproved with keying options 1 and 2 only. Generally the three keys are generated by taking 24 bytes from a strong random generator and only keying option 1 should be used (option 2 needs only 16 random bytes, but strong random generators are hard to assert and it's considered best practice to use only option 1).

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

The short block size of 64 bits makes 3DES vulnerable to block collision attacks if it is used to encrypt large amounts of data with the same key. The Sweet32 attack shows how this can be exploited in TLS and OpenVPN.^[24] Practical Sweet32 attack on 3DES-based cipher-suites in TLS required ${\displaystyle 2^{36.6}}$ blocks (785 GB) for a full attack, but researchers were lucky to get a collision just after around ${\displaystyle 2^{20}}$ blocks, which took only 25 minutes.

The security of TDEA is affected by the number of blocks processed with one key bundle. One key bundle shall not be used to apply cryptographic protection (e.g., encrypt) more than ${\displaystyle 2^{20}}$ 64-bit data blocks.

— Recommendation for Triple Data Encryption Algorithm (TDEA) Block Cipher (SP 800-67 Rev2)^[13]

OpenSSL does not include 3DES by default since version 1.1.0 (August 2016) and considers it a "weak cipher".^[25]

Usage

As of 2008, the

Firefox and Mozilla Thunderbird^[31] use Triple DES in CBC mode to encrypt website authentication login credentials when using a master password.

Implementations

Below is a list of cryptography libraries that support Triple DES:

• Botan
• Bouncy Castle
• cryptlib
• Crypto++
• Libgcrypt
• Nettle
• OpenSSL
• wolfSSL
• Trusted Platform Module (alias TPM, hardware implementation)

Some implementations above may not include 3DES in the default build, in later or more recent versions.

See also

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

References and notes