Unrolled architecture of the combinatorial part of the transformation round More...

Libraries
shacomps
	Basic SHA components library.

Signals
t1_tm4	std_logic_vector ( WORD_WIDTH - 1 downto 0 ) := ( others = > ' 0 ' )
	Output of the \(T_1\) step function of the step \(t-4\).
t2_tm4	std_logic_vector ( WORD_WIDTH - 1 downto 0 ) := ( others = > ' 0 ' )
	Output of the \(T_2\) step function of the step \(t-4\).
t1_tm3	std_logic_vector ( WORD_WIDTH - 1 downto 0 ) := ( others = > ' 0 ' )
	Output of the \(T_1\) step function of the step \(t-3\).
t2_tm3	std_logic_vector ( WORD_WIDTH - 1 downto 0 ) := ( others = > ' 0 ' )
	Output of the \(T_2\) step function of the step \(t-3\).
t1_tm2	std_logic_vector ( WORD_WIDTH - 1 downto 0 ) := ( others = > ' 0 ' )
	Output of the \(T_1\) step function of the step \(t-2\).
t2_tm2	std_logic_vector ( WORD_WIDTH - 1 downto 0 ) := ( others = > ' 0 ' )
	Output of the \(T_2\) step function of the step \(t-2\).
t1_tm1	std_logic_vector ( WORD_WIDTH - 1 downto 0 ) := ( others = > ' 0 ' )
	Output of the \(T_1\) step function of the step \(t-1\).
t2_tm1	std_logic_vector ( WORD_WIDTH - 1 downto 0 ) := ( others = > ' 0 ' )
	Output of the \(T_2\) step function of the step \(t-1\).
b	std_logic_vector ( WORD_WIDTH - 1 downto 0 ) := ( others = > ' 0 ' )
	Value of the accumulator \(B\) at the step \(t\).
c	std_logic_vector ( WORD_WIDTH - 1 downto 0 ) := ( others = > ' 0 ' )
	Value of the accumulator \(C\) at the step \(t\).
d	std_logic_vector ( WORD_WIDTH - 1 downto 0 ) := ( others = > ' 0 ' )
	Value of the accumulator \(D\) at the step \(t\).
f	std_logic_vector ( WORD_WIDTH - 1 downto 0 ) := ( others = > ' 0 ' )
	Value of the accumulator \(F\) at the step \(t\).
g	std_logic_vector ( WORD_WIDTH - 1 downto 0 ) := ( others = > ' 0 ' )
	Value of the accumulator \(G\) at the step \(t\).
h	std_logic_vector ( WORD_WIDTH - 1 downto 0 ) := ( others = > ' 0 ' )
	Value of the accumulator \(H\) at the step \(t\).

Instantiations
t1_m4	T1 <Entity T1>
	\(T_1\) step function of the step \(t-4\)
t2_m4	T2 <Entity T2>
	\(T_2\) step function of the step \(t-4\)
t1_m3	T1 <Entity T1>
	\(T_1\) step function of the step \(t-3\)
t2_m3	T2 <Entity T2>
	\(T_2\) step function of the step \(t-3\)
t1_m2	T1 <Entity T1>
	\(T_1\) step function of the step \(t-2\)
t2_m2	T2 <Entity T2>
	\(T_2\) step function of the step \(t-2\)
t1_m1	T1 <Entity T1>
	\(T_1\) step function of the step \(t-1\)
t2_m1	T2 <Entity T2>
	\(T_2\) step function of the step \(t-1\)

Aliases
K_tm4	is K ( WORD_WIDTH - 1 downto 0 )
	Constant \(K\) for the round \(t-4\).
K_tm3	*is K ( 2 WORD_WIDTH - 1 downto WORD_WIDTH )**
	Constant \(K\) for the round \(t-3\).
K_tm2	*is K ( 3 WORD_WIDTH - 1 downto 2 * WORD_WIDTH )**
	Constant \(K\) for the round \(t-2\).
K_tm1	*is K ( 4 WORD_WIDTH - 1 downto 3 * WORD_WIDTH )**
	Constant \(K\) for the round \(t-1\).
W_tm4	is W ( WORD_WIDTH - 1 downto 0 )
	Expanded word for the round \(t-4\).
W_tm3	*is W ( 2 WORD_WIDTH - 1 downto WORD_WIDTH )**
	Expanded word for the round \(t-3\).
W_tm2	*is W ( 3 WORD_WIDTH - 1 downto 2 * WORD_WIDTH )**
	Expanded word for the round \(t-2\).
W_tm1	*is W ( 4 WORD_WIDTH - 1 downto 3 * WORD_WIDTH )**
	Expanded word for the round \(t-1\).

Detailed Description

Unrolled architecture of the combinatorial part of the transformation round

This architecture performs 4 steps within a single clock cycle.

To perform the unrolling, start from a single step, which is given by:

\begin{align*} T^1_{t-1} & \propto E_{t-1}, F_{t-1}, G_{t-1}, H_{t-1}, K_{t-1}, W_{t-1} \\ T^2_{t-1} & \propto A_{t-1}, B_{t-1}, C_{t-1} \\ A_t & = T^1_{t-1} + T^2_{t-1} \\ B_t & = A_{t-1} \\ C_t & = B_{t-1} \\ D_t & = C_{t-1} \\ E_t & = D_{t-1} + T^1_{t-1} \\ F_t & = E_{t-1} \\ G_t & = F_{t-1} \\ H_t & = G_{t-1} \end{align*}

It is not necessary to specify exactly the structure of the step function, but only the positional dependency from the inputs.

Now it is needed to express outputs of the step \(t\) as functions of the inputs of the stage \(t-2\). The easy part is related to the step function of the step \(t-1\):

\begin{align*} T^1_{t-2} & \propto E_{t-2}, F_{t-2}, G_{t-2}, H_{t-2}, K_{t-2}, W_{t-2} \\ T^2_{t-2} & \propto A_{t-2}, B_{t-2}, C_{t-2} \end{align*}

Now, applying the step expression for the step \(t-1\) and substituting in the expression for the step \(t\) one can obtain:

\begin{align*} T^1_{t-1} & \propto D_{t-2} + T^1_{t-2}, E_{t-2}, F_{t-2}, G_{t-2}, K_{t-1}, W_{t-1} \\ T^2_{t-1} & \propto T^1_{t-2} + T^2_{t-2}, A_{t-2}, B_{t-2} \\ A_t & = T^1_{t-1} + T^2_{t-1} \\ B_t & = T^1_{t-2} + T^2_{t-2} \\ C_t & = A_{t-2} \\ D_t & = B_{t-2} \\ E_t & = C_{t-2} + T^1_{t-1} \\ F_t & = D_{t-2} + T^1_{t-2} \\ G_t & = E_{t-2} \\ H_t & = F_{t-2} \end{align*}

The same methodology can be applied to the step \(t-3\):

\begin{align*} T^1_{t-3} & \propto E_{t-3}, F_{t-3}, G_{t-3}, H_{t-3}, K_{t-3}, W_{t-3} \\ T^2_{t-3} & \propto A_{t-3}, B_{t-3}, C_{t-3} \\ T^1_{t-2} & \propto D_{t-3} + T^1_{t-3}, E_{t-3}, F_{t-3}, G_{t-3}, K_{t-2}, W_{t-2} \\ T^2_{t-2} & \propto T^1_{t-3} + T^2_{t-3}, A_{t-3}, B_{t-3} \\ T^1_{t-1} & \propto C_{t-3} + T^1_{t-2}, D_{t-3} + T^2_{t-3}, E_{t-3}, F_{t-3}, K_{t-1}, W_{t-1} \\ T^2_{t-1} & \propto T^1_{t-2} + T^2_{t-2}, T^1_{t-3} + T^2_{t-3}, A_{t-3} \\ A_t & = T^1_{t-1} + T^2_{t-1} \\ B_t & = T^1_{t-2} + T^2_{t-2} \\ C_t & = T^1_{t-3} + T^2_{t-3} \\ D_t & = A_{t-2} \\ E_t & = B_{t-3} + T^1_{t-1} \\ F_t & = C_{t-3} + T^1_{t-2} \\ G_t & = D_{t-3} + T^1_{t-3} \\ H_t & = E_{t-3} \end{align*}

Another application yields the outputs of the step \(t\) as functions of the inputs of the stage \(t-4\):

\begin{align*} T^1_{t-4} & \propto E_{t-4}, F_{t-4}, G_{t-4}, H_{t-4}, K_{t-4}, W_{t-4} \\ T^2_{t-4} & \propto A_{t-4}, B_{t-4}, C_{t-4} \\ T^1_{t-3} & \propto D_{t-4} + T^1_{t-4}, E_{t-4}, F_{t-4}, G_{t-4}, K_{t-3}, W_{t-3} \\ T^2_{t-3} & \propto T^1_{t-4} + T^2_{t-4}, A_{t-4}, B_{t-4} \\ T^1_{t-2} & \propto C_{t-4} + T^1_{t-3}, D_{t-4} + T^1_{t-4}, E_{t-4}, F_{t-4}, K_{t-2}, W_{t-2} \\ T^2_{t-2} & \propto T^1_{t-3} + T^2_{t-3}, T^1_{t-4} + T^2_{t-4}, A_{t-4} \\ T^1_{t-1} & \propto B_{t-4} + T^1_{t-2}, C_{t-4} + T^1_{t-3}, D_{t-4} + T^1_{t-4}, E_{t-4}, K_{t-1}, W_{t-1} \\ T^2_{t-1} & \propto T^1_{t-2} + T^2_{t-2}, T^1_{t-3} + T^2_{t-3}, T^1_{t-4} + T^2_{t-4} \\ A_t & = T^1_{t-1} + T^2_{t-1} \\ B_t & = T^1_{t-2} + T^2_{t-2} \\ C_t & = T^1_{t-3} + T^2_{t-3} \\ D_t & = T^1_{t-4} + T^2_{t-4} \\ E_t & = A_{t-4} + T^1_{t-1} \\ F_t & = B_{t-4} + T^1_{t-2} \\ G_t & = C_{t-4} + T^1_{t-3} \\ H_t & = D_{t-4} + T^1_{t-4} \end{align*}

Assuming to employ internal signals for the compute outputs, this expression can be rewritten as follows:

\begin{align*} T^1_{t-4} & \propto E_{t-4}, F_{t-4}, G_{t-4}, H_{t-4}, K_{t-4}, W_{t-4} \\ T^2_{t-4} & \propto A_{t-4}, B_{t-4}, C_{t-4} \\ T^1_{t-3} & \propto H_t, E_{t-4}, F_{t-4}, G_{t-4}, K_{t-3}, W_{t-3} \\ T^2_{t-3} & \propto D_t, A_{t-4}, B_{t-4} \\ T^1_{t-2} & \propto G_t, H_t, E_{t-4}, F_{t-4}, K_{t-2}, W_{t-2} \\ T^2_{t-2} & \propto C_t, D_t, A_{t-4} \\ T^1_{t-1} & \propto F_t, G_t, H_t, E_{t-4}, K_{t-1}, W_{t-1} \\ T^2_{t-1} & \propto B_t, G_t, D_t \\ A_t & = T^1_{t-1} + T^2_{t-1} \\ B_t & = T^1_{t-2} + T^2_{t-2} \\ C_t & = T^1_{t-3} + T^2_{t-3} \\ D_t & = T^1_{t-4} + T^2_{t-4} \\ E_t & = A_{t-4} + T^1_{t-1} \\ F_t & = B_{t-4} + T^1_{t-2} \\ G_t & = C_{t-4} + T^1_{t-3} \\ H_t & = D_{t-4} + T^1_{t-4} \end{align*}

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