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refactor readme

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Donovan
2024-06-28 09:37:01 -05:00
parent 3ae5445efe
commit a72ed3f830
2 changed files with 64 additions and 26 deletions
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README.md
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@@ -2,39 +2,67 @@
### translate data
```
alpha_phase_1 = si1_mo3(so1[alphabet]) ^ mi1_mo2(mo1[s_a ^ m_a ^ se_a])
alpha_phase1 = (
((alphabet < sdo1) << (sdi1 < mdo3)) ^
(((spda ^ seda) < mdo1) << (mdi1 < mdo2))
)
```
### receive alphabet
recall:
- `server_persistent_key.alpha = s_a ^ m_a`
- `mutual_persistent_key.alpha = m_a ^ c_a`
- `client_persistent_key.alpha = c_a`
```
result = alpha_phase_1 ^ mi1_mo2(mo1[ce_a ^ c_a ^ m_a ^ c_a])
result = alpha_phase_1 ^ mi1_mo2(mo1[ce_a ^ m_a]) # c_a cancels
result = si1_mo3(so1[alphabet]) ^ mi1_mo2(mo1[s_a ^ m_a ^ se_a]) ^ mi1_mo2(mo1[ce_a ^ m_a]) # expand alpha phase 1
result = si1_mo3(so1[alphabet]) ^ mi1_mo2(mo1[s_a ^ se_a ^ ce_a]) # client_ephemeral_alpha added and m_a cancels
expr1 = result
alpha_phase_2 = mo3_co1_co2[ci1(nmo3[expr1])]
alphabet_phase2 = ((((
alphabet_phase1 ^
(((ceda ^ cpda ^ mpda) < mdo1) << (mdi1 < mdo2))
) < ~mdo3)) << cdi1) < (mdo3 << cdo1 << cdo2)
```
#### Replace Alphabet Phase 1
```
alphabet_phase2 = ((((
((alphabet < sdo1) << (sdi1 < mdo3)) ^
(((spda ^ seda) < mdo1) << (mdi1 < mdo2)) ^
(((ceda ^ cpda ^ mpda) < mdo1) << (mdi1 < mdo2))
) < ~mdo3)) << cdi1) < (mdo3 << cdo1 << cdo2)
```
#### Simplified Expression
```
alphabet_phase2 = ((((
((alphabet < sdo1) << (sdi1 < mdo3)) ^
(((ceda ^ cpda ^ mpda ^ spda ^ seda) < mdo1) << (mdi1 < mdo2))
) < ~mdo3)) << cdi1) < (mdo3 << cdo1 << cdo2)
```
recall:
- `spda = s_a ^ m_a`
- `mpda = m_a ^ c_a`
- `cpda = c_a`
#### Final Alphabet Phase 2
```
alphabet_phase2 = ((((
((alphabet < sdo1) << (sdi1 < mdo3)) ^
(((ceda ^ s_a ^ seda) < mdo1) << (mdi1 < mdo2))
) < ~mdo3)) << cdi1) < (mdo3 << cdo1 << cdo2)
```
### transmit alphabet
```
alphabet_phase3 = (
(alphabet_phase2 << ((~cdi1 << mdpi2) < (mdo3 << cdo1 << cdo2))) ^
((((ceda ^ cpda ^ meda) < mdo1) << ((mdi1 < mdo2) << (mdpi2 < mdo3))) < (cdo1 << cdo2))
)
```
#### Distribute cdo1 << cdo2 term and replace alphabet_phase2
```
result = nceil_ncpi1_mpi2_mo3_co1_co2(alpha_phase_2)
result = nceil_ncpi1_mpi2_mo3_co1_co2(mo3_co1_co2[ci1(nmo3[expr1])])
result = mo3_co1_co2[nceil_ncpi1_mpi2(ci1(nmo3[expr1]))]
result = mo3_co1_co2[mpi2(nmo3[expr1])]
result = mo3_co1_co2[mpi2(nmo3[ si1_mo3(so1[alphabet]) ^ mi1_mo2(mo1[s_a ^ se_a ^ ce_a])])]
result = mo3_co1_co2[mpi2(si1(so1[alphabet]) ^ nmo3[mi1_mo2(mo1[s_a ^ se_a ^ ce_a])])]
alpha_phase_3 = result ^ co1_co2[mi1_mo2_mpi2_mo3(mo1[ce_a ^ c_a ^ m_a ^ c_a])]
alpha_phase_3 = result ^ co1_co2[mi1_mo2_mpi2_mo3(mo1[ce_a ^ m_a])]
alpha_phase_3 = mo3_co1_co2[mpi2(si1(so1[alphabet]) ^ nmo3[mi1_mo2(mo1[s_a ^ se_a ^ ce_a])])] ^ co1_co2[mi1_mo2_mpi2_mo3(mo1[ce_a ^ m_a])]
alpha_phase_3 = co1_co2[ si1_mpi2_mo3(so1[alphabet]) ^ mi1_mo2_mpi2_mo3(mo1[s_a ^ se_a ^ ce_a]) ^ mi1_mo2_mpi2_mo3(mo1[ce_a ^ m_a])]
alpha_phase_3 = co1_co2[ si1_mpi2_mo3(so1[alphabet]) ^ mi1_mo2_mpi2_mo3(mo1[s_a ^ se_a ^ m_a])]
alphabet_phase3 = (
((
(alphabet_phase2 << ((~cdi1 << mdpi2) < (mdo3 << cdo1 << cdo2))) ^
((((ceda ^ cpda ^ meda) < mdo1) << ((mdi1 < mdo2) << (mdpi2 < mdo3))) < (cdo1 << cdo2))
) << ((~cdi1 << mdpi2) < (mdo3 << cdo1_cdo2))) ^
(
(
((ceda ^ cpda ^ meda) < (mdo1 << cdo1 << cdo2)) << ((mdi1 < (mdo2 << cdo1 << cdo2)) << (mdpi2 < (mdo3 << cdo1 << cdo2)))
)
)
)
```