Description
Grains' 160-bit internal state consists of an 80-bit linear feedback shift register (LFSR) and a 80-bit non-linear feedback shift register (NLFSR). Grain updates one bit of LFSR and one bit of NLFSR state for every bit of ciphertext released by a nonlinear filter function. The 80-bit NLFSR is updated with a nonlinear 5-to-1 Boolean function and a 1 bit linear input selected from the LFSR. The nonlinear 5-to-1 function takes as input 5 bits of the NLFSR state. The 80-bit LFSR is updated with a 6-to-1 linear function. During keying operations the output of the cipher is additionally fed-back as linear inputs into both the NLFSR and LFSR update functions.
In the original Grain Version 0.0 submission of Grain, one bit of the 80-bit NLFSR and four bits of the 80-bit LFSR are supplied to a nonlinear 5-to-1 Boolean function (that is chosen to be balanced, correlation immune of the first order and has algebraic degree 3) and the output is linearly combined with 1 bit of the 80-bit NLFSR and released as output.
In the updated Grain Version 1.0 submission of Grain, one bit of the 80-bit NLFSR and four bits of the 80-bit LFSR are supplied to a (slightly revised) nonlinear 5-to-1 Boolean function and the output is linearly combined with 7 bits of the 80-bit NLFSR and released as output.
To initialize the cipher, the 80-bit key is loaded directly into the 80-bits NLFSR and the 64-bit IV is loaded into the low 64-bits of the LFSR and the remaining 16 high bits of the LFSR are filled with ones. The cipher is sealed for 160 rounds where the 160 bits of keystream generated are fed-back linearly into both the LFSR and NLFSR update functions. The cipher releases no keystream output during the initialization process.
Grain's authors discuss the complete diffusion rates of Grain initialization process in the Grain Version 1.0 specifications: "For initialization with two different IVs, differing by only one bit, the probability that a shift register bit is the same for both initializations should be close to 0.5. Simulations show that this is achieved after 160 clockings."
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