[Resource Topic] 2012/656: Security Evaluation of Rakaposhi Stream Cipher

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Security Evaluation of Rakaposhi Stream Cipher

Authors: Mohammad Ali Orumiehchiha, Josef Pieprzyk, Elham Shakour, Ron Steinfeld


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}.

ePrint: https://eprint.iacr.org/2012/656

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