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x=jHZK<7HnQ>M& zAh`S5ov_tQrKPL6#SR^lPe@!W*5a}z$Irz>N2P_Mb8G97TZjA}{jA+L+kfBlJNMt; zD?VS~%n@iR*wo(;XppA(#A%Ju!A0MH3e3KrGK+P${?rWJ6L_`SuxJ6JNw}^` z^_E%nU1!bC%s0Bcac2M7E5_DktZ(~XiHs=?gf)SJG(b-3CXnjmq%>`K-I z*7gs%&aMmOdLG~II@QQlz;s_ML^*>={bR11X|q@X-+i?Z?F{DWA97u`Hk&5M-DeAt zD`{Y@c^x=+0e8%?aL3YSxeYz*dtR|-dsa)ua~8|Ks6RaYVEBq`(PXan~=^PUT4TSQ+d$^^KzeOIcHFg82>RV+T5p+OJ5dK4{1Ho<(+n zxJjeUiN>%Cd?i_e{Jd(P zHTSvZ%MW@~`ZN z-FTrTI|8{Qc$GG=U9dY>Q?b_7e%>p7w-ezTSA9Flq;_~HkMo4K!7 zeGdAvdHvR3S2p?FZQfV@)pqXN!wWK6|M=EAEv{}=u9T~hxxiD$5?~&FS7WU*6 z2Rt2W=N|fPvY@GsEg;mMU1M!_uo{-sCn zOEV%~zcKahmCM|FN;yHKr;*vgc*Xb1J6iH>kF{(53;$z&u5}=H`r7-N^4x~zCKg<( Js;>TSTmUEt_8b5J diff --git a/directions/research_directions.tex b/directions/research_directions.tex index 972117e..ce95f17 100644 --- a/directions/research_directions.tex +++ b/directions/research_directions.tex @@ -276,71 +276,85 @@ A working prototype has been completed. \begin{figure}[h!] \centering - \begin{tikzpicture}[thick,scale=0.8] + \tikzset{% + h/.style = {->, very thick}, + ck/.style = {->, very thick}, + key/.style = {->}, + ki/.style = {key, color=red}, + kr/.style = {key, color=red}, + ke/.style = {dashed}, + ks/.style = {solid}, + phaselbl/.style = {font=\bfseries, anchor=west} + } + \begin{tikzpicture}[scale=0.8] \node(protoname) at (0, 0){\texttt{"Noise\_XX\_25519\_ChaChaPoly\_BLAKE2s"}}; \node[draw,thick,below=1em of protoname] (inithash) {$H$}; - \node[below=2em of inithash, xshift= 10em] (ck){$ck$}; - \node[below=2em of inithash, xshift=-3em] (h){$h$}; + \node[below=2em of inithash, xshift= 6.5em] (ck){$ck$}; + \node[below=2em of inithash, xshift=-6.5em] (h){$h$}; \coordinate (labelbase) at (-5,0); \draw[->] (protoname) -- (inithash); \draw[->] (inithash) -- ++(0,-2em) coordinate(im0) -| (ck); \draw[->] (im0) -| (h); - \node[right=7em of ck] (ei){$e_i$}; - \node[right=8.5em of ck] (er){$e_r$}; - \node[right=10em of ck] (si){$s_i$}; - \node[right=11.5em of ck] (sr){$s_r$}; + \node[right=7em of ck] (ei){$\mathbf{e_i}$}; + \node[right=8.5em of ck] (er){$\mathbf{e_r}$}; + \node[right=10em of ck] (si){$\mathbf{s_i}$}; + \node[right=11.5em of ck] (sr){$\mathbf{s_r}$}; - - \node[draw,thick,below=1em of h] (mix0){MixHash}; - \node[left=1em of mix0] (str0){\texttt{""}}; + \node[draw,thick,below=3em of h] (mix0){MixHash}; + \node[right=1em of mix0] (str0){\texttt{""}}; \node[left] at (str0 -| labelbase) (lbl0){\parbox{10em}{\raggedleft No preamble,\\use empty string}}; - \draw[->] (h) -- (mix0); + \draw[h] (h) -- (mix0); \draw[->] (str0) -- (mix0); +%--- \node[draw,thick,below=2em of mix0] (mix1){MixHash}; \node[left] at (mix1 -| labelbase) (tok0){$e\rightarrow $}; - \draw[->] (mix0) -- (mix1); - \draw[->] (ei) |- (mix1); + \draw[h] (mix0) -- (mix1); + \draw[ki,ke] (ei) |- (mix1); \node[draw,thick,below=2em of mix1] (mix2){MixHash}; - \node[left=1em of mix2] (str2){\texttt{""}}; + \node[right=1em of mix2] (str2){\texttt{""}}; \node[left] at (str2 -| labelbase) (lbl2){\parbox{10em}{\raggedleft EncryptAndHash\\No payload and\\$k$ unset}}; \draw[->] (str2) -- (mix2); - \draw[->] (mix1) -- (mix2); + \draw[h] (mix1) -- (mix2); - \node[draw,thick,below=2em of mix2] (mix3){MixHash}; + \coordinate (a) at ($ (mix0) !0.5! (mix1) $); + \coordinate (b0) at (a -| lbl0.south west); + \draw[dashed] (b0) -- ($ (b0 -| sr) + (1em,0) $); +%--- + \node[draw,thick,below=4em of mix2] (mix3){MixHash}; \node[left] at (mix3 -| labelbase) (tok3){$e\leftarrow $}; - \draw[->] (mix2) -- (mix3); - \draw[->] (er) |- (mix3); + \draw[h] (mix2) -- (mix3); + \draw[kr,ke] (er) |- (mix3); \coordinate (sync4) at (mix3 -| ck); \node[draw,thick,below=2em of sync4] (kmix1){MixKey}; \node[left] at (kmix1 -| labelbase) (tok4){$ee\leftarrow $}; \node[draw,thick,right=1em of kmix1] (dh0){ECDH}; - \draw[->] (ck) -- (kmix1); - \draw[->] (ei) |- ($ (dh0.east) + (0,0.2em) $); - \draw[->] (er) |- ($ (dh0.east) - (0,0.2em) $); + \draw[ck] (ck) -- (kmix1); + \draw[ki,ke] (ei) |- ($ (dh0.east) + (0,0.2em) $); + \draw[kr,ke] (er) |- ($ (dh0.east) - (0,0.2em) $); \draw[->] (dh0) -- (kmix1); \coordinate (sync5) at (kmix1 -| h); \node[draw,thick,below=2em of sync5] (mix5){MixHash}; \node[draw,thick,right=2em of mix5] (enc5){$E$}; \node[left] at (mix5 -| labelbase) (lbl5){$s\leftarrow $}; - \draw[->] (mix3) -- (mix5); + \draw[h] (mix3) -- (mix5); \draw[->] (enc5) -- (mix5); - \draw[->] (kmix1) -| (enc5); - \draw[->] (sr) |- (enc5); + \draw[->] ($ (kmix1.west) - (2em,0) $) -| (enc5); + \draw[kr,ks] (sr) |- (enc5); \coordinate (sync6) at (mix5 -| ck); \node[draw,thick,below=2em of sync6] (kmix6){MixKey}; \node[left] at (kmix6 -| labelbase) (tok6){$es\leftarrow $}; \node[draw,thick,right=1em of kmix6] (dh6){ECDH}; - \draw[->] (kmix1) -- (kmix6); - \draw[->] (ei) |- ($ (dh6.east) + (0,0.2em) $); - \draw[->] (sr) |- ($ (dh6.east) - (0,0.2em) $); + \draw[ck] (kmix1) -- (kmix6); + \draw[ki,ke] (ei) |- ($ (dh6.east) + (0,0.2em) $); + \draw[kr,ks] (sr) |- ($ (dh6.east) - (0,0.2em) $); \draw[->] (dh6) -- (kmix6); \coordinate (sync7) at (kmix6 -| h); @@ -348,27 +362,30 @@ A working prototype has been completed. \node[draw,thick,right=2em of mix7] (enc7){$E$}; \node[right=1em of enc7] (str7){\texttt{""}}; \node[left] at (mix7 -| labelbase) (lbl7){\parbox{10em}{\raggedleft DecryptAndHash\\ No payload}}; - \draw[->] (mix5) -- (mix7); + \draw[h] (mix5) -- (mix7); \draw[->] (enc7) -- (mix7); - \draw[->] (kmix1.west) -- ++(-2em,0) -- ++(0,-5em) -| (enc7); + \draw[->] (kmix1.west) -- ++(-2em,0) |- ($ (enc5.south) !0.25! (enc7.north) $) -- (enc7); \draw[->] (str7) -- (enc7); + \coordinate (a) at ($ (mix2) !0.5! (mix3) $); + \coordinate (b1) at (a -| lbl2.south west); + \draw[dashed] (b1) -- ($ (b1 -| sr) + (1em,0) $); % --- - \node[draw,thick,below=2em of mix7] (mix8){MixHash}; + \node[draw,thick,below=4em of mix7] (mix8){MixHash}; \node[draw,thick,right=2em of mix8] (enc8){$E$}; \node[left] at (mix8 -| labelbase) (lbl8){$s\rightarrow $}; - \draw[->] (mix7) -- (mix8); + \draw[h] (mix7) -- (mix8); \draw[->] (enc8) -- (mix8); - \draw[->] (kmix6.west) -- ++(-2em,0) -- ++(0,-5em) -| (enc8); - \draw[->] (si) |- (enc8); + \draw[->] (kmix6.west) -- ++(-2em,0) |- ($ (enc7.south) !0.25! (enc8.north) $) -- (enc8); + \draw[ki,ks] (si) |- (enc8); \coordinate (sync9) at (mix8 -| ck); \node[draw,thick,below=2em of sync9] (kmix9){MixKey}; \node[left] at (kmix9 -| labelbase) (tok9){$se\rightarrow $}; \node[draw,thick,right=1em of kmix9] (dh9){ECDH}; - \draw[->] (kmix6) -- (kmix9); - \draw[->] (si) |- ($ (dh9.east) - (0,0.2em) $); - \draw[->] (er) |- ($ (dh9.east) + (0,0.2em) $); + \draw[ck] (kmix6) -- (kmix9); + \draw[ki,ks] (si) |- ($ (dh9.east) - (0,0.2em) $); + \draw[kr,ke] (er) |- ($ (dh9.east) + (0,0.2em) $); \draw[->] (dh9) -- (kmix9); \coordinate (sync10) at (kmix9 -| h); @@ -376,28 +393,41 @@ A working prototype has been completed. \node[draw,thick,right=2em of mix10] (enc10){$E$}; \node[right=1em of enc10] (str10){\texttt{""}}; \node[left] at (mix10 -| labelbase) (lbl10){\parbox{10em}{\raggedleft EncryptAndHash\\ No payload}}; - \draw[->] (mix8) -- (mix10); + \draw[h] (mix8) -- (mix10); \draw[->] (enc10) -- (mix10); \draw[->] (kmix9.west) -| (enc10); \draw[->] (str10) -- (enc10); + \coordinate (a) at ($ (mix7) !0.5! (mix8) $); + \coordinate (b2) at (a -| lbl2.south west); + \draw[dashed] (b2) -- ($ (b2 -| sr) + (1em,0) $); % --- \coordinate (sync11) at (mix10 -| ck); \node[draw,thick,below=5em of sync11,xshift=-1em] (finkdf){HKDF}; - \node[below=2em of finkdf,xshift=-1em] (k1){$k_1$}; - \node[below=2em of finkdf,xshift= 1em] (k2){$k_2$}; + \node[below=2em of finkdf,xshift=-1em] (k1){$\mathbf{k_1}$}; + \node[below=2em of finkdf,xshift= 1em] (k2){$\mathbf{k_2}$}; \node[left=1em of finkdf,yshift=2em] (str11){\texttt{""}}; - \draw[->] (kmix9) -- (finkdf.north -| kmix9); - \draw[->] (k1 |- finkdf.south) -- (k1); - \draw[->] (k2 |- finkdf.south) -- (k2); + \draw[ck] (kmix9) -- (finkdf.north -| kmix9); + \draw[ck] (k1 |- finkdf.south) -- (k1); + \draw[ck] (k2 |- finkdf.south) -- (k2); \draw[->] (str11) -| ($ (finkdf.north) - (1em,0) $); \coordinate (sync11a) at (finkdf.south -| h); - \node[below=2em of sync11a] (hout){$h$}; - \draw[->] (mix10) -- (hout); + \node[below=2em of sync11a] (hout){$\mathbf{h}$}; + \draw[h] (mix10) -- (hout); \node[left] at (finkdf -| labelbase) (lbl13){\parbox{10em}{\raggedleft Split}}; + \coordinate (a) at ($ (mix10) !0.5! (finkdf) $); + \coordinate (b3) at (a -| lbl10.south west); + \draw[dashed] (b3) -- ($ (b3 -| sr) + (1em,0) $); +%--- + \node[phaselbl, rectangle] at ($ (b0) !0.5! (b0 |- protoname) $) (setup){setup}; + \node[phaselbl, circle] at ($ (b0) !0.5! (b1) $) (ph0){0}; + \node[phaselbl, circle] at ($ (b1) !0.5! (b2) $) (ph1){1}; + \node[phaselbl, circle] at ($ (b2) !0.5! (b3) $) (ph2){2}; + \node[phaselbl, rectangle] at ($ (b3) !0.5! (b3 |- hout) $) (fin){fin}; + \end{tikzpicture} \caption{Cryptographic flowchart of Noise XX handshake} \label{crypto_diagram}