Ring learning with errors key exchange: Difference between revisions

Revision as of 12:01, 10 June 2015

Revision as of 12:11, 10 June 2015

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## If v_j = (q-1)/4, draw a random bit (b). If b = 0 then v_j = (q-1)/4 otherwise v_j = (q+3)/4

# Two n-long bit streams, cj, and uj, are formed from the coefficients of v(x), (v_n-1, ... , v₀ ), via "Cross Rounding" and "Modular Rounding" respectively. For j = 0 to n-1:

## Set c_j to be the lowest bit of the [[Floor and ceiling functions|floor]] of quotient (4v_j)/q after [[nearest integer function|rounding;]] that is <math display="inline">c_j = \lfloor 4 v_j/q \rceilrfloor\mod 2</math>

## Set uju_j to be the lowest bit of the [[Floor and ceiling functions|floor]] of the quotient (2v_j)/q after [[Nearest integer function|rounding]]; that is <math>u_j = \lfloor 2v_j\rfloorrceil\mod 2</math>

#Form the key (k) as the concatenation of u_n-1, ..., u₀.

# Form an n-long "reconciliation" bit string (c) as the concatenation of c_n-1, ..., c₀.