Variably Modified Permutation Composition
VMPC (Variably Modified Permutation Composition) for cryptography is a stream cipher similar to the well known and popular cipher
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.[citation needed]
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".[2]
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: a := S[i] j := S[j + a] output S[S[S[j]] + 1] swap S[i] and S[j] (b := S[j]; S[i] := b; S[j] := a)) 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).
References
- ^ Alexander Maximov (2007-02-22). "Two Linear Distinguishing Attacks on VMPC and RC4A and Weakness of RC4 Family of Stream Ciphers (Corrected)". Cryptology ePrint Archive. (originally presented at FSE 2006 conference)
- ^ Kulesza, Kamil (2008-10-27). "On Inverting the VMPC One-Way Function" (PDF). Retrieved 9 February 2015.
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
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