Variably Modified Permutation Composition

VMPC (Variably Modified Permutation Composition) for cryptography is a stream cipher similar to the well known and popular cipher RC4 designed by Ron Rivest. It was designed by Bartosz Żółtak, presented in 2004 at the Fast Software Encryption conference.

The core of the cipher is the VMPC function, a transformation of n-element permutations defined as:

for x from 0 to n-1:
    g(x) = VMPC(f)(x) = f(f(f(x))+1)

The function was designed such that inverting it, i.e. obtaining f from g, would be a complex problem. According to computer simulations the average number of operations required to recover f from g for a 16-element permutation is about 2¹¹; for 64-element permutation, about 2⁵³; and for a 256-element permutation, about 2²⁶⁰.

In 2006 at Cambridge University, Kamil Kulesza investigated the problem of inverting VMPC and concluded "results indicate that VMPC is not a good candidate for a cryptographic one-way function".

The VMPC function is used in an encryption algorithm – the VMPC stream cipher. The algorithm allows for efficient in software implementations; to encrypt L bytes of plaintext do:

All arithmetic is performed modulo 256.
i := 0
while GeneratingOutput:
    j := S[j + S[i]]
    
    output S[S[S[j]] + 1]
    swap S[i] and S[j]          (b := S[j]; S[j] := S[i]; S[i] := b))
    
    i := i + 1
endwhile

Where 256-element permutation P and integer value s are obtained from the encryption password using the VMPC-KSA (Key Scheduling Algorithm).

External links

• VMPC Homepage
• Original conference paper on VMPC from okna wrocław (PDF)
• Kamil Kulesza: On inverting the VMPC one-way function
• Unofficial C implementation of VMPC Stream cipher
• Unofficial Delphi implementation of VMPC Stream cipher

• https://eprint.iacr.org/2013/768.pdf VMPC-R: Cryptographically Secure Pseudo-Random Number Generator Alternative to RC4
• https://eprint.iacr.org/2014/985.pdf Statistical weakness in Spritz against VMPC-R: in search for the RC4 replacement
• https://eprint.iacr.org/2014/315.pdf Statistical weaknesses in 20 RC4-like algorithms and (probably) the simplest algorithm free from these weaknesses - VMPC-R
• https://eprint.iacr.org/2019/041.pdf Message Authentication (MAC) Algorithm For The VMPC-R (RC4-like) Stream Cipher