chore: correct phrasing and add tutorial link

app.py

@@ -366,17 +366,22 @@ with demo:
             <a href="https://twitter.com/zama_fhe"> <img style="vertical-align: middle; display:inline-block; margin-right: 3px;" width=15 src="https://user-images.githubusercontent.com/5758427/197975044-bab9d199-e120-433b-b3be-abd73b211a54.png">@zama_fhe</a>
         </p>
         <p align="center">
-            <img src="https://user-images.githubusercontent.com/56846628/219113256-ab5f1fd3-b144-45b0-a7de-3c0501f5c238.png" width="70%" height="70%">
+            Experiment with photo filtering using Homomorphic Encryption by following our
+            <a href="https://zama.ai/post/encrypted-image-filtering-using-homomorphic-encryption"> tutorial</a>
+            .
+        </p>
+        <p align="center">
+            <img src="https://user-images.githubusercontent.com/56846628/219403891-96591b1d-cbeb-4e81-91a9-7907c7ea91df.png" width="70%" height="70%">
         </p>
         """
     )
 
     gr.Markdown("## Client side")
-    gr.Markdown("### Step 1. Upload an image. ")
+    gr.Markdown("### Step 1: Upload an image. ")
     gr.Markdown(
-        f"The image will automatically be resized to shape ({INPUT_SHAPE[0]}x{INPUT_SHAPE[1]})."
-        "The image displayed here is however using its original resolution. The true image used "
-        "in this demo can be seen in Step. 8."
+        f"The image will automatically be resized to shape ({INPUT_SHAPE[0]}x{INPUT_SHAPE[1]}). "
+        "The image here, however, is displayed in its original resolution. The true image used "
+        "in this demo can be seen in Step 8."
     )
     with gr.Row():
         input_image = gr.Image(
@@ -387,7 +392,7 @@ with demo:
             examples=EXAMPLES, inputs=[input_image], examples_per_page=5, label="Examples to use."
         )
 
-    gr.Markdown("### Step 2. Choose your filter")
+    gr.Markdown("### Step 2: Choose your filter.")
     filter_name = gr.Dropdown(
         choices=AVAILABLE_FILTERS, value="inverted", label="Choose your filter", interactive=True
     )
@@ -395,12 +400,12 @@ with demo:
     gr.Markdown("#### Notes")
     gr.Markdown(
         """
-        - The private key is used to encrypt and decrypt the data and shall never be shared.
-        - No public key are required for these filter operators.
+        - The private key is used to encrypt and decrypt the data and will never be shared.
+        - No public key is required for these filter operators.
         """
     )
     
-    gr.Markdown("### Step 3. Generate the private key.")
+    gr.Markdown("### Step 3: Generate the private key.")
     keygen_button = gr.Button("Generate the private key.")
 
     with gr.Row():
@@ -412,7 +417,7 @@ with demo:
 
     user_id = gr.Textbox(label="", max_lines=2, interactive=False, visible=False)
     
-    gr.Markdown("### Step 4. Encrypt the image using FHE.")
+    gr.Markdown("### Step 4: Encrypt the image using FHE.")
     encrypt_button = gr.Button("Encrypt the image using FHE.")
 
     with gr.Row():
@@ -431,19 +436,19 @@ with demo:
         "the encrypted results to the client."
     )
 
-    gr.Markdown("### Step 5. Send the encrypted image to the server.")
+    gr.Markdown("### Step 5: Send the encrypted image to the server.")
     send_input_button = gr.Button("Send the encrypted image to the server.")
     send_input_checkbox = gr.Checkbox(label="Encrypted image sent.", interactive=False)
 
-    gr.Markdown("### Step 6. Run FHE execution.")
+    gr.Markdown("### Step 6: Run FHE execution.")
     execute_fhe_button = gr.Button("Run FHE execution.")
     fhe_execution_time = gr.Textbox(
         label="Total FHE execution time (in seconds):", max_lines=1, interactive=False
     )
 
-    gr.Markdown("### Step 7. Receive the encrypted output image from the server.")
+    gr.Markdown("### Step 7: Receive the encrypted output image from the server.")
     gr.Markdown(
-        "The image displayed here is the encrypted result sent by the server which has been "
+        "The image displayed here is the encrypted result sent by the server, which has been "
         "decrypted using a different private key. This is only used to visually represent an "
         "encrypted image."
     )
@@ -461,11 +466,11 @@ with demo:
 
     gr.Markdown("## Client side")
     gr.Markdown(
-        "The encrypted output is sent back to client, who can finally decrypt it with its "
+        "The encrypted output is sent back to the client, who can finally decrypt it with the "
         "private key. Only the client is aware of the original image and its transformed version."
     )
 
-    gr.Markdown("### Step 8. Decrypt the output")
+    gr.Markdown("### Step 8: Decrypt the output.")
     gr.Markdown(
         "The image displayed on the left is the input image used during the demo. The output image "
         "can be seen on the right."