diff --git a/src/components/run_window/key_store_tab.rs b/src/components/run_window/key_store_tab.rs
index 4154531..6f3d76e 100644
--- a/src/components/run_window/key_store_tab.rs
+++ b/src/components/run_window/key_store_tab.rs
@@ -9,36 +9,38 @@ use leptos::{
     SignalWith, View,
 };
 use simfony::{elements, simplicity};
+use elements::secp256k1_zkp::rand;
 
 use crate::components::copy_to_clipboard::CopyToClipboard;
 
 #[derive(Copy, Clone, Debug)]
 pub struct SigningKeys {
+    pub key_offset: RwSignal<u32>,
     pub key_count: RwSignal<u32>,
     pub secret_keys: Signal<Vec<secp256k1_zkp::Keypair>>,
 }
 
 impl Default for SigningKeys {
     fn default() -> Self {
-        Self::new(1)
+        Self::new(rand::random(), 1)
     }
 }
 
 impl SigningKeys {
-    pub fn new(key_count: u32) -> Self {
-        let key_count = create_rw_signal(key_count);
+    pub fn new(key_offset: u32, key_count: u32) -> Self {
         let secret_keys = Signal::derive(move || -> Vec<secp256k1_zkp::Keypair> {
             let mut index = 0;
-            (0..key_count.get())
+            (0..key_count)
                 .map(|_| {
-                    let (key, new_index) = new_key(index);
+                    let (key, new_index) = new_key(key_offset, index);
                     index = new_index;
                     key
                 })
                 .collect()
         });
         Self {
-            key_count,
+            key_offset: create_rw_signal(key_offset),
+            key_count: create_rw_signal(key_count),
             secret_keys,
         }
     }
@@ -82,11 +84,12 @@ impl SigningKeys {
     }
 }
 
-fn new_key(start_index: u32) -> (secp256k1_zkp::Keypair, u32) {
+fn new_key(start_offset: u32, start_index: u32) -> (secp256k1_zkp::Keypair, u32) {
     let mut offset = 1;
     loop {
         let index = start_index + offset;
         let mut secret_key_bytes = [0u8; 32];
+        secret_key_bytes[24..28].copy_from_slice(&start_offset.to_be_bytes());
         secret_key_bytes[28..].copy_from_slice(&index.to_be_bytes());
         match secp256k1_zkp::Keypair::from_seckey_slice(secp256k1_zkp::SECP256K1, &secret_key_bytes)
         {
diff --git a/src/components/state.rs b/src/components/state.rs
index e940c33..0ef09b9 100644
--- a/src/components/state.rs
+++ b/src/components/state.rs
@@ -18,15 +18,18 @@ pub trait ToParams {
 
 impl FromParams for SigningKeys {
     fn from_map(map: &ParamsMap) -> Option<Self> {
-        map.get("keys")
-            .and_then(|s| s.parse::<u32>().ok())
-            .map(Self::new)
+        let key_offset = map.get("seed").and_then(|s| s.parse::<u32>().ok())?;
+        let key_count = map.get("keys").and_then(|s| s.parse::<u32>().ok())?;
+        Some(Self::new(key_offset, key_count))
     }
 }
 
 impl ToParams for SigningKeys {
     fn to_params(&self) -> impl Iterator<Item = (&'static str, String)> {
-        [("keys", self.key_count.get_untracked().to_string())].into_iter()
+        [
+            ("seed", self.key_offset.get_untracked().to_string()),
+            ("keys", self.key_count.get_untracked().to_string()),
+        ].into_iter()
     }
 }