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1. VMPC Stream Cipher
2. VMPC Key Scheduling Algorithm
3. Test output of the VMPC Stream Cipher
4. Authenticated encrypion with VMPC Stream Cipher Download FSE'04 paper
"VMPC One-Way Function
and Stream Cipher":
vmpc.pdf (171 KB)
vmpc.ps (289 KB)
vmpc.dvi (55 KB)
Earlier paper "VMPC Stream Cipher"
available also at IACR ePrint archive

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

For a scheme of authenticated encryption based on the VMPC Stream Cipher, see the VMPC-MAC specification

For further analysis of the algorithms, see the Research section