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[book] sha256: Simplify compression region to reuse message schedule gates
This commit is contained in:
therealyingtong
parent
9612656fd6
commit
42988ce1d0
1 changed files with 97 additions and 101 deletions
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@ -349,22 +349,22 @@ Input from previous operations:
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- $evens$ is defined as $\mathtt{spread}(2^{32} - 1)$
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- $evens$ is defined as $\mathtt{spread}(2^{32} - 1)$
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- $evens_0 = evens_1 = \mathtt{spread}(2^{16} - 1)$
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- $evens_0 = evens_1 = \mathtt{spread}(2^{16} - 1)$
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sn|sc| $a_0$ | $a_1$ | $a_2$ | $a_3$ | $a_4$ |
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s_neg|s_ch| $a_0$ | $a_1$ | $a_2$ | $a_3$ | $a_4$ |
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--|--|-------------|-------------|-----------------------------|------------------------------------|------------------------------------|
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-----|----|-------------|-------------|-----------------------------|------------------------------------|------------------------------------|
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0 |0 |{0,1,2,3,4,5}|$P_0^{even}$ |$\texttt{spread}(P_0^{even})$| $\mathtt{spread}(E^{lo})$ | $\mathtt{spread}(E^{hi})$ |
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0 | 0 |{0,1,2,3,4,5}|$P_0^{even}$ |$\texttt{spread}(P_0^{even})$| $\mathtt{spread}(E^{lo})$ | $\mathtt{spread}(E^{hi})$ |
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0 |1 |{0,1,2,3,4,5}|$P_0^{odd}$ |$\texttt{spread}(P_0^{odd})$ |$\texttt{spread}(P_1^{odd})$ | |
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0 | 1 |{0,1,2,3,4,5}|$P_0^{odd}$ |$\texttt{spread}(P_0^{odd})$ |$\texttt{spread}(P_1^{odd})$ | |
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0 |0 |{0,1,2,3,4,5}|$P_1^{even}$ |$\texttt{spread}(P_1^{even})$| $\mathtt{spread}(F^{lo})$ | $\mathtt{spread}(F^{hi})$ |
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0 | 0 |{0,1,2,3,4,5}|$P_1^{even}$ |$\texttt{spread}(P_1^{even})$| $\mathtt{spread}(F^{lo})$ | $\mathtt{spread}(F^{hi})$ |
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0 |0 |{0,1,2,3,4,5}|$P_1^{odd}$ |$\texttt{spread}(P_1^{odd})$ | $evens_0$ | $evens_1$ |
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0 | 0 |{0,1,2,3,4,5}|$P_1^{odd}$ |$\texttt{spread}(P_1^{odd})$ | $evens_0$ | $evens_1$ |
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1 |0 |{0,1,2,3,4,5}|$Q_0^{even}$ |$\texttt{spread}(Q_0^{even})$|$\mathtt{spread}(E^{lo})$ | $\mathtt{spread}(E^{hi})$ |
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1 | 0 |{0,1,2,3,4,5}|$Q_0^{even}$ |$\texttt{spread}(Q_0^{even})$|$\mathtt{spread}(E^{lo})$ | $\mathtt{spread}(E^{hi})$ |
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0 |0 |{0,1,2,3,4,5}|$Q_0^{odd}$ |$\texttt{spread}(Q_0^{odd})$ |$evens_0 - \mathtt{spread}(E^{lo})$ |$evens_1 - \mathtt{spread}(E^{hi})$ |
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0 | 0 |{0,1,2,3,4,5}|$Q_0^{odd}$ |$\texttt{spread}(Q_0^{odd})$ |$evens_0 - \mathtt{spread}(E^{lo})$ |$evens_1 - \mathtt{spread}(E^{hi})$ |
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0 |1 |{0,1,2,3,4,5}|$Q_1^{even}$ |$\texttt{spread}(Q_1^{even})$|$\texttt{spread}(Q_1^{odd})$ | |
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0 | 1 |{0,1,2,3,4,5}|$Q_1^{even}$ |$\texttt{spread}(Q_1^{even})$|$\texttt{spread}(Q_1^{odd})$ | |
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0 |0 |{0,1,2,3,4,5}|$Q_1^{odd}$ |$\texttt{spread}(Q_1^{odd})$ |$\mathtt{spread}(G^{lo})$ | $\mathtt{spread}(G^{hi})$ |
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0 | 0 |{0,1,2,3,4,5}|$Q_1^{odd}$ |$\texttt{spread}(Q_1^{odd})$ |$\mathtt{spread}(G^{lo})$ | $\mathtt{spread}(G^{hi})$ |
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Constraints:
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Constraints:
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- `sc` (choice): $LHS - RHS = 0$
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- `s_ch` (choice): $LHS - RHS = 0$
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- $LHS = a_3 \omega^{-1} + a_3 \omega + 2^{32}(a_4 \omega^{-1} + a_4 \omega)$
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- $LHS = a_3 \omega^{-1} + a_3 \omega + 2^{32}(a_4 \omega^{-1} + a_4 \omega)$
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- $RHS = a_2 \omega^{-1} + 2* a_2 + 2^{32}(a_2 \omega + 2* a_3)$
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- $RHS = a_2 \omega^{-1} + 2* a_2 + 2^{32}(a_2 \omega + 2* a_3)$
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- `sn` (negation):
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- `s_neg` (negation):
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- $a_3\omega^{-1} - a_3 - a_3\omega = 0$
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- $a_3\omega^{-1} - a_3 - a_3\omega = 0$
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- $a_4\omega^{-1} - a_4 - a_4\omega = 0$
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- $a_4\omega^{-1} - a_4 - a_4\omega = 0$
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- $\mathtt{spread}$ lookup on $(a_0, a_1, a_2)$
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- $\mathtt{spread}$ lookup on $(a_0, a_1, a_2)$
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@ -378,15 +378,15 @@ Input from previous operations:
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- $A', B', C',$ 64-bit spread forms of 32-bit words $A, B, C$, assumed to be constrained by previous operations
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- $A', B', C',$ 64-bit spread forms of 32-bit words $A, B, C$, assumed to be constrained by previous operations
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- in practice, we'll have the spread forms of $A', B', C'$ after they've been decomposed into $16$-bit subpieces
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- in practice, we'll have the spread forms of $A', B', C'$ after they've been decomposed into $16$-bit subpieces
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sm| $a_0$ | $a_1$ | $a_2$ | $a_3$ | $a_4$ | $a_5$ |
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s_maj| $a_0$ | $a_1$ | $a_2$ | $a_3$ | $a_4$ | $a_5$ |
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--|-------------|------------|-----------------------------|----------------------------|--------------------------|--------------------------|
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-----|-------------|------------|-----------------------------|----------------------------|--------------------------|--------------------------|
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0 |{0,1,2,3,4,5}|$M_0^{even}$|$\texttt{spread}(M_0^{even})$| |$\mathtt{spread}(A^{lo})$ |$\mathtt{spread}(A^{hi})$ |
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0 |{0,1,2,3,4,5}|$M_0^{even}$|$\texttt{spread}(M_0^{even})$| |$\mathtt{spread}(A^{lo})$ |$\mathtt{spread}(A^{hi})$ |
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1 |{0,1,2,3,4,5}|$M_0^{odd}$ |$\texttt{spread}(M_0^{odd})$ |$\texttt{spread}(M_1^{odd})$|$\mathtt{spread}(B^{lo})$ |$\mathtt{spread}(B^{hi})$ |
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1 |{0,1,2,3,4,5}|$M_0^{odd}$ |$\texttt{spread}(M_0^{odd})$ |$\texttt{spread}(M_1^{odd})$|$\mathtt{spread}(B^{lo})$ |$\mathtt{spread}(B^{hi})$ |
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0 |{0,1,2,3,4,5}|$M_1^{even}$|$\texttt{spread}(M_1^{even})$| |$\mathtt{spread}(C^{lo})$ |$\mathtt{spread}(C^{hi})$ |
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0 |{0,1,2,3,4,5}|$M_1^{even}$|$\texttt{spread}(M_1^{even})$| |$\mathtt{spread}(C^{lo})$ |$\mathtt{spread}(C^{hi})$ |
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0 |{0,1,2,3,4,5}|$M_1^{odd}$ |$\texttt{spread}(M_1^{odd})$ | | | |
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0 |{0,1,2,3,4,5}|$M_1^{odd}$ |$\texttt{spread}(M_1^{odd})$ | | | |
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Constraints:
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Constraints:
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- `sm` (majority): $LHS - RHS = 0$
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- `s_maj` (majority): $LHS - RHS = 0$
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- $LHS = \mathtt{spread}(M^{even}_0) + 2 \cdot \mathtt{spread}(M^{odd}_0) + 2^{32} \cdot \mathtt{spread}(M^{even}_1) + 2^{33} \cdot \mathtt{spread}(M^{odd}_1)$
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- $LHS = \mathtt{spread}(M^{even}_0) + 2 \cdot \mathtt{spread}(M^{odd}_0) + 2^{32} \cdot \mathtt{spread}(M^{even}_1) + 2^{33} \cdot \mathtt{spread}(M^{odd}_1)$
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- $RHS = A' + B' + C'$
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- $RHS = A' + B' + C'$
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- $\mathtt{spread}$ lookup on $(a_0, a_1, a_2)$
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- $\mathtt{spread}$ lookup on $(a_0, a_1, a_2)$
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@ -405,17 +405,16 @@ $$
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\end{array}
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\end{array}
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$$
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$$
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ss| $a_0$ | $a_1$ | $a_2$ | $a_3$ | $a_4$ | $a_5$ | $a_6$ |
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s_upp_sigma_0| $a_0$ | $a_1$ | $a_2$ | $a_3$ | $a_4$ | $a_5$ | $a_6$ |
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--|-------------|------------|-----------------------------|------------|-----------------------------|-----------------------------|-----------------------------|
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-------------|-------------|------------|-----------------------------|------------------------------|----------------------------|------------------------|-----------------------------|
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0 | {0,1} | $d(10)$ | $\texttt{spread}(d(10))$ | $a(2)$ | $\texttt{spread}(a(2))$ | $c(9)^{lo}$ | $\texttt{spread}(c(9)^{lo})$|
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0 |{0,1,2,3,4,5}|$R_0^{even}$|$\texttt{spread}(R_0^{even})$| $c(9)^{lo}$ |$\texttt{spread}(c(9)^{lo})$| $c(9)^{mid}$ |$\texttt{spread}(c(9)^{mid})$|
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1 |{0,1,2,3,4,5}|$R_0^{even}$|$\texttt{spread}(R_0^{even})$| $A$ | $\texttt{spread}(R_0^{odd})$|$\texttt{spread}(R_1^{even})$| $\texttt{spread}(R_1^{odd})$|
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1 |{0,1,2,3,4,5}|$R_0^{odd}$ |$\texttt{spread}(R_0^{odd})$ | $\texttt{spread}(R_1^{odd})$ | $\texttt{spread}(d(10))$ |$\texttt{spread}(b(11))$| $c(9)$ |
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0 | {0,1,2} | $b(11)$ | $\texttt{spread}(b(11))$ |$c(9)^{mid}$|$\texttt{spread}(c(9)^{mid})$| $c(9)^{hi}$ | $\texttt{spread}(c(9)^{hi})$|
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0 |{0,1,2,3,4,5}|$R_1^{even}$|$\texttt{spread}(R_1^{even})$| $a(2)$ |$\texttt{spread}(a(2))$ | $c(9)^{hi}$ |$\texttt{spread}(c(9)^{hi})$ |
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0 |{0,1,2,3,4,5}|$R_0^{odd}$ |$\texttt{spread}(R_0^{odd})$ | | | | |
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0 |{0,1,2,3,4,5}|$R_1^{odd}$ |$\texttt{spread}(R_1^{odd})$ | | | | |
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0 |{0,1,2,3,4,5}|$R_1^{even}$|$\texttt{spread}(R_1^{even})$| | | | |
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0 |{0,1,2,3,4,5}|$R_1^{odd}$ |$\texttt{spread}(R_1^{odd})$ | | | | |
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Constraints:
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Constraints:
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- `ss` ($\Sigma_0$ constraint): $LHS - RHS + tag + decompose = 0$
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- `s_upp_sigma_0` ($\Sigma_0$ constraint): $LHS - RHS + tag + decompose = 0$
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$$
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$$
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\begin{array}{ccc}
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\begin{array}{ccc}
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@ -450,17 +449,16 @@ $$
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\end{array}
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\end{array}
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$$
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$$
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ss| $a_0$ | $a_1$ | $a_2$ | $a_3$ | $a_4$ | $a_5$ | $a_6$ |
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s_upp_sigma_1| $a_0$ | $a_1$ | $a_2$ | $a_3$ | $a_4$ | $a_5$ | $a_6$ | $a_7$ |
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--|-------------|------------|-----------------------------|------------|-----------------------------|-----------------------------|-----------------------------|
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-------------|-------------|------------|-----------------------------|------------------------------|----------------------------|------------------------|-----------------------------|------------|
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0 | 0 | $d(7)$ | $\texttt{spread}(d(7))$ | $b(5)^{lo}$| $\texttt{spread}(b(5)^{lo})$| $b(5)^{hi}$ | $\texttt{spread}(b(5)^{hi})$|
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0 |{0,1,2,3,4,5}|$R_0^{even}$|$\texttt{spread}(R_0^{even})$| $b(5)^{lo}$ |$\texttt{spread}(b(5)^{lo})$| $b(5)^{hi}$ |$\texttt{spread}(b(5)^{hi})$ | $b(5)$ |
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1 |{0,1,2,3,4,5}|$R_0^{even}$|$\texttt{spread}(R_0^{even})$| $E$ | $\texttt{spread}(R_0^{odd})$|$\texttt{spread}(R_1^{even})$| $\texttt{spread}(R_1^{odd})$|
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1 |{0,1,2,3,4,5}|$R_0^{odd}$ |$\texttt{spread}(R_0^{odd})$ | $\texttt{spread}(R_1^{odd})$ | $\texttt{spread}(d(7))$ |$\texttt{spread}(c(14))$| | |
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0 | {0,1,2,3,4} | $c(14)$ | $\texttt{spread}(c(14))$ | $a(6)^{lo}$| $\texttt{spread}(a(6)^{lo})$| $a(6)^{hi}$ | $\texttt{spread}(a(6)^{hi})$|
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0 |{0,1,2,3,4,5}|$R_1^{even}$|$\texttt{spread}(R_1^{even})$| $a(6)^{lo}$ |$\texttt{spread}(a(6)^{lo})$| $a(6)^{hi}$ |$\texttt{spread}(a(6)^{hi})$ | $a(6)$ |
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0 |{0,1,2,3,4,5}|$R_0^{odd}$ |$\texttt{spread}(R_0^{odd})$ | | | | |
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0 |{0,1,2,3,4,5}|$R_1^{odd}$ |$\texttt{spread}(R_1^{odd})$ | | | | | |
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0 |{0,1,2,3,4,5}|$R_1^{even}$|$\texttt{spread}(R_1^{even})$| | | | |
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0 |{0,1,2,3,4,5}|$R_1^{odd}$ |$\texttt{spread}(R_1^{odd})$ | | | | |
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Constraints:
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Constraints:
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- `ss` ($\Sigma_1$ constraint): $LHS - RHS + tag + decompose = 0$
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- `s_upp_sigma_1` ($\Sigma_1$ constraint): $LHS - RHS + tag + decompose = 0$
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$$
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$$
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\begin{array}{ccc}
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\begin{array}{ccc}
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@ -492,15 +490,15 @@ v1 of the $\sigma_0$ gate takes in a word that's split into $(3, 4, 11, 14)$-bit
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$(X ⋙ 7) \oplus (X ⋙ 18) \oplus (X ≫ 3)$ is equivalent to
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$(X ⋙ 7) \oplus (X ⋙ 18) \oplus (X ≫ 3)$ is equivalent to
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$(X ⋙ 7) \oplus (X ⋘ 14) \oplus (X ≫ 3)$.
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$(X ⋙ 7) \oplus (X ⋘ 14) \oplus (X ≫ 3)$.
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ss0| $a_0$ | $a_1$ | $a_2$ | $a_3$ | $a_4$ | $a_5$ | $a_6$ |
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s_low_sigma_0| $a_0$ | $a_1$ | $a_2$ | $a_3$ | $a_4$ | $a_5$ | $a_6$ |
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---|-------------|------------|-----------------------------|-----------------------------|----------------------------|--------------------|----------------------------|
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-------------|-------------|------------|-----------------------------|-----------------------------|----------------------------|--------------------|----------------------------|
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0 |{0,1,2,3,4,5}|$R_0^{even}$|$\texttt{spread}(R_0^{even})$| $b(4)^{lo}$ |$\texttt{spread}(b(4)^{lo})$| $b(4)^{hi}$ |$\texttt{spread}(b(4)^{hi})$|
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0 |{0,1,2,3,4,5}|$R_0^{even}$|$\texttt{spread}(R_0^{even})$| $b(4)^{lo}$ |$\texttt{spread}(b(4)^{lo})$| $b(4)^{hi}$ |$\texttt{spread}(b(4)^{hi})$|
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1 |{0,1,2,3,4,5}|$R_0^{odd}$ |$\texttt{spread}(R_0^{odd})$ |$\texttt{spread}(R_1^{odd})$ |$\texttt{spread}(c)$ |$\texttt{spread}(d)$| $b(4)$ |
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1 |{0,1,2,3,4,5}|$R_0^{odd}$ |$\texttt{spread}(R_0^{odd})$ |$\texttt{spread}(R_1^{odd})$ |$\texttt{spread}(c)$ |$\texttt{spread}(d)$| $b(4)$ |
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0 |{0,1,2,3,4,5}|$R_1^{even}$|$\texttt{spread}(R_1^{even})$| $0$ | $0$ | $a$ | $\texttt{spread}(a)$ |
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0 |{0,1,2,3,4,5}|$R_1^{even}$|$\texttt{spread}(R_1^{even})$| $0$ | $0$ | $a$ | $\texttt{spread}(a)$ |
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0 |{0,1,2,3,4,5}|$R_1^{odd}$ |$\texttt{spread}(R_1^{odd})$ | | | | |
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0 |{0,1,2,3,4,5}|$R_1^{odd}$ |$\texttt{spread}(R_1^{odd})$ | | | | |
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Constraints:
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Constraints:
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- `ss` ($\sigma_0$ v1 constraint): $LHS - RHS = 0$
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- `s_low_sigma_0` ($\sigma_0$ v1 constraint): $LHS - RHS = 0$
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$$
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$$
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\begin{array}{ccc}
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\begin{array}{ccc}
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@ -527,15 +525,15 @@ v2 of the $\sigma_0$ gate takes in a word that's split into $(3, 4, 3, 7, 1, 1,
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$(X ⋙ 7) \oplus (X ⋙ 18) \oplus (X ≫ 3)$ is equivalent to
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$(X ⋙ 7) \oplus (X ⋙ 18) \oplus (X ≫ 3)$ is equivalent to
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$(X ⋙ 7) \oplus (X ⋘ 14) \oplus (X ≫ 3)$.
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$(X ⋙ 7) \oplus (X ⋘ 14) \oplus (X ≫ 3)$.
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ss0_v2| $a_0$ | $a_1$ | $a_2$ | $a_3$ | $a_4$ | $a_5$ | $a_6$ | $a_7$ |
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s_low_sigma_0_v2| $a_0$ | $a_1$ | $a_2$ | $a_3$ | $a_4$ | $a_5$ | $a_6$ | $a_7$ |
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------|-------------|------------|-----------------------------|-----------------------------|----------------------------|------------------------|----------------------------|------------|
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----------------|-------------|------------|-----------------------------|-----------------------------|----------------------------|------------------------|----------------------------|------------|
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0 |{0,1,2,3,4,5}|$R_0^{even}$|$\texttt{spread}(R_0^{even})$| $b(4)^{lo}$ |$\texttt{spread}(b(4)^{lo})$| $b(4)^{hi}$ |$\texttt{spread}(b(4)^{hi})$| |
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0 |{0,1,2,3,4,5}|$R_0^{even}$|$\texttt{spread}(R_0^{even})$| $b(4)^{lo}$ |$\texttt{spread}(b(4)^{lo})$| $b(4)^{hi}$ |$\texttt{spread}(b(4)^{hi})$| |
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1 |{0,1,2,3,4,5}|$R_0^{odd}$ |$\texttt{spread}(R_0^{odd})$ | $\texttt{spread}(R_1^{odd})$| $\texttt{spread}(d(7))$ |$\texttt{spread}(g(13))$| $b(4)$ | $e(1)$ |
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1 |{0,1,2,3,4,5}|$R_0^{odd}$ |$\texttt{spread}(R_0^{odd})$ | $\texttt{spread}(R_1^{odd})$| $\texttt{spread}(d(7))$ |$\texttt{spread}(g(13))$| $b(4)$ | $e(1)$ |
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0 |{0,1,2,3,4,5}|$R_1^{even}$|$\texttt{spread}(R_1^{even})$| $a(3)$ |$\texttt{spread}(a(3))$ | $c(3)$ |$\texttt{spread}(c(3))$ | $f(1)$ |
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0 |{0,1,2,3,4,5}|$R_1^{even}$|$\texttt{spread}(R_1^{even})$| $a(3)$ |$\texttt{spread}(a(3))$ | $c(3)$ |$\texttt{spread}(c(3))$ | $f(1)$ |
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0 |{0,1,2,3,4,5}|$R_1^{odd}$ |$\texttt{spread}(R_1^{odd})$ | | | | | |
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0 |{0,1,2,3,4,5}|$R_1^{odd}$ |$\texttt{spread}(R_1^{odd})$ | | | | | |
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Constraints:
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Constraints:
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- `ss0_v2` ($\sigma_0$ v2 constraint): $LHS - RHS = 0$
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- `s_low_sigma_0_v2` ($\sigma_0$ v2 constraint): $LHS - RHS = 0$
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$$
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$$
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\begin{array}{ccc}
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\begin{array}{ccc}
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@ -562,15 +560,15 @@ v1 of the $\sigma_1$ gate takes in a word that's split into $(10, 7, 2, 13)$-bit
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$(X ⋙ 17) \oplus (X ⋙ 19) \oplus (X ≫ 10)$ is equivalent to
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$(X ⋙ 17) \oplus (X ⋙ 19) \oplus (X ≫ 10)$ is equivalent to
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$(X ⋘ 15) \oplus (X ⋘ 13) \oplus (X ≫ 10)$.
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$(X ⋘ 15) \oplus (X ⋘ 13) \oplus (X ≫ 10)$.
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ss1| $a_0$ | $a_1$ | $a_2$ | $a_3$ | $a_4$ | $a_5$ | $a_6$ |
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s_low_sigma_1| $a_0$ | $a_1$ | $a_2$ | $a_3$ | $a_4$ | $a_5$ | $a_6$ |
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---|-------------|------------|-----------------------------|------------------------------|----------------------------|------------------------|-----------------------------|
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-------------|-------------|------------|-----------------------------|------------------------------|----------------------------|------------------------|-----------------------------|
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0 |{0,1,2,3,4,5}|$R_0^{even}$|$\texttt{spread}(R_0^{even})$| $b(7)^{lo}$ |$\texttt{spread}(b(7)^{lo})$| $b(7)^{mid}$ |$\texttt{spread}(b(7)^{mid})$|
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0 |{0,1,2,3,4,5}|$R_0^{even}$|$\texttt{spread}(R_0^{even})$| $b(7)^{lo}$ |$\texttt{spread}(b(7)^{lo})$| $b(7)^{mid}$ |$\texttt{spread}(b(7)^{mid})$|
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1 |{0,1,2,3,4,5}|$R_0^{odd}$ |$\texttt{spread}(R_0^{odd})$ | $\texttt{spread}(R_1^{odd})$ | $\texttt{spread}(a(10))$ |$\texttt{spread}(d(13))$| $b(7)$ |
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1 |{0,1,2,3,4,5}|$R_0^{odd}$ |$\texttt{spread}(R_0^{odd})$ | $\texttt{spread}(R_1^{odd})$ | $\texttt{spread}(a(10))$ |$\texttt{spread}(d(13))$| $b(7)$ |
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0 |{0,1,2,3,4,5}|$R_1^{even}$|$\texttt{spread}(R_1^{even})$| $c(2)$ |$\texttt{spread}(c(2))$ | $b(7)^{hi}$ |$\texttt{spread}(b(7)^{hi})$ |
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0 |{0,1,2,3,4,5}|$R_1^{even}$|$\texttt{spread}(R_1^{even})$| $c(2)$ |$\texttt{spread}(c(2))$ | $b(7)^{hi}$ |$\texttt{spread}(b(7)^{hi})$ |
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||||||
0 |{0,1,2,3,4,5}|$R_1^{odd}$ |$\texttt{spread}(R_1^{odd})$ | | | | |
|
0 |{0,1,2,3,4,5}|$R_1^{odd}$ |$\texttt{spread}(R_1^{odd})$ | | | | |
|
||||||
|
|
||||||
Constraints:
|
Constraints:
|
||||||
- `ss1` ($\sigma_1$ v1 constraint): $LHS - RHS = 0$
|
- `s_low_sigma_1` ($\sigma_1$ v1 constraint): $LHS - RHS = 0$
|
||||||
$$
|
$$
|
||||||
\begin{array}{ccc}
|
\begin{array}{ccc}
|
||||||
LHS &=& \mathtt{spread}(R^{even}_0) + 2 \cdot \mathtt{spread}(R^{odd}_0) + 2^{32} \cdot \mathtt{spread}(R^{even}_1) + 2^{33} \cdot \mathtt{spread}(R^{odd}_1)
|
LHS &=& \mathtt{spread}(R^{even}_0) + 2 \cdot \mathtt{spread}(R^{odd}_0) + 2^{32} \cdot \mathtt{spread}(R^{even}_1) + 2^{33} \cdot \mathtt{spread}(R^{odd}_1)
|
||||||
|
|
@ -596,15 +594,15 @@ v2 of the $\sigma_1$ gate takes in a word that's split into $(3, 4, 3, 7, 1, 1,
|
||||||
$(X ⋙ 17) \oplus (X ⋙ 19) \oplus (X ≫ 10)$ is equivalent to
|
$(X ⋙ 17) \oplus (X ⋙ 19) \oplus (X ≫ 10)$ is equivalent to
|
||||||
$(X ⋘ 15) \oplus (X ⋘ 13) \oplus (X ≫ 10)$.
|
$(X ⋘ 15) \oplus (X ⋘ 13) \oplus (X ≫ 10)$.
|
||||||
|
|
||||||
ss1_v2| $a_0$ | $a_1$ | $a_2$ | $a_3$ | $a_4$ | $a_5$ | $a_6$ | $a_7$ |
|
s_low_sigma_1_v2| $a_0$ | $a_1$ | $a_2$ | $a_3$ | $a_4$ | $a_5$ | $a_6$ | $a_7$ |
|
||||||
------|-------------|------------|-----------------------------|-----------------------------|----------------------------|-------------------------|----------------------------|------------|
|
----------------|-------------|------------|-----------------------------|-----------------------------|----------------------------|-------------------------|----------------------------|------------|
|
||||||
0 |{0,1,2,3,4,5}|$R_0^{even}$|$\texttt{spread}(R_0^{even})$| $b(4)^{lo}$ |$\texttt{spread}(b(4)^{lo})$| $b(4)^{hi}$ |$\texttt{spread}(b(4)^{hi})$| |
|
0 |{0,1,2,3,4,5}|$R_0^{even}$|$\texttt{spread}(R_0^{even})$| $b(4)^{lo}$ |$\texttt{spread}(b(4)^{lo})$| $b(4)^{hi}$ |$\texttt{spread}(b(4)^{hi})$| |
|
||||||
1 |{0,1,2,3,4,5}|$R_0^{odd}$ |$\texttt{spread}(R_0^{odd})$ | $\texttt{spread}(R_1^{odd})$| $\texttt{spread}(d(7))$ | $\texttt{spread}(g(13))$| $b(4)$ | $e(1)$ |
|
1 |{0,1,2,3,4,5}|$R_0^{odd}$ |$\texttt{spread}(R_0^{odd})$ | $\texttt{spread}(R_1^{odd})$| $\texttt{spread}(d(7))$ | $\texttt{spread}(g(13))$| $b(4)$ | $e(1)$ |
|
||||||
0 |{0,1,2,3,4,5}|$R_1^{even}$|$\texttt{spread}(R_1^{even})$| $a(3)$ |$\texttt{spread}(a(3))$ | $c(3)$ |$\texttt{spread}(c(3))$ | $f(1)$ |
|
0 |{0,1,2,3,4,5}|$R_1^{even}$|$\texttt{spread}(R_1^{even})$| $a(3)$ |$\texttt{spread}(a(3))$ | $c(3)$ |$\texttt{spread}(c(3))$ | $f(1)$ |
|
||||||
0 |{0,1,2,3,4,5}|$R_1^{odd}$ |$\texttt{spread}(R_1^{odd})$ | | | | | |
|
0 |{0,1,2,3,4,5}|$R_1^{odd}$ |$\texttt{spread}(R_1^{odd})$ | | | | | |
|
||||||
|
|
||||||
Constraints:
|
Constraints:
|
||||||
- `ss1_v2` ($\sigma_1$ v2 constraint): $LHS - RHS = 0$
|
- `s_low_sigma_1_v2` ($\sigma_1$ v2 constraint): $LHS - RHS = 0$
|
||||||
|
|
||||||
$$
|
$$
|
||||||
\begin{array}{ccc}
|
\begin{array}{ccc}
|
||||||
|
|
@ -825,39 +823,37 @@ Constraints:
|
||||||
|
|
||||||
#### Initial round:
|
#### Initial round:
|
||||||
|
|
||||||
sd_abcd|sd_efgh|ss0|ss1|s_maj|s_neg|s_ch| $a_0$ | $a_1$ | $a_2$ | $a_3$ | $a_4$ | $a_5$ | $a_6$ | $a_7$ | $a_8$ |
|
sd_abcd|sd_efgh|ss0|ss1|s_maj|s_neg|s_ch| $a_0$ | $a_1$ | $a_2$ | $a_3$ | $a_4$ | $a_5$ | $a_6$ | $a_7$ | $a_8$ | $a_9$ |
|
||||||
-------|-------|---|---|-----|-----|----|-------------|------------|-----------------------------|-------------------------------------|-------------------------------------|----------------------------------------|------------------------------------|------------------------------------|------------------------------------|
|
-------|-------|---|---|-----|-----|----|-------------|------------|-----------------------------|-------------------------------------|-------------------------------------|----------------------------------------|------------------------------------|------------------------------------|------------------------------------|------------------------------------|
|
||||||
0 | 1 | 0 | 0 | 0 | 0 | 0 | {0,1,2} |$IV[4]d(7)$ |$\texttt{spread}(IV[4]d(7)) $| $IV[4]b(5)^{lo}$ | $\texttt{spread}(IV[4]b(5)^{lo})$ | $IV[4]b(5)^{hi}$ | $\texttt{spread}(IV[4]b(5)^{hi}) $ | $E_0^{lo}$ | $\mathtt{spread}(E_0^{lo})$ |
|
0 | 1 | 0 | 0 | 0 | 0 | 0 | {0,1,2} |$F_0 d(7)$ |$\texttt{spread}(E_0 d(7)) $ | $E_0 b(5)^{lo}$ | $\texttt{spread}(E_0 b(5)^{lo})$ | $E_0 b(5)^{hi}$ | $\texttt{spread}(E_0 b(5)^{hi}) $ | $E_0^{lo}$ | $\mathtt{spread}(E_0^{lo})$ | |
|
||||||
0 | 0 | 0 | 1 | 0 | 0 | 0 |{0,1,2,3,4,5}|$R_0^{odd}$ |$\texttt{spread}(R_0^{odd})$ | $\texttt{spread}(R_1^{odd})$ | $\texttt{spread}(R_0^{even})$ | $\texttt{spread}(R_1^{even})$ | | $E_0^{hi}$ | $\mathtt{spread}(E_0^{hi})$ |
|
0 | 0 | 0 | 0 | 0 | 0 | 0 | {0,1} |$E_0 c(14)$ |$\texttt{spread}(E_0 c(14))$ | $E_0 a(6)^{lo}$ | $\texttt{spread}(E_0 a(6)^{lo})$ | $E_0 a(6)^{hi}$ | $\texttt{spread}(E_0 a(6)^{hi}) $ | $E_0^{hi}$ | $\mathtt{spread}(E_0^{hi})$ | |
|
||||||
0 | 0 | 0 | 0 | 0 | 0 | 0 | {0,1} |$IV[4]c(14)$|$\texttt{spread}(IV[4]c(14))$| $IV[4]a(6)^{lo}$ | $\texttt{spread}(IV[4]a(6)^{lo})$ | $IV[4]a(6)^{hi}$ | $\texttt{spread}(IV[4]a(6)^{hi}) $ | | |
|
0 | 0 | 0 | 0 | 0 | 0 | 0 |{0,1,2,3,4,5}|$R_0^{even}$|$\texttt{spread}(R_0^{even})$| $\texttt{spread}(E_0 b(5)^{lo})$ | $\texttt{spread}(E_0 b(5)^{hi})$ | | | | | |
|
||||||
0 | 0 | 0 | 0 | 0 | 0 | 0 |{0,1,2,3,4,5}|$R_1^{odd}$ |$\texttt{spread}(R_1^{odd})$ | $K_0^{lo}$ | $W_0^{lo}$ | $Ch(E_0,F_0,G_0)_{lo}$ | $Hprime_0^{lo}$ | $H_0^{lo}$ | $\mathtt{spread}(H_0^{lo})$ |
|
0 | 0 | 0 | 1 | 0 | 0 | 0 |{0,1,2,3,4,5}|$R_0^{odd}$ |$\texttt{spread}(R_0^{odd})$ | $\texttt{spread}(R_1^{odd})$ | $\texttt{spread}(E_0 d(7))$ | $\texttt{spread}(E_0 c(14))$ | | | | |
|
||||||
0 | 0 | 0 | 0 | 0 | 0 | 0 |{0,1,2,3,4,5}|$R_0^{even}$|$\texttt{spread}(R_0^{even})$| $K_0^{hi}$ | $W_0^{hi}$ | $Ch(E_0,F_0,G_0)_{hi}$ | $Hprime_0^{hi}$ | $H_0^{hi}$ | $\mathtt{spread}(H_0^{hi})$ |
|
0 | 0 | 0 | 0 | 0 | 0 | 0 |{0,1,2,3,4,5}|$R_1^{even}$|$\texttt{spread}(R_1^{even})$| $\texttt{spread}(E_0 a(6)^{lo})$ | $\texttt{spread}(E_0 a(6)^{hi})$ | | | | | |
|
||||||
0 | 0 | 0 | 0 | 0 | 0 | 0 |{0,1,2,3,4,5}|$R_1^{even}$|$\texttt{spread}(R_1^{even})$| | | | $Hprime_0 carry$ | | |
|
0 | 0 | 0 | 0 | 0 | 0 | 0 |{0,1,2,3,4,5}|$R_1^{odd}$ |$\texttt{spread}(R_1^{odd})$ | | | | | | | |
|
||||||
0 | 1 | 0 | 0 | 0 | 0 | 0 | {0,1,2} |$IV[5]d(7)$ |$\texttt{spread}(IV[5]d(7)) $| $IV[5]b(5)^{lo}$ | $\texttt{spread}(IV[5]b(5)^{lo})$ | $IV[5]b(5)^{hi}$ | $\texttt{spread}(IV[5]b(5)^{hi}) $ | $F_0^{lo}$ | $\mathtt{spread}(F_0^{lo})$ |
|
0 | 1 | 0 | 0 | 0 | 0 | 0 | {0,1,2} |$F_0 d(7)$ |$\texttt{spread}(F_0 d(7)) $ | $F_0 b(5)^{lo}$ | $\texttt{spread}(F_0 b(5)^{lo})$ | $F_0 b(5)^{hi}$ | $\texttt{spread}(F_0 b(5)^{hi}) $ | $F_0^{lo}$ | $\mathtt{spread}(F_0^{lo})$ | |
|
||||||
0 | 0 | 0 | 0 | 0 | 0 | 0 | {0,1} |$IV[5]c(14)$|$\texttt{spread}(IV[5]c(14))$| $IV[5]a(6)^{lo}$ | $\texttt{spread}(IV[5]a(6)^{lo})$ | $IV[5]a(6)^{hi}$ | $\texttt{spread}(IV[5]a(6)^{hi}) $ | $F_0^{hi}$ | $\mathtt{spread}(F_0^{hi})$ |
|
0 | 0 | 0 | 0 | 0 | 0 | 0 | {0,1} |$F_0 c(14)$ |$\texttt{spread}(F_0 c(14))$ | $F_0 a(6)^{lo}$ | $\texttt{spread}(F_0 a(6)^{lo})$ | $F_0 a(6)^{hi}$ | $\texttt{spread}(F_0 a(6)^{hi}) $ | $F_0^{hi}$ | $\mathtt{spread}(F_0^{hi})$ | |
|
||||||
0 | 1 | 0 | 0 | 0 | 0 | 0 | {0,1,2} |$IV[6]d(7)$ |$\texttt{spread}(IV[6]d(7)) $| $IV[6]b(5)^{lo}$ | $\texttt{spread}(IV[6]b(5)^{lo})$ | $IV[6]b(5)^{hi}$ | $\texttt{spread}(IV[6]b(5)^{hi}) $ | $G_0^{lo}$ | $\mathtt{spread}(G_0^{lo})$ |
|
0 | 1 | 0 | 0 | 0 | 0 | 0 | {0,1,2} |$G_0 d(7)$ |$\texttt{spread}(G_0 d(7)) $ | $G_0 b(5)^{lo}$ | $\texttt{spread}(G_0 b(5)^{lo})$ | $G_0 b(5)^{hi}$ | $\texttt{spread}(G_0 b(5)^{hi}) $ | $G_0^{lo}$ | $\mathtt{spread}(G_0^{lo})$ | |
|
||||||
0 | 0 | 0 | 0 | 0 | 0 | 0 | {0,1} |$IV[6]c(14)$|$\texttt{spread}(IV[6]c(14))$| $IV[6]a(6)^{lo}$ | $\texttt{spread}(IV[6]a(6)^{lo})$ | $IV[6]a(6)^{hi}$ | $\texttt{spread}(IV[6]a(6)^{hi}) $ | $G_0^{hi}$ | $\mathtt{spread}(G_0^{hi})$ |
|
0 | 0 | 0 | 0 | 0 | 0 | 0 | {0,1} |$G_0 c(14)$ |$\texttt{spread}(G_0 c(14))$ | $G_0 a(6)^{lo}$ | $\texttt{spread}(G_0 a(6)^{lo})$ | $G_0 a(6)^{hi}$ | $\texttt{spread}(G_0 a(6)^{hi}) $ | $G_0^{hi}$ | $\mathtt{spread}(G_0^{hi})$ | |
|
||||||
0 | 0 | 0 | 0 | 0 | 0 | 0 |{0,1,2,3,4,5}|$P_0^{even}$|$\texttt{spread}(P_0^{even})$| $\mathtt{spread}(E_0^{lo})$ | $\mathtt{spread}(E_0^{hi})$ | $\texttt{spread}(Q_0^{odd})$ | | | |
|
0 | 0 | 0 | 0 | 0 | 0 | 0 |{0,1,2,3,4,5}|$P_0^{even}$|$\texttt{spread}(P_0^{even})$| $\mathtt{spread}(E_0^{lo})$ | $\mathtt{spread}(E_0^{hi})$ | $\texttt{spread}(Q_0^{odd})$ | $K_0^{lo}$ | $H_0^{lo}$ | $\mathtt{spread}(H_0^{lo})$ | $W_0^{lo}$ |
|
||||||
0 | 0 | 0 | 0 | 0 | 0 | 1 |{0,1,2,3,4,5}|$P_0^{odd}$ |$\texttt{spread}(P_0^{odd})$ | $\texttt{spread}(P_1^{odd})$ | | $Ch(E,F,G)_0$ | | | |
|
0 | 0 | 0 | 0 | 0 | 0 | 1 |{0,1,2,3,4,5}|$P_0^{odd}$ |$\texttt{spread}(P_0^{odd})$ | $\texttt{spread}(P_1^{odd})$ | $\Sigma_1(E_0)^{lo}$ | $\Sigma_1(E_0)^{hi}$ | $K_0^{hi}$ | $H_0^{hi}$ | $\mathtt{spread}(H_0^{hi})$ | $W_0^{hi}$ |
|
||||||
0 | 0 | 0 | 0 | 0 | 0 | 0 |{0,1,2,3,4,5}|$P_1^{even}$|$\texttt{spread}(P_1^{even})$| $\mathtt{spread}(F^{lo})$ | $\mathtt{spread}(F^{hi})$ | $\texttt{spread}(Q_1^{odd})$ | | | |
|
0 | 0 | 0 | 0 | 0 | 0 | 0 |{0,1,2,3,4,5}|$P_1^{even}$|$\texttt{spread}(P_1^{even})$| $\mathtt{spread}(F^{lo})$ | $\mathtt{spread}(F^{hi})$ | $\texttt{spread}(Q_1^{odd})$ | | $Hprime_0^{lo}$ | $Hprime_0^{hi}$ | $Hprime_0 carry$ |
|
||||||
0 | 0 | 0 | 0 | 0 | 0 | 0 |{0,1,2,3,4,5}|$P_1^{odd}$ |$\texttt{spread}(P_1^{odd})$ | $evens_0$ | $evens_1$ | $Ch(E,F,G)_1$ | | | |
|
0 | 0 | 0 | 0 | 0 | 0 | 0 |{0,1,2,3,4,5}|$P_1^{odd}$ |$\texttt{spread}(P_1^{odd})$ | | | | $D_0^{lo}$ | $E_1^{lo}$ | $\mathtt{spread}(E_1^{lo})$ | |
|
||||||
0 | 0 | 0 | 0 | 0 | 1 | 0 |{0,1,2,3,4,5}|$Q_0^{even}$|$\texttt{spread}(Q_0^{even})$| $\mathtt{spread}(E_0^{lo})$ | $\mathtt{spread}(E_0^{hi})$ | | | | |
|
0 | 0 | 0 | 0 | 0 | 1 | 0 |{0,1,2,3,4,5}|$Q_0^{even}$|$\texttt{spread}(Q_0^{even})$| $\mathtt{spread}(E_0^{lo})$ | $\mathtt{spread}(E_0^{hi})$ | | $D_0^{hi}$ | $E_1^{hi}$ | $\mathtt{spread}(E_1^{hi})$ | $E_1 carry$ |
|
||||||
0 | 0 | 0 | 0 | 0 | 0 | 0 |{0,1,2,3,4,5}|$Q_0^{odd}$ |$\texttt{spread}(Q_0^{odd})$ |$evens_0 - \mathtt{spread}(E_0^{lo})$|$evens_1 - \mathtt{spread}(E_0^{hi})$| | | | |
|
0 | 0 | 0 | 0 | 0 | 0 | 0 |{0,1,2,3,4,5}|$Q_0^{odd}$ |$\texttt{spread}(Q_0^{odd})$ |$evens_0 - \mathtt{spread}(E_0^{lo})$|$evens_1 - \mathtt{spread}(E_0^{hi})$| | | $D_0^{lo}$ | $\mathtt{spread}(D_0^{lo})$ | |
|
||||||
0 | 0 | 0 | 0 | 0 | 0 | 1 |{0,1,2,3,4,5}|$Q_1^{even}$|$\texttt{spread}(Q_1^{even})$| $\texttt{spread}(Q_1^{odd})$ | | | | | |
|
0 | 0 | 0 | 0 | 0 | 0 | 1 |{0,1,2,3,4,5}|$Q_1^{even}$|$\texttt{spread}(Q_1^{even})$| $\texttt{spread}(Q_1^{odd})$ | | | | $D_0^{hi}$ | $\mathtt{spread}(D_0^{hi})$ | |
|
||||||
0 | 0 | 0 | 0 | 0 | 0 | 0 |{0,1,2,3,4,5}|$Q_1^{odd}$ |$\texttt{spread}(Q_1^{odd})$ | $\mathtt{spread}(G^{lo})$ | $\mathtt{spread}(G^{hi})$ | | | | |
|
0 | 0 | 0 | 0 | 0 | 0 | 0 |{0,1,2,3,4,5}|$Q_1^{odd}$ |$\texttt{spread}(Q_1^{odd})$ | $\mathtt{spread}(G^{lo})$ | $\mathtt{spread}(G^{hi})$ | | | | | |
|
||||||
1 | 0 | 0 | 0 | 0 | 0 | 0 | {0,1,2} |$IV[0]b(11)$|$\texttt{spread}(IV[0]b(11))$| $IV[0]c(9)^{lo}$ | $\texttt{spread}(IV[0]c(9)^{lo})$ | $IV[0]c(9)^{mid}$ | $\texttt{spread}(IV[0]c(9)^{mid})$ | $A_0^{lo}$ | $\mathtt{spread}(A_0^{lo})$ |
|
1 | 0 | 0 | 0 | 0 | 0 | 0 | {0,1,2} |$A_0 b(11)$ |$\texttt{spread}(A_0 b(11))$ | $A_0 c(9)^{lo}$ | $\texttt{spread}(A_0 c(9)^{lo})$ | $A_0 c(9)^{mid}$ | $\texttt{spread}(A_0 c(9)^{mid})$ | $A_0^{lo}$ | $\mathtt{spread}(A_0^{lo})$ | |
|
||||||
0 | 0 | 0 | 0 | 0 | 0 | 0 |{0,1,2,3,4,5}|$R_0^{odd}$ |$\texttt{spread}(R_0^{odd})$ | $\texttt{spread}(R_1^{odd})$ | $\texttt{spread}(R_0^{even})$ | $\texttt{spread}(R_1^{even})$ | | $A_0^{hi}$ | $\mathtt{spread}(A_0^{hi})$ |
|
0 | 0 | 0 | 0 | 0 | 0 | 0 | {0,1} |$A_0 d(10)$ |$\texttt{spread}(A_0 d(10))$ | $A_0 a(2)$ | $\texttt{spread}(A_0 a(2))$ | $A_0 c(9)^{hi}$ | $\texttt{spread}(A_0 c(9)^{hi})$ | $A_0^{hi}$ | $\mathtt{spread}(A_0^{hi})$ | |
|
||||||
0 | 0 | 0 | 0 | 0 | 0 | 0 | {0,1} |$IV[0]d(10)$|$\texttt{spread}(IV[0]d(10))$| $IV[0]a(2)$ | $\texttt{spread}(IV[0]a(2))$ | $IV[0]c(9)^{hi}$ | $\texttt{spread}(IV[0]c(9)^{hi})$ | | |
|
0 | 0 | 0 | 0 | 0 | 0 | 0 |{0,1,2,3,4,5}|$R_0^{even}$|$\texttt{spread}(R_0^{even})$| $\texttt{spread}(c(9)^{lo})$ | $\texttt{spread}(c(9)^{mid})$ | | | | | |
|
||||||
0 | 0 | 0 | 0 | 0 | 0 | 0 |{0,1,2,3,4,5}|$R_1^{odd}$ |$\texttt{spread}(R_1^{odd})$ | | | $Maj(A_0,B_0,C_0)_{lo}$ | $Hprime_0^{lo}$ | $A_1^{lo}$ | $\mathtt{spread}(A_1^{lo})$ |
|
0 | 0 | 0 | 1 | 0 | 0 | 0 |{0,1,2,3,4,5}|$R_0^{odd}$ |$\texttt{spread}(R_0^{odd})$ | $\texttt{spread}(R_1^{odd})$ | $\texttt{spread}(d(10))$ | $\texttt{spread}(b(11))$ | | | | |
|
||||||
0 | 0 | 1 | 0 | 0 | 0 | 0 |{0,1,2,3,4,5}|$R_0^{even}$|$\texttt{spread}(R_0^{even})$| | | $Maj(A_0,B_0,C_0)_{hi}$ | $Hprime_0^{hi}$ | $A_1^{hi}$ | $\mathtt{spread}(A_1^{hi})$ |
|
0 | 0 | 0 | 0 | 0 | 0 | 0 |{0,1,2,3,4,5}|$R_1^{even}$|$\texttt{spread}(R_1^{even})$| $\texttt{spread}(a(2))$ | $\texttt{spread}(c(9)^{hi})$ | | | | | |
|
||||||
0 | 0 | 0 | 0 | 0 | 0 | 0 |{0,1,2,3,4,5}|$R_1^{even}$|$\texttt{spread}(R_1^{even})$| | | | $A_1 carry$ | | |
|
0 | 0 | 0 | 0 | 0 | 0 | 0 |{0,1,2,3,4,5}|$R_1^{odd}$ |$\texttt{spread}(R_1^{odd})$ | | | | | | | |
|
||||||
1 | 0 | 0 | 0 | 0 | 0 | 0 | {0,1,2} |$IV[1]b(11)$|$\texttt{spread}(IV[1]b(11))$| $IV[1]c(9)^{lo}$ | $\texttt{spread}(IV[1]c(9)^{lo})$ | $IV[1]c(9)^{mid}$ | $\texttt{spread}(IV[1]c(9)^{mid})$ | $B_0^{lo}$ | $\mathtt{spread}(B_0^{lo})$ |
|
1 | 0 | 0 | 0 | 0 | 0 | 0 | {0,1,2} |$B_0 b(11)$ |$\texttt{spread}(B_0 b(11))$ | $B_0 c(9)^{lo}$ | $\texttt{spread}(B_0 c(9)^{lo})$ | $B_0 c(9)^{mid}$ | $\texttt{spread}(B_0 c(9)^{mid})$ | $B_0^{lo}$ | $\mathtt{spread}(B_0^{lo})$ | |
|
||||||
0 | 0 | 0 | 0 | 0 | 0 | 0 | {0,1} |$IV[1]d(10)$|$\texttt{spread}(IV[1]d(10))$| $IV[1]a(2)$ | $\texttt{spread}(IV[1]a(2))$ | $IV[1]c(9)^{hi}$ | $\texttt{spread}(IV[1]c(9)^{hi})$ | $B_0^{hi}$ | $\mathtt{spread}(B_0^{hi})$ |
|
0 | 0 | 0 | 0 | 0 | 0 | 0 | {0,1} |$B_0 d(10)$ |$\texttt{spread}(B_0 d(10))$ | $B_0 a(2)$ | $\texttt{spread}(B_0 a(2))$ | $B_0 c(9)^{hi}$ | $\texttt{spread}(B_0 c(9)^{hi})$ | $B_0^{hi}$ | $\mathtt{spread}(B_0^{hi})$ | |
|
||||||
1 | 0 | 0 | 0 | 0 | 0 | 0 | {0,1,2} |$IV[2]b(11)$|$\texttt{spread}(IV[2]b(11))$| $IV[2]c(9)^{lo}$ | $\texttt{spread}(IV[2]c(9)^{lo})$ | $IV[2]c(9)^{mid}$ | $\texttt{spread}(IV[2]c(9)^{mid})$ | $C_0^{lo}$ | $\mathtt{spread}(C_0^{lo})$ |
|
1 | 0 | 0 | 0 | 0 | 0 | 0 | {0,1,2} |$C_0 b(11)$ |$\texttt{spread}(C_0 b(11))$ | $C_0 c(9)^{lo}$ | $\texttt{spread}(C_0 c(9)^{lo})$ | $C_0 c(9)^{mid}$ | $\texttt{spread}(C_0 c(9)^{mid})$ | $C_0^{lo}$ | $\mathtt{spread}(C_0^{lo})$ | |
|
||||||
0 | 0 | 0 | 0 | 0 | 0 | 0 | {0,1} |$IV[2]d(10)$|$\texttt{spread}(IV[2]d(10))$| $IV[2]a(2)$ | $\texttt{spread}(IV[2]a(2))$ | $IV[2]c(9)^{hi}$ | $\texttt{spread}(IV[2]c(9)^{hi})$ | $C_0^{hi}$ | $\mathtt{spread}(C_0^{hi})$ |
|
0 | 0 | 0 | 0 | 0 | 0 | 0 | {0,1} |$C_0 d(10)$ |$\texttt{spread}(C_0 d(10))$ | $C_0 a(2)$ | $\texttt{spread}(C_0 a(2))$ | $C_0 c(9)^{hi}$ | $\texttt{spread}(C_0 c(9)^{hi})$ | $C_0^{hi}$ | $\mathtt{spread}(C_0^{hi})$ | |
|
||||||
0 | 0 | 0 | 0 | 0 | 0 | 0 |{0,1,2,3,4,5}|$M_0^{even}$|$\texttt{spread}(M_0^{even})$| $\mathtt{spread}(A_0^{lo})$ | $\mathtt{spread}(A_0^{hi})$ | $E_1^{lo}$ | $Hprime_0^{lo}$ | $D_0^{lo}$ | $\mathtt{spread}(D_0^{lo})$ |
|
0 | 0 | 0 | 0 | 0 | 0 | 0 |{0,1,2,3,4,5}|$M_0^{even}$|$\texttt{spread}(M_0^{even})$| $\mathtt{spread}(A_0^{lo})$ | $\mathtt{spread}(A_0^{hi})$ | | | $Hprime_0^{lo}$ | $Hprime_0^{hi}$ | |
|
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0 | 0 | 0 | 0 | 1 | 0 | 0 |{0,1,2,3,4,5}|$M_0^{odd}$ |$\texttt{spread}(M_0^{odd})$ | $\mathtt{spread}(B_0^{lo})$ | $\mathtt{spread}(B_0^{hi})$ | $E_1^{hi}$ | $Hprime_0^{hi}$ | $D_0^{hi}$ | $\mathtt{spread}(D_0^{hi})$ |
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0 | 0 | 0 | 0 | 1 | 0 | 0 |{0,1,2,3,4,5}|$M_0^{odd}$ |$\texttt{spread}(M_0^{odd})$ | $\mathtt{spread}(B_0^{lo})$ | $\mathtt{spread}(B_0^{hi})$ | | $\Sigma_0(A_0)^{lo}$ | $A_1^{lo}$ | $\mathtt{spread}(A_1^{lo})$ | $A_1 carry$ |
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0 | 0 | 0 | 0 | 0 | 0 | 0 |{0,1,2,3,4,5}|$M_1^{even}$|$\texttt{spread}(M_1^{even})$| $\mathtt{spread}(C_0^{lo})$ | $\mathtt{spread}(C_0^{hi})$ | $\texttt{spread}(M_1^{odd})$ | $E_1 carry$ | | |
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0 | 0 | 0 | 0 | 0 | 0 | 0 |{0,1,2,3,4,5}|$M_1^{even}$|$\texttt{spread}(M_1^{even})$| $\mathtt{spread}(C_0^{lo})$ | $\mathtt{spread}(C_0^{hi})$ | $\texttt{spread}(M_1^{odd})$ | $\Sigma_0(A_0)^{hi}$ | $A_1^{hi}$ | $\mathtt{spread}(A_1^{hi})$ | |
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0 | 0 | 0 | 0 | 0 | 0 | 0 |{0,1,2,3,4,5}|$M_1^{odd}$ |$\texttt{spread}(M_1^{odd})$ | | | | | | |
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0 | 0 | 0 | 0 | 0 | 0 | 0 |{0,1,2,3,4,5}|$M_1^{odd}$ |$\texttt{spread}(M_1^{odd})$ | | | | | | | |
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#### TODO: steady-state
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Loading…
Reference in a new issue