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Update olm.md

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Richard van der Hoff 2019-11-08 14:00:59 +00:00
parent a9c7bde457
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1 changed files with 21 additions and 18 deletions
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@ -10,13 +10,13 @@ $`\parallel`$ appears on the right hand side of an $`=`$ it means that
the inputs are concatenated. When $`\parallel`$ appears on the left hand the inputs are concatenated. When $`\parallel`$ appears on the left hand
side of an $`=`$ it means that the output is split. side of an $`=`$ it means that the output is split.
When this document uses $`ECDH\left(K_A,\,K_B\right)`$ it means that each When this document uses $`\operatorname{ECDH}\left(K_A,K_B\right)`$ it means
party computes a Diffie-Hellman agreement using their private key and the that each party computes a Diffie-Hellman agreement using their private key
remote party's public key. and the remote party's public key.
So party $`A`$ computes $`ECDH\left(K_B^{public},\,K_A^{private}\right)`$ So party $`A`$ computes $`\operatorname{ECDH}\left(K_B^{public},K_A^{private}\right)`$
and party $`B`$ computes $`ECDH\left(K_A^{public},\,K_B^{private}\right)`$. and party $`B`$ computes $`\operatorname{ECDH}\left(K_A^{public},K_B^{private}\right)`$.
Where this document uses $`HKDF\left(salt,\,IKM,\,info,\,L\right)`$ it Where this document uses $`\operatorname{HKDF}\left(salt,IKM,info,L\right)`$ it
refers to the [HMAC-based key derivation function][] with a salt value of refers to the [HMAC-based key derivation function][] with a salt value of
$`salt`$, input key material of $`IKM`$, context string $`info`$, $`salt`$, input key material of $`IKM`$, context string $`info`$,
and output keying material length of $`L`$ bytes. and output keying material length of $`L`$ bytes.
@ -35,10 +35,12 @@ HMAC-based Key Derivation Function using [SHA-256][] as the hash function
```math ```math
\begin{aligned} \begin{aligned}
S&=ECDH\left(I_A,\,E_B\right)\;\parallel\;ECDH\left(E_A,\,I_B\right)\; S&=\operatorname{ECDH}\left(I_A,E_B\right)\;\parallel\;
\parallel\;ECDH\left(E_A,\,E_B\right)\\ \operatorname{ECDH}\left(E_A,I_B\right)\;\parallel\;
\operatorname{ECDH}\left(E_A,E_B\right)\\
R_0\;\parallel\;C_{0,0}&= R_0\;\parallel\;C_{0,0}&=
HKDF\left(0,\,S,\,\text{"OLM\_ROOT"},\,64\right) \operatorname{HKDF}\left(0,S,\text{``OLM\_ROOT"},64\right)
\end{aligned} \end{aligned}
``` ```
@ -55,10 +57,11 @@ info.
```math ```math
\begin{aligned} \begin{aligned}
R_i\;\parallel\;C_{i,0}&=HKDF\left( R_i\;\parallel\;C_{i,0}&=
R_{i-1},\, \operatorname{HKDF}\left(
ECDH\left(T_{i-1},\,T_i\right),\, R_{i-1},
\text{"OLM\_RATCHET"},\, \operatorname{ECDH}\left(T_{i-1},T_i\right),
\text{``OLM\_RATCHET"},
64 64
\right) \right)
\end{aligned} \end{aligned}
@ -72,7 +75,7 @@ previous chain key as the key.
```math ```math
\begin{aligned} \begin{aligned}
C_{i,j}&=HMAC\left(C_{i,j-1},\,\text{"\x02"}\right) C_{i,j}&=\operatorname{HMAC}\left(C_{i,j-1},\text{``\char`\\x02"}\right)
\end{aligned} \end{aligned}
``` ```
@ -86,7 +89,7 @@ by Bob to encrypt messages.
```math ```math
\begin{aligned} \begin{aligned}
M_{i,j}&=HMAC\left(C_{i,j},\,\text{"\x01"}\right) M_{i,j}&=\operatorname{HMAC}\left(C_{i,j},\text{``\char`\\x01"}\right)
\end{aligned} \end{aligned}
``` ```
@ -263,7 +266,7 @@ message key using [HKDF-SHA-256][] using the default salt and an info of
```math ```math
\begin{aligned} \begin{aligned}
AES\_KEY_{i,j}\;\parallel\;HMAC\_KEY_{i,j}\;\parallel\;AES\_IV_{i,j} AES\_KEY_{i,j}\;\parallel\;HMAC\_KEY_{i,j}\;\parallel\;AES\_IV_{i,j}
&= HKDF\left(0,\,M_{i,j},\text{"OLM\_KEYS"},\,80\right) \\ &= \operatorname{HKDF}\left(0,M_{i,j},\text{``OLM\_KEYS"},80\right)
\end{aligned} \end{aligned}
``` ```