Paper 2012/656

Security Evaluation of Rakaposhi Stream Cipher

Mohammad Ali Orumiehchiha, Josef Pieprzyk, Elham Shakour, and Ron Steinfeld

Abstract

Rakaposhi is a synchronous stream cipher, which uses three main components a non-linear feedback shift register (NLFSR), a dynamic linear feedback shift register (DLFSR) and a non-linear filtering function ($NLF$). NLFSR consists of 128 bits and is initialised by the secret key $K$. DLFSR holds 192 bits and is initialised by an initial vector ($IV$). $NLF$ takes 8-bit inputs and returns a single output bit. The work identifies weaknesses and properties of the cipher. The main observation is that the initialisation procedure has the so-called sliding property. The property can be used to launch distinguishing and key recovery attacks. The distinguisher needs four observations of the related $(K,IV)$ pairs. The key recovery algorithm allows to discover the secret key $K$ after observing $2^{9}$ pairs of $(K,IV)$. In the proposed related-key attack, the number of related $(K,IV)$ pairs is $2^{(128+192)/4}$ pairs. The key recovery algorithm allows to discover the secret key $K$ after observing $2^9$ related $(K,IV)$ pairs. Further the cipher is studied when the registers enter short cycles. When NLFSR is set to all ones, then the cipher degenerates to a linear feedback shift register with a non-linear filter. Consequently, the initial state (and Secret Key and $IV$) can be recovered with complexity $2^{63.87}$. If DLFSR is set to all zeros, then $NLF$ reduces to a low non-linearity filter function. As the result, the cipher is insecure allowing the adversary to distinguish it from a random cipher after $2^{17}$ observations of keystream bits. There is also the key recovery algorithm that allows to find the secret key with complexity $2^{54}$.