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FIPS 46-3: TRIPLE DATA ENCRYPTION STANDARD

Welcome

This document is a literate Cryptol document. This means that if you install Cryptol from the website you can run cryptol TripleDES.md in your terminal and all of the definitions will be typecheck, and the test cases can be run.

All text in this document is directly from the Data Encryption Standard.

module Primitive::Symmetric::Cipher::Block::TripleDES where

import Primitive::Symmetric::Cipher::Block::DES (DES)

E = DES.encrypt
D = DES.decrypt

TRIPLE DATA ENCRYPTION ALGORITHM

Let EK(I) and DK(I) represents the DES encryption and decryption of I using DES key K respectively. Each TDEA encryption/decryption operation (as specified in ANSI X9.52) is a compound operation of DES encryption and decryption operations. The following operations are used:

  1. TDEA encryption operation: the transformation of a 64-bit block I into a 64-bit block O that is defined as follows:
encrypt : [3][64] -> [64] -> [64]
encrypt [K1, K2, K3] I = O
    where
        O = E K3 (D K2 (E K1 I))

// Maintain backwards compatibility
blockEncrypt : ([64], [64], [64], [64]) -> [64]
blockEncrypt (k1, k2, k3, data) = encrypt [k1, k2, k3] data
  1. TDEA decryption operation: the transformation of a 64-bit block I into a 64-bit block O that is defined as follows:
decrypt : [3][64] -> [64] -> [64]
decrypt [K1, K2, K3] I = O
    where
        O = D K1 (E K2 (D K3 I))

The standard specifies the following keying options for bundle (K1, K2, K3)

  1. Keying Option 1: K1, K2, and K3 are independent keys;

  2. Keying Option 2: K1 and K2 are independent keys and K3 = K1;

  3. Keying Option 3: K1 = K2 = K3.

A TDEA mode of operation is backward compatible with its single DES counterpart if, with compatible keying options for TDEA operations,

  1. an encrypted plaintext computed using a single DES mode of operation can be decrypted correctly be a corresponding TDEA mode of operation; and

  2. an encrypted plaintext computed using a TDEA mode of operation can be decrypted correctly by a corresponding single DES mode of operation.

When using Keying Option 3 (K1 = K2 = K3), TECB, TCBC, TCFB and TOFB modes are backward compatible with single DES modes of operation ECB, CBC, CFB, OFB respectively.

The diagram in Appendix 2 illustrates TDEA encryption and TDEA decryption.

APPENDIX 2: TRIPLE DES BLOCK DIAGRAM (ECB Mode)

TDEA Encryption Operation:

I -> DES EK1 -> DES DK2 -> DES EK2 -> O

TDEA Decryption Operation:

I -> DES DK3 -> DES EK2 -> DES DK1 -> O

Test Vectors

2-Key Tests

The following test vectors are pulled from Project NESSIE.

property test_twokey = encrypt k0' pt0 == ct0
                    /\ encrypt k1' pt1 == ct1
                    /\ encrypt k2' pt2 == ct2
    where
        k0  = 0x80000000000000000000000000000000
        k0' = [take`{64} k0, drop`{64} k0, take`{64} k0]
        pt0 = 0x0000000000000000
        ct0 = 0xFAFD5084374FCE34
        k1  = 0x40000000000000000000000000000000
        k1' = [take`{64} k1, drop`{64} k1, take`{64} k1]
        pt1 = 0x0000000000000000
        ct1 = 0x60CC37B7B537A1DC
        k2  = 0x20000000000000000000000000000000
        k2' = [take`{64} k2, drop`{64} k2, take`{64} k2]
        pt2 = 0x0000000000000000
        ct2 = 0xBE3E7304FE92C2BC