1. VMPC Stream Cipher

The VMPC Stream Cipher is a proposed extension of the VMPC one-way function into an encryption algorithm.

The cipher generates a stream of 8-bit values from a 256-element permutation. The initial state of the permutation is determined by the VMPC Key Scheduling Algorithm described in section 2.

Notation :

	P	:	256-byte table storing the permutation
	s	:	8-bit variable initialized by the VMPC Key Scheduling Algorithm
	n	:	8-bit variable

Table 1.1. VMPC Stream Cipher

1. Set n to 0

2. Add modulo 256 n-th element of P to s 3. Set s to s-th element of P 4. Output s-th element of permutation VMPC(P) 5. Swap n-th element of P with s-th element of P 6. Increment modulo 256 n

7. Go to step 2 if more output is needed

Table 1.2. VMPC Stream Cipher - pseudo code

To generate Len bytes of output, execute: 1. n = 0 2. Repeat steps 3-6 Len times:    3. s = P[ (s + P[n]) and 255 ]    4. Output = P[ (P[P[s]]+1) and 255 ]    5. Temp = P[n]       P[n] = P[s]       P[s] = Temp    6. n = (n + 1) and 255

2. VMPC Key Scheduling Algorithm

The VMPC Key Scheduling Algorithm transforms a cryptographic key and (optionally) and Initialization Vector into a 256-element permutation P.

Notation: as in section 1, with:

	c	:	fixed length of the cryptographic key in bytes, c in {16...64}
	K	:	c-element table storing the cryptographic key
	z	:	fixed length of the Initialization Vector in bytes, z in {16...64}
	V	:	z-element table storing the Initialization Vector
	m	:	16-bit variable

Table 2.1. VMPC Key Scheduling Algorithm

1. Set s to 0 2. Set i-th element of P to i for i in {0,1,...,255}

3. Set m to 0 4. Add modulo 256 (m modulo 256)-th element of P to s 5. Add modulo 256 (m modulo c)-th element of K to s 6. Set s to s-th element of P 7. Swap (m modulo 256)-th element of P with s-th element of P 8. Increment m 9. Go to step 4 if m is lower than 768

10. If Initialization Vector is not used: terminate the algorithm

11. Set m to 0 12. Add modulo 256 (m modulo 256)-th element of P to s 13. Add modulo 256 (m modulo z)-th element of V to s 14. Set s to s-th element of P 15. Swap (m modulo 256)-th element of P with s-th element of P 16. Increment m 17. Go to step 12 if m is lower than 768

Table 2.2. VMPC Key Scheduling Algorithm - pseudo code

1. s = 0 2. for i from 0 to 255: P[i]=i 3. for m from 0 to 767: execute steps 4-6:    4. n = m and 255    5. s = P[ (s + P[n] + K[m mod c]) and 255 ]    6. Temp = P[n]       P[n] = P[s]       P[s] = Temp 7. If Initialization Vector is used: execute step 8: 8. for m from 0 to 767: execute steps 9-11:     9. n = m and 255    10. s = P[ (s + P[n] + V[m mod z]) and 255 ]    11. Temp = P[n]        P[n] = P[s]        P[s] = Temp

3. Test output of the VMPC Stream Cipher

16 bytes of a 102.400-byte data-stream generated by the VMPC Stream Cipher for a given key and a given Initialization Vector are shown in Table 3.


Table 3. Example data-stream generated by the VMPC Stream Cipher

Key (hex)	96, 61, 41, 0A, B7, 97, D8, A9, EB, 76, 7C, 21, 17, 2D, F6, C7
Initialization Vector (hex)	4B, 5C, 2F, 00, 3E, 67, F3, 95, 57, A8, D2, 6F, 3D, A2, B1, 55
Output-byte number (dec)	0	1	2	3	252	253	254	255
Output-byte value (hex)	A8	24	79	F5	B8	FC	66	A4
Output-byte number (dec)	1020	1021	1022	1023	102396	102397	102398	102399
Output-byte value (hex)	E0	56	40	A5	81	CA	49	9A