Blowfish Decryption Algorithm

This section describes the Blowfish decryption algorithm, which is identical to the encryption algorithm step by step in the same order, only with the sub-keys 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 Blowfish 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 sub-keys applied in the reverse order.

To help us to approve the decryption algorithm, we have to write the encryption algorithm and the decryption algorithm with temporary variables.

Encryption algorithm with temporary variables:

Input: 
   T: 64 bits of clear text
   P1, P2, ..., P18: 18 sub-keys
   F(): Round function
   
Output: 
   C: 64 bits of cipher text

Algorithm:
   (L0, R0) = T, dividing T into two 32-bit parts
   L1 = L0 XOR P1
   R2 = R0 XOR F(L1) XOR P2
   L3 = L1 XOR F(R2) XOR P3
   R4 = R2 XOR F(L3) XOR P4
   L5 = L3 XOR F(R4) XOR P5
   R6 = R4 XOR F(L5) XOR P6
   L7 = L5 XOR F(R6) XOR P7
   R8 = R6 XOR F(L7) XOR P8
   L9 = L7 XOR F(R8) XOR P9
   R10 = R8 XOR F(L9) XOR P10
   L11 = L9 XOR F(R10) XOR P11
   R12 = R10 XOR F(L11) XOR P12
   L13 = L11 XOR F(R12) XOR P13
   R14 = R12 XOR F(L13) XOR P14
   L15 = L13 XOR F(R14) XOR P15
   R16 = R14 XOR F(L15) XOR P16
   L17 = L15 XOR F(R16) XOR P17
   R18 = R16 XOR P18
   C = (R18, L17)

Decryption algorithm with temporary variables:

Input: 
   CC: 64 bits of cipher text
   P1, P2, ..., P18: 18 sub-keys
   F(): Round function
   
Output: 
   TT: 64 bits of clear text

Algorithm:
   (LL0, RR0) = CC, dividing CC into two 32-bit parts
   LL1 = LL0 XOR P18
   RR2 = RR0 XOR F(LL1) XOR P17
   LL3 = LL1 XOR F(RR2) XOR P16
   RR4 = RR2 XOR F(LL3) XOR P15
   LL5 = LL3 XOR F(RR4) XOR P14
   RR6 = RR4 XOR F(LL5) XOR P13
   LL7 = LL5 XOR F(RR6) XOR P12
   RR8 = RR6 XOR F(LL7) XOR P11
   LL9 = LL7 XOR F(RR8) XOR P10
   RR10 = RR8 XOR F(LL9) XOR P9
   LL11 = LL9 XOR F(RR10) XOR P8
   RR12 = RR10 XOR F(LL11) XOR P7
   LL13 = LL11 XOR F(RR12) XOR P6
   RR14 = RR12 XOR F(LL13) XOR P5
   LL15 = LL13 XOR F(RR14) XOR P4
   RR16 = RR14 XOR F(LL15) XOR P3
   LL17 = LL15 XOR F(RR16) XOR P2
   RR18 = R16 XOR P1
   TT = (RR18, LL17)

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:
   (LL0, RR0) = CC            Initializing step in decryption
      = C                     Assumption of CC = C
      = (R18, L17)            Finalizing step in encryption

   LL1 = LL0 XOR P18          Applying P18 in decryption
      = R18 XOR P18           Previous result
      = R16 XOR P18 XOR P18   Applying P18 in encryption
      = R16

   RR2 = RR0 XOR F(LL1) XOR P17
                              Applying P17 in decryption
      = L17 XOR F(R16) XOR P17
                              Previous result
      = L15 XOR F(R16) XOR P17 XOR F(R16) XOR P17
                              Applying P17 in encryption
      = L15

   ......
   
   LL17 = LL15 XOR F(RR16) XOR P2
                              Applying P2 in decryption
      = R2 XOR F(L1) XOR P2
                              Previous result
      = R0 XOR F(L1) XOR P2 XOR F(L1) XOR P2
                              Applying P2 in encryption
      = R0

   RR18 = RR16 XOR P1         Applying P1 in decryption
      = L1 XOR P1             Previous result
      = L0 XOR P1 XOR P1      Applying P1 in encryption
      = L0

   TT = (RR18, LL17)          Finalizing step in decryption
      = (L0, R0)              Initializing step in encryption
      = T 

Last update: 2015.

Table of Contents

 About This Book

 Cryptography Terminology

 Cryptography Basic Concepts

 Introduction to AES (Advanced Encryption Standard)

 Introduction to DES 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

 What Is Block Cipher?

 Blowfish Cipher Algorithm

 Key Schedule (Sub-Keys Generation) Algorithm

 BlowfishJ - Java Implementation by Markus Hahn

Blowfish Decryption Algorithm

 First 8336 Hex Digits of PI

 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

 PDF Printing Version