The Grain 128a stream cipher was first purposed at Symmetric Key Encryption Workshop (SKEW) in 2011[1] as an improvement of the predecessor Grain 128, which added security enhancements and optional message authentication using the Encrypt & MAC approach. One of the important features of the Grain family is that the throughput can be increased at the expense of additional hardware. Grain 128a is designed by Martin Ågren,[1] Martin Hell, Thomas Johansson and Willi Meier.

Description of the cipher

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View of grain 128a

Grain 128a consists of two large parts: Pre-output function and MAC. The pre-output function has an internal state size of 256 bits, consisting of two registers of size 128 bit: NLFSR and LFSR. The MAC supports variable tag lengths w such that  . The cipher uses a 128 bit key.

The cipher supports two modes of operation: with or without authentication, which is configured via the supplied   such that if   then authentication of the message is enabled, and if   authentication of the message is disabled.

Pre-output function

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The pre-output function consists of two registers of size 128 bit: NLFSR ( ) and LFSR ( ) along with 2 feedback polynomials   and   and a boolean function  .

 

 

 

In addition to the feedback polynomials, the update functions for the NLFSR and the LFSR are:

 

 

The pre-output stream ( ) is defined as:

 

Initialisation

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Diagram showing the start up procedure of the pre-output which feeds the pre-output stream back into the functions   and  

Upon initialisation we define an   of 96 bit, where the   dictates the mode of operation.

The LFSR is initialised as:

  for  

  for  

 

The last 0 bit ensures that similar key-IV pairs do not produce shifted versions of each other.

The NLFSR is initialised by copying the entire 128 bit key ( ) into the NLFSR:

  for  

Start up clocking

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Before the pre-output function can begin to output its pre-output stream it has to be clocked 256 times to warm up, during this stage the pre-output stream is fed into the feedback polynomials   and  .

Key stream

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The key stream ( ) and MAC functionality in Grain 128a both share the same pre-output stream ( ). As authentication is optional our key stream definition depends upon the  .

When authentication is enabled, the MAC functionality uses the first   bits (where   is the tag size) after the start up clocking to initialise. The key stream is then assigned every other bit due to the shared pre-output stream.

If authentication is enabled:

 

If authentication is disabled:

 

 
View of grain 128a

Grain 128a supports tags of size   up to 32 bit, to do this 2 registers of size   is used, a shift register( ) and an accumulator( ). To create a tag of a message   where   is the length of   as we have to set   to ensure that i.e.   and   has different tags, and also making it impossible to generate a tag that completely ignores the input from the shift register after initialisation.

For each bit   in the accumulator we at time   we denounce a bit in the accumulator as  .

Initialisation

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When authentication is enabled Grain 128a uses the first   bits of the pre-output stream( ) to initialise the shift register and the accumulator. This is done by:

Shift register:

  for  

Accumulator:

  for  

Tag generation

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Shift register:

The shift register is fed all the odd bits of the pre-output stream( ):

 

Accumulator:

  for  

Final tag

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When the cipher has completed the L iterations the final tag( ) is the content of the accumulator:

  for  

References

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  1. ^ a b "Publications by Martin Ågren". Martin Ågren. Archived from the original on 12 March 2014. Retrieved 9 May 2013.
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