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[book] Add compression region to table16.md
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@ -819,105 +819,74 @@ Constraints:
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```plaintext
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+----------------------------------------------------------+
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| Σ_0(A) |
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| +---------------------------------------+
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| | reduce_7() to get A |
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+------------------+---------------------------------------+
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| Maj(A,B,C) |
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+----------------------------------------------------------+
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| decompose E, |
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| Σ_1(E) |
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| +---------------------------------------+
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| | reduce_5() to get H' |
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| | reduce_6() to get E |
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+------------------+---------------------------------------+
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+----------------------------------------------------------+
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| decompose F, decompose G |
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| Ch(E,F,G) |
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+----------------------------------------------------------+
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| decompose A, |
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| Σ_0(A) |
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| +---------------------------------------+
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| | reduce_7() to get A_new, |
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| | using H' |
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+------------------+---------------------------------------+
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| decompose B, decompose C |
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| Maj(A,B,C) |
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| +---------------------------------------+
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| | reduce_6() to get E_new, |
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| | using H' |
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+------------------+---------------------------------------+
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```
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#### Round 1
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sd_abcd|sd_efgh|ss0|ss1|sm |sn |sc |s23|s33| $a_0$ | $a_1$ | $a_2$ | $a_3$ | $a_4$ | $a_5$ | $a_6$ | $a_7$ |
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-------|-------|---|---|---|---|---|---|---|-------------|------------|-----------------------------|-------------------------------------|-------------------------------------|----------------------------------------|------------------------------------|------------------------------------|
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0 | 1 | 0 | 0 | 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}) $ | $\mathtt{spread}(E_0^{lo})$ |
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0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |{0,1,2,3,4,5}|$R_0^{odd}$ |$\texttt{spread}(R_0^{odd})$ | $\texttt{spread}(R_1^{odd})$ | $\texttt{spread}(R_0^{even})$ | $\texttt{spread}(R_1^{even})$ | | $\mathtt{spread}(E_0^{hi})$ |
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| | | | | | | | | {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}) $ | |
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0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |{0,1,2,3,4,5}|$R_1^{odd}$ |$\texttt{spread}(R_1^{odd})$ | $\mathtt{spread}(K_0^{lo})$ | $\mathtt{spread}(W_0^{lo})$ |$\texttt{spread}(Ch(E_0,F_0,G_0)_{lo})$ | $\mathtt{spread}(Hprime_0^{lo})$ | $\mathtt{spread}(H_0^{lo})$ |
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0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |{0,1,2,3,4,5}|$R_0^{even}$|$\texttt{spread}(R_0^{even})$| $\mathtt{spread}(K_0^{hi})$ | $\mathtt{spread}(W_0^{hi})$ |$\texttt{spread}(Ch(E_0,F_0,G_0)_{hi})$ | $\mathtt{spread}(Hprime_0^{hi})$ | $\mathtt{spread}(H_0^{hi})$ |
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0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |{0,1,2,3,4,5}|$R_1^{even}$|$\texttt{spread}(R_1^{even})$| | | | $Hprime_0 carry$ | |
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0 | 1 | 0 | 0 | 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}) $ | $\mathtt{spread}(F_0^{lo})$ |
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| | | | | | | | | {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}) $ | $\mathtt{spread}(F_0^{hi})$ |
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0 | 1 | 0 | 0 | 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}) $ | $\mathtt{spread}(G_0^{lo})$ |
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| | | | | | | | | {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}) $ | $\mathtt{spread}(G_0^{hi})$ |
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0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |{0,1,2,3,4,5}|$P_0^{even}$|$\texttt{spread}(P_0^{even})$| $\mathtt{spread}(E_0^{lo})$ | $\mathtt{spread}(E_0^{hi})$ | $\texttt{spread}(Q_0^{odd})$ | | |
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0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 |{0,1,2,3,4,5}|$P_0^{odd}$ |$\texttt{spread}(P_0^{odd})$ | $\texttt{spread}(P_1^{odd})$ | | $\texttt{spread}(Ch(E,F,G)_0)$ | | |
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0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |{0,1,2,3,4,5}|$P_1^{even}$|$\texttt{spread}(P_1^{even})$| $\mathtt{spread}(F^{lo})$ | $\mathtt{spread}(F^{hi})$ | $\texttt{spread}(Q_1^{odd})$ | | |
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0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |{0,1,2,3,4,5}|$P_1^{odd}$ |$\texttt{spread}(P_1^{odd})$ | $evens_0$ | $evens_1$ | $\texttt{spread}(Ch(E,F,G)_1)$ | | |
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0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 |{0,1,2,3,4,5}|$Q_0^{even}$|$\texttt{spread}(Q_0^{even})$| $\mathtt{spread}(E_0^{lo})$ | $\mathtt{spread}(E_0^{hi})$ | | | |
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0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |{0,1,2,3,4,5}|$Q_0^{odd}$ |$\texttt{spread}(Q_0^{odd})$ |$evens_0 - \mathtt{spread}(E_0^{lo})$|$evens_1 - \mathtt{spread}(E_0^{hi})$| | | |
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0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 |{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 | 0 | 0 | 0 | 0 | 0 | 0 |{0,1,2,3,4,5}|$Q_1^{odd}$ |$\texttt{spread}(Q_1^{odd})$ | $\mathtt{spread}(G^{lo})$ | $\mathtt{spread}(G^{hi})$ | | | |
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1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | {0,1,2} |$IV[0]b(11)$|$\texttt{spread}(IV[0]b(11))$| $IV[0]c(9)^{lo}$ | $\texttt{spread}(IV[0]c(9)^{lo})$ | $IV[0]c(9)^{mid}$ | $\texttt{spread}(IV[0]c(9)^{mid})$ | $\mathtt{spread}(A_0^{lo})$ |
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0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |{0,1,2,3,4,5}|$R_0^{odd}$ |$\texttt{spread}(R_0^{odd})$ | $\texttt{spread}(R_1^{odd})$ | $\texttt{spread}(R_0^{even})$ | $\texttt{spread}(R_1^{even})$ | | $\mathtt{spread}(A_0^{hi})$ |
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| | | | | | | | | {0,1} |$IV[0]d(10)$|$\texttt{spread}(IV[0]d(10))$| $IV[0]a(2)$ | $\texttt{spread}(IV[0]a(2))$ | $IV[0]c(9)^{hi}$ | $\texttt{spread}(IV[0]c(9)^{hi})$ | |
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0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |{0,1,2,3,4,5}|$R_1^{odd}$ |$\texttt{spread}(R_1^{odd})$ | | |$\texttt{spread}(Maj(A_0,B_0,C_0)_{lo})$| $\mathtt{spread}(Hprime_0^{lo})$ | $\mathtt{spread}(A_1^{lo})$ |
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0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |{0,1,2,3,4,5}|$R_0^{even}$|$\texttt{spread}(R_0^{even})$| | |$\texttt{spread}(Maj(A_0,B_0,C_0)_{hi})$| $\mathtt{spread}(Hprime_0^{hi})$ | $\mathtt{spread}(A_1^{hi})$ |
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0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |{0,1,2,3,4,5}|$R_1^{even}$|$\texttt{spread}(R_1^{even})$| | | $A_1 carry$ | $Hprime_0 carry$ | |
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1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | {0,1,2} |$IV[1]b(11)$|$\texttt{spread}(IV[1]b(11))$| $IV[1]c(9)^{lo}$ | $\texttt{spread}(IV[1]c(9)^{lo})$ | $IV[1]c(9)^{mid}$ | $\texttt{spread}(IV[1]c(9)^{mid})$ | $\mathtt{spread}(B_0^{lo})$ |
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| | | | | | | | | {0,1} |$IV[1]d(10)$|$\texttt{spread}(IV[1]d(10))$| $IV[1]a(2)$ | $\texttt{spread}(IV[1]a(2))$ | $IV[1]c(9)^{hi}$ | $\texttt{spread}(IV[1]c(9)^{hi})$ | $\mathtt{spread}(B_0^{hi})$ |
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1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | {0,1,2} |$IV[2]b(11)$|$\texttt{spread}(IV[2]b(11))$| $IV[2]c(9)^{lo}$ | $\texttt{spread}(IV[2]c(9)^{lo})$ | $IV[2]c(9)^{mid}$ | $\texttt{spread}(IV[2]c(9)^{mid})$ | $\mathtt{spread}(C_0^{lo})$ |
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| | | | | | | | | {0,1} |$IV[2]d(10)$|$\texttt{spread}(IV[2]d(10))$| $IV[2]a(2)$ | $\texttt{spread}(IV[2]a(2))$ | $IV[2]c(9)^{hi}$ | $\texttt{spread}(IV[2]c(9)^{hi})$ | $\mathtt{spread}(C_0^{hi})$ |
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0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |{0,1,2,3,4,5}|$M_0^{even}$|$\texttt{spread}(M_0^{even})$| $\mathtt{spread}(A^{lo})$ | $\mathtt{spread}(A^{hi})$ | $\mathtt{spread}(E_1^{lo})$ | $\mathtt{spread}(Hprime_0^{lo})$ | $\mathtt{spread}(D_0^{lo})$ |
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0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 |{0,1,2,3,4,5}|$M_0^{odd}$ |$\texttt{spread}(M_0^{odd})$ | $\mathtt{spread}(B^{lo})$ | $\mathtt{spread}(B^{hi})$ | $\mathtt{spread}(E_1^{hi})$ | $\mathtt{spread}(Hprime_0^{hi})$ | $\mathtt{spread}(D_0^{hi})$ |
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0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |{0,1,2,3,4,5}|$M_1^{even}$|$\texttt{spread}(M_1^{even})$| $\mathtt{spread}(C^{lo})$ | $\mathtt{spread}(C^{hi})$ | $E_1 carry$ | $Hprime_0 carry$ | |
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0 | 0 | 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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1. decompose $A$ into $A_0, A_1$ 16-bit subpieces
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2. $\Sigma_0(A)$
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- decomposes $A$ into $(2, 11, 3, 3, 3, 10)$-bit subpieces
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- spreads each of the subpieces
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- outputs $R_0^{even}, R_1^{even}$
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3. decompose $B$
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- into $16$-bit subpieces
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- spread each of the subpieces
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4. decompose $C$
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- into $16$-bit subpieces
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- spread each of the subpieces
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5. $Maj(A,B,C)$
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- takes in the 16-bit spread subpieces of $A,B,C$
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- outputs $M_0^{odd}, M_1^{odd}$
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6. decompose $E$ into $E_0, E_1$ 16-bit subpieces
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7. $\Sigma_1(E)$
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- decomposes $E$ into $(3, 3, 2, 3, 13, 7)$-bit subpieces
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- spreads each of the subpieces
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- outputs $R_0^{even}, R_1^{even}$
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8. decompose $F$
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- into $16$-bit subpieces
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- spread each of the subpieces
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9. decompose $G$
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- into $16$-bit subpieces
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- spread each of the subpieces
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10. $Ch(E,F,G)$
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- takes in the 16-bit spread subpieces of $E,F,G$
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- outputs $P_0^{odd}, Q_0^{odd}, P_1^{odd}, Q_1^{odd}$
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11. decompose $H$ into $16$-bit subpieces
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#### Round 2 (steady-state)
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1. $reduce_7$ to get $A$
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- $H' = H_{prev} + Ch(E_{prev}, F_{prev}, G_{prev}) + \Sigma_1(E_{prev}) + K_1 + W_1$
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- $reduce_7(H' + Maj(A_{prev}, B_{prev}, C_{prev}) + \Sigma_0(A_{prev}))$
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- outputs $A_0, A_1$ 16-bit subpieces
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2. $\Sigma_0(A)$
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- decomposes $A$ into $(2, 11, 3, 3, 3, 10)$-bit subpieces
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- spreads each of the subpieces
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- outputs $R_0^{even}, R_1^{even}$
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3. $B = A_{prev}$
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4. $C = B_{prev}$
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5. $Maj(A,B,C)$
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- takes in the 16-bit spread subpieces of $A,B,C$
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- outputs $M_0^{odd}, M_1^{odd}$
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6. $reduce_6$ to get $E$
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- $H' = H_{prev} + Ch(E_{prev}, F_{prev}, G_{prev}) + \Sigma_1(E_{prev}) + K_1 + W_1$
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- $reduce_6(H' + D_{prev})$
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- outputs $E_0, E_1$ 16-bit subpieces
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7. $\Sigma_1(E)$
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- decomposes $E$ into $(3, 3, 2, 3, 13, 7)$-bit subpieces
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- spreads each of the subpieces
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- outputs $R_0^{even}, R_1^{even}$
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8. $F = E_{prev}$
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9. $G = F_{prev}$
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10. $Ch(E,F,G)$
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- takes in the 16-bit spread subpieces of $E,F,G$
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- outputs $P_0^{odd}, Q_0^{odd}, P_1^{odd}, Q_1^{odd}$
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11. $H = G_{prev}$
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