Cryptography Tutorials - Herong's Tutorial Examples - Version 5.21, by Dr. Herong Yang

DES Decryption Algorithm

This section describes DES decryption algorithm - identical to the encryption algorithm step by step in the same order, only with the subkeys applied in the reverse order.

The decryption algorithm of a block cipher should be identical to encryption algorithm step by step in reverse order. But for DES cipher, the encryption algorithm is so well designed, that the decryption algorithm is identical to the encryption algorithm step by step in the same order, only with the subkeys applied in the reverse order.

DES decryption algorithm:

Input: 
   CC: 64 bits of cipher text
   k16, k15, ..., k1: 16 round keys
   IP: Initial permutation
   FP: Final permutation
   f(): Round function
   
Output: 
   TT: 64 bits of clear text

Algorithm:
   CC' = IP(CC), applying initial permutation
   (LL0, RR0) = CC', dividing CC' into two 32-bit parts
   (LL1, RR1) = (RR0, LL0 ^ f(RR0, k16))
   (LL2, RR2) = (RR1, LL1 ^ f(RR1, k15))
   ......
   TT' = (RR16, LL16), swapping the two parts
   TT = FP(TT'), applying final permutation

Here is how to approve the decryption algorithm:

Let: 
   T: 64 bits of clear text
   C: 64 bits of cipher text encrypted from T
   CC: 64 bits of cipher text
   TT: 64 bits of clear text decrypted from CC

If: 
   CC = C
   
Then: 
   TT = T

Prove:
   CC' = IP(CC)               First step of decryption
      = IP(C)                 Assumption of CC = C
      = IP(FP(C'))            Last step of encryption
      = C'                    IP is the inverse permutation of FP

   (LL0, RR0) = CC'           Initializing step in decryption
      = C'                    CC' = C'
      = (R16, L16)            Swapping step in encryption
       
   (LL1, RR1) = (RR0, LL0 ^ f(RR0, k16))
                              First round of decryption
      = (L16, R16 ^ f(L16, k16))
                              Previous result
      = (R15, (L15 ^ f(R15,k16)) ^ f(R15, k16))
                              (L16, R16) = (R15, L15 ^ f(R15, k16))
      = (R15, L15)           ^ reverse itself
       
   ......   

   (LL16, RR16) = (R0, L0)
   
   TT' = (RR16, LL16)         Swapping in decryption
      = (L0, R0)              Previous result
      = T'                    Initializing step in encryption

   TT = FP(TT')               Last step in decryption
      = FP(T')                Previous result
      = FP(IP(T))             First step in encryption
      = T                     FP is the inverse permutation of IP

Table of Contents

 About This Book

 Cryptography Terminology

 Cryptography Basic Concepts

Introduction to DES Algorithm

 What Is Block Cipher?

 DES (Data Encryption Standard) Cipher Algorithm

 DES Key Schedule (Round Keys Generation) Algorithm

DES Decryption Algorithm

 DES Algorithm - Illustrated with Java Programs

 DES Algorithm Java Implementation

 DES Algorithm - Java Implementation in JDK JCE

 DES Encryption Operation Modes

 DES in Stream Cipher Modes

 PHP Implementation of DES - mcrypt

 Blowfish - 8-Byte Block Cipher

 Secret Key Generation and Management

 Cipher - Secret Key Encryption and Decryption

 Introduction of RSA Algorithm

 RSA Implementation using java.math.BigInteger Class

 Introduction of DSA (Digital Signature Algorithm)

 Java Default Implementation of DSA

 Private key and Public Key Pair Generation

 PKCS#8/X.509 Private/Public Encoding Standards

 Cipher - Public Key Encryption and Decryption

 MD5 Mesasge Digest Algorithm

 SHA1 Mesasge Digest Algorithm

 OpenSSL Introduction and Installation

 OpenSSL Generating and Managing RSA Keys

 OpenSSL Managing Certificates

 OpenSSL Generating and Signing CSR

 OpenSSL Validating Certificate Path

 "keytool" and "keystore" from JDK

 "OpenSSL" Signing CSR Generated by "keytool"

 Migrating Keys from "keystore" to "OpenSSL" Key Files

 Certificate X.509 Standard and DER/PEM Formats

 Migrating Keys from "OpenSSL" Key Files to "keystore"

 Using Certificates in IE (Internet Explorer)

 Using Certificates in Firefox

 Using Certificates in Google Chrome

 Outdated Tutorials

 References

 Printable Copy - PDF Version

DES Decryption Algorithm - Updated in 2014, by Dr. Herong Yang