From d23fcd1ccd07b9918936e6caf0ef980cafc1a68f Mon Sep 17 00:00:00 2001 From: therealyingtong Date: Mon, 11 Jan 2021 13:45:20 +0800 Subject: [PATCH] [book] SHA-256: add compression digest gate --- book/src/design/gadgets/sha256/table16.md | 105 +++++++++++++++------- 1 file changed, 71 insertions(+), 34 deletions(-) diff --git a/book/src/design/gadgets/sha256/table16.md b/book/src/design/gadgets/sha256/table16.md index d4a60419..d45e8455 100644 --- a/book/src/design/gadgets/sha256/table16.md +++ b/book/src/design/gadgets/sha256/table16.md @@ -826,37 +826,74 @@ Constraints: #### Initial round: -sd_abcd|sd_efgh|ss0|ss1|s_maj|s_ch_neg|s_ch|s_a_new |s_e_new |s_h_prime| $a_0$ | $a_1$ | $a_2$ | $a_3$ | $a_4$ | $a_5$ | $a_6$ | $a_7$ | $a_8$ | $a_9$ | --------|-------|---|---|-----|--------|----|--------|--------|---------|-------------|------------|-----------------------------|-------------------------------------|-------------------------------------|----------------------------------------|------------------------------------|------------------------------------|------------------------------------|------------------------------------| - 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 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 | 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 | 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 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |{0,1,2,3,4,5}|$R_0^{odd}$ |$\texttt{spread}(R_0^{odd})$ | $\texttt{spread}(R_1^{odd})$ | $\texttt{spread}(E_0 d(7))$ | $\texttt{spread}(E_0 c(14))$ | | | | | - 0 | 0 | 0 | 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 | 0 | 0 |{0,1,2,3,4,5}|$R_1^{odd}$ |$\texttt{spread}(R_1^{odd})$ | | | | | | | | - 0 | 1 | 0 | 0 | 0 | 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 | 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 | 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 | 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 | 0 | 0 |{0,1,2,3,4,5}|$P_0^{even}$|$\texttt{spread}(P_0^{even})$| $\mathtt{spread}(E^{lo})$ | $\mathtt{spread}(E^{hi})$ | $Q_0^{odd}$ | $K_0^{lo}$ | $H_0^{lo}$ | $W_0^{lo}$ | | - 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 |{0,1,2,3,4,5}|$P_0^{odd}$ |$\texttt{spread}(P_0^{odd})$ | $\texttt{spread}(P_1^{odd})$ | $\Sigma_1(E_0)^{lo}$ | $\Sigma_1(E_0)^{hi}$ | $K_0^{hi}$ | $H_0^{hi}$ | $W_0^{hi}$ | | - 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |{0,1,2,3,4,5}|$P_1^{even}$|$\texttt{spread}(P_1^{even})$| $\mathtt{spread}(F^{lo})$ | $\mathtt{spread}(F^{hi})$ | $Q_1^{odd}$ | $P_1^{odd}$ | $Hprime_0^{lo}$ | $Hprime_0^{hi}$ | $Hprime_0 carry$ | - 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |{0,1,2,3,4,5}|$P_1^{odd}$ |$\texttt{spread}(P_1^{odd})$ | | | | | $D_0^{lo}$ | $E_1^{lo}$ | | - 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 |{0,1,2,3,4,5}|$Q_0^{even}$|$\texttt{spread}(Q_0^{even})$| $\mathtt{spread}(E_{neg}^{lo})$ | $\mathtt{spread}(E_{neg}^{hi})$ | $\mathtt{spread}(E^{lo})$ | | $D_0^{hi}$ | $E_1^{hi}$ | $E_1 carry$ | - 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 |{0,1,2,3,4,5}|$Q_0^{odd}$ |$\texttt{spread}(Q_0^{odd})$ | $\texttt{spread}(Q_1^{odd})$ | | $\mathtt{spread}(E^{hi})$ | | | | | - 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |{0,1,2,3,4,5}|$Q_1^{even}$|$\texttt{spread}(Q_1^{even})$| $\mathtt{spread}(G^{lo})$ | $\mathtt{spread}(G^{hi})$ | | | | | | - 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |{0,1,2,3,4,5}|$Q_1^{odd}$ |$\texttt{spread}(Q_1^{odd})$ | | | | | | | | - 1 | 0 | 0 | 0 | 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 | 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 | 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 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |{0,1,2,3,4,5}|$R_0^{odd}$ |$\texttt{spread}(R_0^{odd})$ | $\texttt{spread}(R_1^{odd})$ | $\texttt{spread}(d(10))$ | $\texttt{spread}(b(11))$ | | | | | - 0 | 0 | 0 | 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 | 0 | 0 |{0,1,2,3,4,5}|$R_1^{odd}$ |$\texttt{spread}(R_1^{odd})$ | | | | | | | | - 1 | 0 | 0 | 0 | 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 | 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 | 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 | 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 | 0 | 0 |{0,1,2,3,4,5}|$M_0^{even}$|$\texttt{spread}(M_0^{even})$| $M_1^{odd}$ | $\mathtt{spread}(A_0^{lo})$ | $\mathtt{spread}(A_0^{hi})$ | | $Hprime_0^{lo}$ | $Hprime_0^{hi}$ | | - 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 |{0,1,2,3,4,5}|$M_0^{odd}$ |$\texttt{spread}(M_0^{odd})$ | $\texttt{spread}(M_1^{odd})$ | $\mathtt{spread}(B_0^{lo})$ | $\mathtt{spread}(B_0^{hi})$ | $\Sigma_0(A_0)^{lo}$ | | $A_1^{lo}$ | $A_1 carry$ | - 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |{0,1,2,3,4,5}|$M_1^{even}$|$\texttt{spread}(M_1^{even})$| | $\mathtt{spread}(C_0^{lo})$ | $\mathtt{spread}(C_0^{hi})$ | $\Sigma_0(A_0)^{hi}$ | | $A_1^{hi}$ | | - 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |{0,1,2,3,4,5}|$M_1^{odd}$ |$\texttt{spread}(M_1^{odd})$ | | | | | | | | +s_digest|sd_abcd|sd_efgh|ss0|ss1|s_maj|s_ch_neg|s_ch|s_a_new |s_e_new |s_h_prime| $a_0$ | $a_1$ | $a_2$ | $a_3$ | $a_4$ | $a_5$ | $a_6$ | $a_7$ | $a_8$ | $a_9$ | +--------|-------|-------|---|---|-----|--------|----|--------|--------|---------|-------------|------------|-----------------------------|-------------------------------------|-------------------------------------|----------------------------------------|------------------------------------|------------------------------------|------------------------------------|------------------------------------| + 0 | 0 | 1 | 0 | 0 | 0 | 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 | 0 | 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 | 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 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |{0,1,2,3,4,5}|$R_0^{odd}$ |$\texttt{spread}(R_0^{odd})$ | $\texttt{spread}(R_1^{odd})$ | $\texttt{spread}(E_0 d(7))$ | $\texttt{spread}(E_0 c(14))$ | | | | | + 0 | 0 | 0 | 0 | 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 | 0 | 0 | 0 |{0,1,2,3,4,5}|$R_1^{odd}$ |$\texttt{spread}(R_1^{odd})$ | | | | | | | | + 0 | 0 | 1 | 0 | 0 | 0 | 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 | 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 | 0 | 1 | 0 | 0 | 0 | 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 | 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 | 0 | 0 | 0 |{0,1,2,3,4,5}|$P_0^{even}$|$\texttt{spread}(P_0^{even})$| $\mathtt{spread}(E^{lo})$ | $\mathtt{spread}(E^{hi})$ | $Q_0^{odd}$ | $K_0^{lo}$ | $H_0^{lo}$ | $W_0^{lo}$ | | + 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 |{0,1,2,3,4,5}|$P_0^{odd}$ |$\texttt{spread}(P_0^{odd})$ | $\texttt{spread}(P_1^{odd})$ | $\Sigma_1(E_0)^{lo}$ | $\Sigma_1(E_0)^{hi}$ | $K_0^{hi}$ | $H_0^{hi}$ | $W_0^{hi}$ | | + 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |{0,1,2,3,4,5}|$P_1^{even}$|$\texttt{spread}(P_1^{even})$| $\mathtt{spread}(F^{lo})$ | $\mathtt{spread}(F^{hi})$ | $Q_1^{odd}$ | $P_1^{odd}$ | $Hprime_0^{lo}$ | $Hprime_0^{hi}$ | $Hprime_0 carry$ | + 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |{0,1,2,3,4,5}|$P_1^{odd}$ |$\texttt{spread}(P_1^{odd})$ | | | | | $D_0^{lo}$ | $E_1^{lo}$ | | + 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 |{0,1,2,3,4,5}|$Q_0^{even}$|$\texttt{spread}(Q_0^{even})$| $\mathtt{spread}(E_{neg}^{lo})$ | $\mathtt{spread}(E_{neg}^{hi})$ | $\mathtt{spread}(E^{lo})$ | | $D_0^{hi}$ | $E_1^{hi}$ | $E_1 carry$ | + 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 |{0,1,2,3,4,5}|$Q_0^{odd}$ |$\texttt{spread}(Q_0^{odd})$ | $\texttt{spread}(Q_1^{odd})$ | | $\mathtt{spread}(E^{hi})$ | | | | | + 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |{0,1,2,3,4,5}|$Q_1^{even}$|$\texttt{spread}(Q_1^{even})$| $\mathtt{spread}(G^{lo})$ | $\mathtt{spread}(G^{hi})$ | | | | | | + 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |{0,1,2,3,4,5}|$Q_1^{odd}$ |$\texttt{spread}(Q_1^{odd})$ | | | | | | | | + 0 | 1 | 0 | 0 | 0 | 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 | 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 | 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 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |{0,1,2,3,4,5}|$R_0^{odd}$ |$\texttt{spread}(R_0^{odd})$ | $\texttt{spread}(R_1^{odd})$ | $\texttt{spread}(d(10))$ | $\texttt{spread}(b(11))$ | | | | | + 0 | 0 | 0 | 0 | 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 | 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 | 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 | 0 | 0 | 0 | {0,1} |$B_0 d(10)$ |$\texttt{spread}(B_0 d(10))$ | $B_0 a(2)$ | $\texttt{spread}(B_0 a(2))$ | $B_0 c(9)^{hi}$ | $\texttt{spread}(B_0 c(9)^{hi})$ | $B_0^{hi}$ | $\mathtt{spread}(B_0^{hi})$ | | + 0 | 1 | 0 | 0 | 0 | 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 | 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 | 0 | 0 | 0 |{0,1,2,3,4,5}|$M_0^{even}$|$\texttt{spread}(M_0^{even})$| $M_1^{odd}$ | $\mathtt{spread}(A_0^{lo})$ | $\mathtt{spread}(A_0^{hi})$ | | $Hprime_0^{lo}$ | $Hprime_0^{hi}$ | | + 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 |{0,1,2,3,4,5}|$M_0^{odd}$ |$\texttt{spread}(M_0^{odd})$ | $\texttt{spread}(M_1^{odd})$ | $\mathtt{spread}(B_0^{lo})$ | $\mathtt{spread}(B_0^{hi})$ | $\Sigma_0(A_0)^{lo}$ | | $A_1^{lo}$ | $A_1 carry$ | + 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |{0,1,2,3,4,5}|$M_1^{even}$|$\texttt{spread}(M_1^{even})$| | $\mathtt{spread}(C_0^{lo})$ | $\mathtt{spread}(C_0^{hi})$ | $\Sigma_0(A_0)^{hi}$ | | $A_1^{hi}$ | | + 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |{0,1,2,3,4,5}|$M_1^{odd}$ |$\texttt{spread}(M_1^{odd})$ | | | | | | | | + +#### Steady-state: + +s_digest|sd_abcd|sd_efgh|ss0|ss1|s_maj|s_ch_neg|s_ch|s_a_new |s_e_new |s_h_prime| $a_0$ | $a_1$ | $a_2$ | $a_3$ | $a_4$ | $a_5$ | $a_6$ | $a_7$ | $a_8$ | $a_9$ | +--------|-------|-------|---|---|-----|--------|----|--------|--------|---------|-------------|------------|-----------------------------|-------------------------------------|-------------------------------------|----------------------------------------|------------------------------------|------------------------------------|------------------------------------|------------------------------------| + 0 | 0 | 1 | 0 | 0 | 0 | 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 | 0 | 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 | 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 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |{0,1,2,3,4,5}|$R_0^{odd}$ |$\texttt{spread}(R_0^{odd})$ | $\texttt{spread}(R_1^{odd})$ | $\texttt{spread}(E_0 d(7))$ | $\texttt{spread}(E_0 c(14))$ | | | | | + 0 | 0 | 0 | 0 | 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 | 0 | 0 | 0 |{0,1,2,3,4,5}|$R_1^{odd}$ |$\texttt{spread}(R_1^{odd})$ | | | | | | | | + 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |{0,1,2,3,4,5}|$P_0^{even}$|$\texttt{spread}(P_0^{even})$| $\mathtt{spread}(E^{lo})$ | $\mathtt{spread}(E^{hi})$ | $Q_0^{odd}$ | $K_0^{lo}$ | $H_0^{lo}$ | $W_0^{lo}$ | | + 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 |{0,1,2,3,4,5}|$P_0^{odd}$ |$\texttt{spread}(P_0^{odd})$ | $\texttt{spread}(P_1^{odd})$ | $\Sigma_1(E_0)^{lo}$ | $\Sigma_1(E_0)^{hi}$ | $K_0^{hi}$ | $H_0^{hi}$ | $W_0^{hi}$ | | + 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |{0,1,2,3,4,5}|$P_1^{even}$|$\texttt{spread}(P_1^{even})$| $\mathtt{spread}(F^{lo})$ | $\mathtt{spread}(F^{hi})$ | $Q_1^{odd}$ | $P_1^{odd}$ | $Hprime_0^{lo}$ | $Hprime_0^{hi}$ | $Hprime_0 carry$ | + 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |{0,1,2,3,4,5}|$P_1^{odd}$ |$\texttt{spread}(P_1^{odd})$ | | | | | $D_0^{lo}$ | $E_1^{lo}$ | | + 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 |{0,1,2,3,4,5}|$Q_0^{even}$|$\texttt{spread}(Q_0^{even})$| $\mathtt{spread}(E_{neg}^{lo})$ | $\mathtt{spread}(E_{neg}^{hi})$ | $\mathtt{spread}(E^{lo})$ | | $D_0^{hi}$ | $E_1^{hi}$ | $E_1 carry$ | + 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 |{0,1,2,3,4,5}|$Q_0^{odd}$ |$\texttt{spread}(Q_0^{odd})$ | $\texttt{spread}(Q_1^{odd})$ | | $\mathtt{spread}(E^{hi})$ | | | | | + 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |{0,1,2,3,4,5}|$Q_1^{even}$|$\texttt{spread}(Q_1^{even})$| $\mathtt{spread}(G^{lo})$ | $\mathtt{spread}(G^{hi})$ | | | | | | + 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |{0,1,2,3,4,5}|$Q_1^{odd}$ |$\texttt{spread}(Q_1^{odd})$ | | | | | | | | + 0 | 1 | 0 | 0 | 0 | 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 | 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 | 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 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |{0,1,2,3,4,5}|$R_0^{odd}$ |$\texttt{spread}(R_0^{odd})$ | $\texttt{spread}(R_1^{odd})$ | $\texttt{spread}(d(10))$ | $\texttt{spread}(b(11))$ | | | | | + 0 | 0 | 0 | 0 | 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 | 0 | 0 | 0 |{0,1,2,3,4,5}|$R_1^{odd}$ |$\texttt{spread}(R_1^{odd})$ | | | | | | | | + 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |{0,1,2,3,4,5}|$M_0^{even}$|$\texttt{spread}(M_0^{even})$| $M_1^{odd}$ | $\mathtt{spread}(A_0^{lo})$ | $\mathtt{spread}(A_0^{hi})$ | | $Hprime_0^{lo}$ | $Hprime_0^{hi}$ | | + 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 |{0,1,2,3,4,5}|$M_0^{odd}$ |$\texttt{spread}(M_0^{odd})$ | $\texttt{spread}(M_1^{odd})$ | $\mathtt{spread}(B_0^{lo})$ | $\mathtt{spread}(B_0^{hi})$ | $\Sigma_0(A_0)^{lo}$ | | $A_1^{lo}$ | $A_1 carry$ | + 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |{0,1,2,3,4,5}|$M_1^{even}$|$\texttt{spread}(M_1^{even})$| | $\mathtt{spread}(C_0^{lo})$ | $\mathtt{spread}(C_0^{hi})$ | $\Sigma_0(A_0)^{hi}$ | | $A_1^{hi}$ | | + 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |{0,1,2,3,4,5}|$M_1^{odd}$ |$\texttt{spread}(M_1^{odd})$ | | | | | | | | + +#### Final digest: +s_digest|sd_abcd|sd_efgh|ss0|ss1|s_maj|s_ch_neg|s_ch|s_a_new |s_e_new |s_h_prime| $a_0$ | $a_1$ | $a_2$ | $a_3$ | $a_4$ | $a_5$ | $a_6$ | $a_7$ | $a_8$ | $a_9$ | +--------|-------|-------|---|---|-----|--------|----|--------|--------|---------|-------------|-------------|------------------------------|-------------------------------------|-------------------------------------|----------------------------------------|------------------------------------|------------------------------------|------------------------------------|------------------------------------| + 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | $A_{63}^{lo}$ | $A_{63}^{hi}$ | $A_{63}$ | $B_{63}^{lo}$ | $B_{63}^{hi}$ | $B_{63}$ | | + 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | $C_{63}^{lo}$ | $C_{63}^{hi}$ | $C_{63}$ | $C_{63}^{lo}$ | $C_{63}^{hi}$ | $C_{63}$ | | + 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | $E_{63}^{lo}$ | $E_{63}^{hi}$ | $E_{63}$ | $G_{63}^{lo}$ | $G_{63}^{hi}$ | $G_{63}$ | | + 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | $F_{63}^{lo}$ | $F_{63}^{hi}$ | $F_{63}$ | $H_{63}^{lo}$ | $H_{63}^{hi}$ | $H_{63}$ | |