1. Let Ln, Rn, Kn denote 32-bit, 32-bit and 48-bit random numbers respectively, and let Re(Ln, Rn,Kn) = (Ln+1, Rn+1) represent the DES encryption round shown in the left diagram in Figure 3.6 in the textbook, which has included 2 functional mappings:

   • LnRnKn Ln+1 (this means Ln+1 is a function of Ln, Rn, Kn)

   • LnRnKn Rn+1 (this means Rn+1 is a function of Ln, Rn, Kn)

1) Prove that Re(Rn+1, Ln+1, Kn) = (Rn, Ln)

64-bit input 64-bit output 32-bit L 32-bit Ly 32-bit Rn 32-bit _, _32-bit R Mangler Function Mangler Function K 32-bit loud 32-bit An:1 32-bit L:1) 32-bit Anti 64-bit output 64-bit input Encryption Decryption Figure 3-6. DES Round 64-bit input 64-bit output 32-bit L 32-bit Ly 32-bit Rn 32-bit _, _32-bit R Mangler Function Mangler Function K 32-bit loud 32-bit An:1 32-bit L:1) 32-bit Anti 64-bit output 64-bit input Encryption Decryption Figure 3-6. DES Round