diff --git a/PROTOCOL.md b/PROTOCOL.md
index 19150de..dd3c27d 100644
--- a/PROTOCOL.md
+++ b/PROTOCOL.md
@@ -104,7 +104,7 @@ In each request, the client will send a pair of time-scrambled hashes $(x_1, x_2
 
 The client implements 3 protocols according to the **keyset state** :
 - 0 : `NORMAL` - default authentication protocol.
-- 1 : `SWITCH` - default protocol variation to switch to a new keyset when the current one is consumed (*i.e. when $n$ if less or equal to $min+belt$*).
+- 1 : `SWITCH` - default protocol variation to switch to a new keyset when the current one is consumed (*i.e. when $n$ \leq $min+belt$*).
 - 2 : `RESCUE` - process the proof of work after receiving the server's challenge when there is a desynchronisation and generate a new keyset.
 
 When the client switches to a new key, it has to store the new keyset along the current one, in order not to lose its authentication if the network fails.
@@ -116,7 +116,7 @@ When the client switches to a new key, it has to store the new keyset along the
 
 | Step | Calculation |
 |:--------:|:------|
-| `1` | Decrement $i$ |
+| `1` | Decrement $n$ |
 | `2` | $t\_c = \mid \frac{t\_{now}}{W}\mid$ |
 | `3` | $x\_1 = h^{n}(K) \oplus h(t\_c)$ |
 | `4` | $x\_2 = x\_1 \oplus (t\_c \ \mathbb{Z}\_{(2)})$ |
@@ -130,7 +130,7 @@ Send $x_1$ and $x_2$.
 |:--------:|:------|
 | `1` | $t\_c = \mid \frac{t\_{now}}{W}\mid$ |
 | `2` | $x\_1 = h^{n}(K) \oplus h(t\_c)$ |
-| `3` | Generate $(K',n',s')$ until <br><ul><li>$[(h^n(K) \oplus h^{n'}(K')) \And 1] \ \mathbb{Z}\_{(2)} = m\_c$</li><li>$[(h^N(K) \oplus h^{n'}(K')) \And 11110000] \ \mathbb{Z}\_{(3)} = s$</li></ul> |
+| `3` | Generate $(K',n',s')$ until <br><ul><li>$[(h^n(K) \oplus h^{n'}(K')) \And 0x1] \ \mathbb{Z}\_{(2)} = m\_c$</li><li>$[(h^N(K) \oplus h^{n'}(K')) \And 0xf0] \ \mathbb{Z}\_{(3)} = s$</li></ul> |
 | `4` | $x\_2 = h^{n'}(K') \oplus h(t\_c)$ |
 
 Send $x_1$ and $x_2$.