diff --git a/README.md b/README.md
index 02f62f6..3ef8708 100644
--- a/README.md
+++ b/README.md
@@ -10,7 +10,7 @@ This code has not been formally audited, Use at your own risk or ask a cryptogra
 [Lioness](https://www.cl.cam.ac.uk/~rja14/Papers/bear-lion.pdf) is a large block cipher built from 
 - Stream cipher, 
 - Hash function,
-- Key derivation function (KDF), although this can be remove if the input key is large enough to cover the four sub-keys used.
+- Key derivation function (KDF), although this can be removed if the input key is large enough to cover the four sub-keys used.
 
 In here we use:
 - Chacha20 from [rustcrypto streamciphers](https://github.com/RustCrypto/stream-ciphers)
@@ -52,12 +52,12 @@ Some notes:
 
 - Encryption and decryption are both in-place for now.
 - The block length need to be bigger than `32` bytes because Lioness splits the block into two where the left part is 32-byte, and the right part can't be empty. might support small blocks in the future, but for Sphinx use-case, this should work.
-- If you need authenticity, make sure to prepend the plaintext with `k` zeros and check the zeros after decryption. This will be supported in the future... see [integrity example](./examples/integrity.rs)
+- If you need authenticity, make sure to prepend the plaintext with `k = 128-bits` zeros and check the zeros after decryption. This will be supported in the future... see [integrity example](./examples/integrity.rs)
 
 ### TODO
 - [ ] Add more tests, examples, and benchmarks ...
 - [ ] Make it generic for any compatible cipher, keyed_hash, and KDF. 
-- [ ] Compare with another implementation ... maybe with Haskel when available.
+- [ ] Compare with existing implementation + maybe with Haskel when available.
 - [ ] Add a version with API which prepend the plaintext with k-zeros and checks authenticity after decryption.
 - [ ] impl enc and dec to the API to work beside encrypt_in_place and decrypt_in_place.
 - ...
diff --git a/examples/integrity.rs b/examples/integrity.rs
index aedfa93..f7fd7e0 100644
--- a/examples/integrity.rs
+++ b/examples/integrity.rs
@@ -1,7 +1,7 @@
 use anyhow::Result;
 use lioness_blockcipher::{Lioness, MasterKey};
 
-const K: usize = 32;
+const K: usize = 16;
 
 fn main() -> Result<()> {
     let key: MasterKey = [0x42; 32];
diff --git a/src/lib.rs b/src/lib.rs
index 299eddb..c94ddd9 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -9,11 +9,11 @@ use sha3::{
 };
 use zeroize::{Zeroize, ZeroizeOnDrop};
 
-// We expect the input key to be of size 32 bytes (128-bits)
+// We expect the input key to be of size 32 bytes (256-bits)
 // because in sphinx this is the size of the shared key `s` between the sender and each hop.
 // This shared key is then used to derive all the needed keys to encrypt the payload
 pub const MASTER_KEY_LEN: usize = 32;
-// For LIONESS, the length of the left part of the key (after splitting block into left `L` and right `R`)
+// For LIONESS, the length of the left part (after splitting block into left `L` and right `R`)
 // must be the same size as:
 // - the stream cipher key
 // - the output (digest) of the keyed-hash function
@@ -58,7 +58,7 @@ struct RoundKeys {
 /// WARNING: integrity/authenticity is not guaranteed by the LIONESS large-block cipher
 /// This is because LIONESS is not an AEAD but one can add an authentication check by
 /// simply prepending the plaintext with `k` bytes of zeros
-/// a safe value for `k` would be 32 bytes which is what the Sphinx paper suggests.
+/// a safe value for `k` would be 16-bytes which is what the Sphinx paper suggests.
 /// However, this prepending is not part of the code here.
 #[derive(Clone, ZeroizeOnDrop)]
 pub struct Lioness {