1. Simplified DES

2. S-DES algorithm The S-DES encryption algorithm takes
an 8-bit block of plaintext (e.g., )
10-bit key as input and
produces an 8-bit block of ciphertext as output.
The S-DES decryption algorithm takes
an 8-bit block of ciphertext and
the same 10-bit key used
produce the original 8-bit block of plaintext.

3. Simplified DES 10-Bit key Decryption Encryption 8-bit Plaintext
Shift IP
IP-1 K1 P8 K1 fk fk
Shift SW SW K2 P8 K2
Encryption involves 5 functions executed in the following order
1. Initial permutation IP
2. A function fk (combo of permutation & susbstutution)
3. A switch function SW that swaps halves.
4. The function fkagain
5. The inverse of IP, IP-1
Decryption is the symmetrical inverse of encryption
Runs the algorithm backwards - undoing encryption fk fk
IP-1 IP
8-bit Ciphertext
8-bit Ciphertext

4. S-DES encryption The encryption algorithm involves five functions:
an initial permutation (IP);
a complex function labeled fk, which involves both permutation and substitution operations and depends on a key input;
a simple permutation function that switches (SW) the two halves of the data;
The function fk again; and
a permutation function that is the inverse of the initial permutation (IP-1).

5. The encryption algorithm as a composition of functions
Decryption is essentially the reverse of encryption

6. Simplified DES - Key Generation
10 bits
P10
Permutation
Split Key, Circular Shift
Permutation - K1 output
Permutation, K2 output
5 bits
5 bits
LS-1
LS-1
5 bits
5 bits P8 K1
8 bits
LS-2
LS-2
Sub-key generation consists of 3 functions/in 5 steps
1. A 10 bit permutation [ ] Input bits
[ ] Output bits
2. A left shift
3. An 8 bit permutation for the 1st sub-key
4. A second left shift
5. A final permutation producing the 2nd key.
5 bits
5 bits P8 K2
8 bits

7. S-DES Key Generation
S-DES depends on the use of a 10-bit key shared between sender and receiver.
Two 8-bit subkeys are produced for use in particular stages of the encryption and decryption algorithm.

8. Simplified DES - Key Generation
P10 Permutation:
P10(in-order) = k1, k2, k3, k4, k5, k6, k7, k8, k9, k10 ( )
P10(out-order)= k3, k5, k2, k7, k4, k10, k1, k9, k8, k6 ( )
Split the permuted key into 2 five-bit halves and circular left shift 1
Input = Output =
P8 Permutation - selects and permutes 8 of the 10 bits
Result is Sub-key K1 = P8

9. Simplified DES - Key Generation
To get sub-key K2:
Take output of original circular left shift 1 and shift an additional 2
Input = Output =
Apply P8 to this value to produce K2
K2 =
This completes the generation of K1 and K2

10. Simplified DES - Encryption
Two permutation functions (initial - IP, and final IP-1), where
IP-1 is the inverse of IP; that is IP-1(IP(X)) = X.
Two permutation/substitution functions fk each using one sub-key,
on the left (L) and right (R) data elements. That is:
fk(L,R) = (L  F(R, SK), R)
where SK is a sub-key and  is the bit-by-bit Exclusive OR.
One switch function SW that interchanges the left and right 4 bits
so the second instance of fk operates on a different set of bits.

11. Simplified DES - Initial & Final PermutationIP IP
Input =
Output =
IP-1
IP-1
Input =
Output =
Result is IP-1(IP(X)) = X

12. Simplified DES - Function fk
Assume output of the IP stage is =
Then L, R = 1011, 1101
And fk(L,R) = (L  F(R, SK), R)
So fk(1011, 1101) = (1011  F(R, SK), 1101)
Now assume F(R, SK) = F(1101, SK) for some sub-key = 1110 (this
value will change depending on the sub-key).
Then: fk(1011, 1101) = (1011  1110, 1101) = 0101, 1101
Next we need to describe the complex function F(R,SK).

13. Simplified DES - Function F(R,SK)IP
4 bits
Expand/Permute
8 bits 
4 bits
4 bits S0 S1
4 bits
F(R,SK)
2 bits
2 bits
4 bits P4
4 bits 
4 bits SW

14. Simplified DES - Function Parts of F(R,SK)
Expansion/Permutation (4 bits n1, n2, n3, n4) to 8 bits
E/P
Arrange these bits as follows:
n4 | n1 , n2 | n3 (left half of expansion/permutation)
n2 | n3 , n4 | n1 (right half)
Compute: n4  k11 | n1  k12 , n2  k13 | n3  k14
n2  k15 | n3  k16 , n4  k17 | n1  k18

15. Simplified DES - Function Parts of F(R,SK)
Rename these 8 bits:
Row 1 p0,0 | p0,1 p0,2 | p0,3
Row 2 p1,0 | p1,1 p1,2 | p1,3
The first 4 bits, row 1 are input to the s-box S0, 2nd row to S-box S1
to produce a 2-bit output for each input bit as follows;
S S
For example, S0, p0,0 = 01; S1, p1,1 = 00

16. Simplified DES - Function Parts of F(R,SK)
P4 Permutation: 2 bit input from S0, 2 bits from S1 P4
P4 output = output of fk
Switch function: interchanges the left and right halves so the second
instance of fk using the second key operates on different data.
The second instance of fk operates the same as described above
using the k2 sub-key and the switched input.
Decryption uses all the same functions run backwards.

17. Simplified DES Encryption Detail

18. Simplified DES Key Generation
10 bit Key
10 bit Key
P10 5 5
10000 | P10 5 5
00001
11000
LS-1
LS-1 5 5 5 5 P8 8 K1 8 K1
00100
00011
LS-2
LS-2 5 5 5 5 P8 8 8 K2 K2

19. Simplified DES 8 4 2 K1 K2 SW Plaintext Ciphertext S0 S1 E/P P4 IP

20. Simplified DES 1 2 3
S0= 8
Plaintext PT IP 4 4
1011 | 1101 IP
E/P 8
E/P 8 K1 K1 4 4 1 2 3
Xor S0 S1 2 2
S1=
11 S0
11 S1 P4 4
1111 P4
1011 L 4
0100 Xor SW
1101
0100

21. Simplified DES
1101
0100 1 2 3
S0= 4 4
E/P
E/P 8 K2 8 K2
Xor 4 4 1 2 3 S0 S1
10 S0
01 S1 2 2
S1=
0101 P4 P4
1101 L 4
1000 Xor 4 RS
IP-1 8
Ciphertext