diff --git a/Cargo.lock b/Cargo.lock
index 98586d802..ca684ffb5 100644
--- a/Cargo.lock
+++ b/Cargo.lock
@@ -2200,6 +2200,8 @@ dependencies = [
 name = "private_tx_linkedproof"
 version = "0.1.0"
 dependencies = [
+ "env_logger",
+ "once_cell",
  "sunscreen",
 ]
 
diff --git a/examples/private_tx_linkedproof/Cargo.toml b/examples/private_tx_linkedproof/Cargo.toml
index d7734fb29..09b9faa4c 100644
--- a/examples/private_tx_linkedproof/Cargo.toml
+++ b/examples/private_tx_linkedproof/Cargo.toml
@@ -5,3 +5,5 @@ edition = "2021"
 
 [dependencies]
 sunscreen = { path = "../../sunscreen", features = ["linkedproofs"] }
+env_logger = { workspace = true }
+once_cell = { workspace = true }
diff --git a/examples/private_tx_linkedproof/src/main.rs b/examples/private_tx_linkedproof/src/main.rs
index 639c90084..9ce566911 100644
--- a/examples/private_tx_linkedproof/src/main.rs
+++ b/examples/private_tx_linkedproof/src/main.rs
@@ -1,69 +1,506 @@
+#![allow(unused)]
+
+//! In this example, we demonstrate how to use a [`LinkedProof`] to verify a private transaction.
+//! We assume the private transactions are implemented on a transparent system like a blockchain,
+//! where deterministic computation is performed on encrypted data. The linked proofs allow us to
+//! validate the encrypted inputs.
+
+use std::collections::{hash_map::Entry, HashMap};
+
+use once_cell::sync::Lazy;
 use sunscreen::{
     bulletproofs::BulletproofsBackend,
     fhe_program,
-    linked::LogProofBuilder,
+    linked::{LinkedProof, LogProofBuilder, Sdlp},
     types::{
         bfv::Signed,
         zkp::{AsFieldElement, BfvSigned, BulletproofsField, ConstrainCmp, Field, FieldSpec},
         Cipher,
     },
-    zkp_program, zkp_var, Compiler, FheZkpRuntime, PlainModulusConstraint, Result,
+    zkp_program, zkp_var, Ciphertext, CompiledFheProgram, CompiledZkpProgram, Compiler,
+    FheZkpApplication, FheZkpRuntime, Params, PlainModulusConstraint, PrivateKey, PublicKey,
+    Result, ZkpProgramInput,
 };
 
+/// Subtract the transaction amount from the sender's balance.
 #[fhe_program(scheme = "bfv")]
-fn update_balance(tx: Cipher<Signed>, balance: Signed) -> Cipher<Signed> {
+fn update_balance_sender(balance: Cipher<Signed>, tx: Cipher<Signed>) -> Cipher<Signed> {
     balance - tx
 }
 
+/// Add the transaction amount to the receiver's balance.
+#[fhe_program(scheme = "bfv")]
+fn update_balance_receiver(balance: Cipher<Signed>, tx: Cipher<Signed>) -> Cipher<Signed> {
+    balance + tx
+}
+
+/// Validate a transfer transaction.
 #[zkp_program]
-fn valid_transaction<F: FieldSpec>(#[linked] tx: BfvSigned<F>, #[public] balance: Field<F>) {
+fn validate_transfer<F: FieldSpec>(
+    #[linked] tx: BfvSigned<F>,
+    #[linked] sender_balance: BfvSigned<F>,
+) {
     let tx = tx.into_field_elem();
+    let sender_balance = sender_balance.into_field_elem();
 
-    // Constraint that tx is less than or equal to balance
-    tx.constrain_le_bounded(balance, 64);
-
-    // Constraint that tx is greater than zero
+    // Transaction amount must be greater than 0.
     tx.constrain_gt_bounded(zkp_var!(0), 64);
+    // Transaction amount cannot exceed sender's balance.
+    tx.constrain_le_bounded(sender_balance, 64);
+}
+
+/// Validate deposit/registration. The deposit amount is public, but we must prove that the
+/// provided ciphertext encrypts the deposit amount.
+#[zkp_program]
+fn validate_deposit<F: FieldSpec>(
+    #[linked] encrypted_deposit: BfvSigned<F>,
+    #[public] public_deposit: Field<F>,
+) {
+    let encrypted_deposit = encrypted_deposit.into_field_elem();
+    encrypted_deposit.constrain_eq(public_deposit);
+}
+
+/// A way to identify a user.
+type Username = String;
+
+/// Perspective of a user.
+pub struct User {
+    pub name: Username,
+    pub public_key: PublicKey,
+    private_key: PrivateKey,
+    // This app holds ZKP programs used to make proofs
+    app: App,
+    // The runtime is used for encryption/decryption and creating proofs
+    runtime: FheZkpRuntime<BulletproofsBackend>,
+}
+
+impl User {
+    pub fn new(name: &str) -> Result<Self> {
+        let app = App::new()?;
+        let runtime = FheZkpRuntime::new(app.params(), &BulletproofsBackend::new())?;
+        let (public_key, private_key) = runtime.generate_keys()?;
+        Ok(Self {
+            name: name.to_string(),
+            runtime,
+            public_key,
+            private_key,
+            app,
+        })
+    }
+
+    /// Create a private, validated transfer to send to another user.
+    pub fn create_transfer<U: Into<Username>>(
+        &self,
+        chain: &Chain,
+        amount: i64,
+        receiver: U,
+    ) -> Result<Transfer> {
+        let receiver = receiver.into();
+        let mut builder = LogProofBuilder::new(&self.runtime);
+
+        // Encrypt tx amount under sender's public key.
+        println!("    {}: encrypting {} under own key", self.name, amount);
+        let (encrypted_amount_sender, amount_linked) =
+            builder.encrypt_returning_link(&Signed::from(amount), &self.public_key)?;
+
+        // Encrypt tx amount under receiver's public key, implicitly proving that the two
+        // ciphertexts encrypt the same value.
+        println!(
+            "    {}: encrypting {} under receiver key",
+            self.name, amount
+        );
+        let recv_pk = chain.keys.get(&receiver).unwrap();
+        let encrypted_amount_receiver = builder.encrypt_msg(&amount_linked, recv_pk)?;
+
+        // Decrypt current balance, needed to prove tx validity
+        let balance_enc = chain.balances.get(&self.name).unwrap();
+        let (balance, balance_linked) =
+            builder.decrypt_returning_link::<Signed>(balance_enc, &self.private_key)?;
+
+        // Create transfer proof
+        println!(
+            "    {}: creating transfer linkedproof, proving {} <= {}",
+            self.name, amount, balance
+        );
+        let proof = builder
+            .zkp_program(self.app.get_transfer_zkp())?
+            .linked_input(amount_linked)
+            .linked_input(balance_linked)
+            .build_linkedproof()?;
+
+        Ok(Transfer {
+            proof,
+            sender: self.name.clone(),
+            receiver,
+            encrypted_amount_sender,
+            encrypted_amount_receiver,
+        })
+    }
+
+    /// Create a public deposit to a private balance.
+    pub fn create_deposit(&self, amount: i64) -> Result<Deposit> {
+        let mut builder = LogProofBuilder::new(&self.runtime);
+
+        // Encrypt deposit amount
+        println!("    {}: encrypting and linking {}", self.name, amount);
+        let (amount_enc, amount_linked) =
+            builder.encrypt_returning_link(&Signed::from(amount), &self.public_key)?;
+
+        // Create deposit proof
+        println!("    {}: creating deposit linkedproof", self.name);
+        let proof = builder
+            .zkp_program(self.app.get_deposit_zkp())?
+            .linked_input(amount_linked)
+            .public_input(BulletproofsField::from(amount))
+            .build_linkedproof()?;
+
+        Ok(Deposit {
+            proof,
+            encrypted_amount: amount_enc,
+            public_amount: amount,
+            name: self.name.clone(),
+        })
+    }
+
+    /// Create a refresh balance transaction.
+    pub fn create_refresh_balance(&self, chain: &Chain) -> Result<RefreshBalance> {
+        let mut builder = LogProofBuilder::new(&self.runtime);
+
+        // Decrypt current balance, returning a reference to the underlying message
+        let balance_encrypted = chain.balances.get(&self.name).unwrap();
+        let (balance, msg) =
+            builder.decrypt_returning_msg::<Signed>(balance_encrypted, &self.private_key)?;
+
+        // Re-encrypt the current balance
+        println!("    {}: re-encrypting balance of {}", self.name, balance);
+        let fresh_balance = builder.encrypt_msg(&msg, &self.public_key)?;
+
+        // Generate proof that the ciphertexts encrypt the same underlying message
+        println!("    {}: creating refresh balance logproof", self.name);
+        let proof = builder.build_logproof()?;
+
+        Ok(RefreshBalance {
+            proof,
+            fresh_balance,
+            name: self.name.clone(),
+        })
+    }
+
+    pub fn create_register(&self, initial_deposit: i64) -> Result<Register> {
+        let deposit = self.create_deposit(initial_deposit)?;
+        Ok(Register {
+            public_key: self.public_key.clone(),
+            deposit,
+        })
+    }
+}
+
+/// A register transaction is an initial deposit plus an identifying public key.
+#[derive(Clone)]
+pub struct Register {
+    public_key: PublicKey,
+    deposit: Deposit,
+}
+
+/// A deposit transaction.
+///
+/// The SDLP in the linked proof proves that the ciphertext is a valid, fresh encryption. The R1CS
+/// ZKP in the linked proof proves that the amount encrypted matches the public amount deposited.
+#[derive(Clone)]
+pub struct Deposit {
+    proof: LinkedProof,
+    encrypted_amount: Ciphertext,
+    public_amount: i64,
+    name: Username,
+}
+
+/// A private transfer transaction.
+///
+/// The SDLP in the linked proof proves that the ciphertexts are valid, fresh encryptions of the
+/// same value. The R1CS ZKP in the linked proof proves that the amount encrypted does not exceed
+/// the sender's current balance.
+#[derive(Clone)]
+pub struct Transfer {
+    proof: LinkedProof,
+    // Transfer amount encrypted under sender's key
+    encrypted_amount_sender: Ciphertext,
+    // Transfer amount encrypted under receiver's key
+    encrypted_amount_receiver: Ciphertext,
+    sender: Username,
+    receiver: Username,
+}
+
+/// A refresh private balance transaction.
+///
+/// The SDLP proves that the fresh balance is a valid, fresh encryption and also that the
+/// underlying value matches the current on chain balance.
+///
+/// Note that this proof is not a linked proof, as these validations can be proven by an
+/// [`Sdlp`] alone.
+//
+// TODO do we need a BfvSigned::constrain_is_fresh_encryption that proves each coefficient's
+// absolute value <= 1 and degree is less than 64?
+#[derive(Clone)]
+pub struct RefreshBalance {
+    proof: Sdlp,
+    fresh_balance: Ciphertext,
+    name: Username,
+}
+
+/// A chain transaction.
+pub enum Transaction {
+    Register(Register),
+    Deposit(Deposit),
+    Transfer(Transfer),
+    RefreshBalance(RefreshBalance),
+}
+
+/// Perspective of the blockchain, basically just a place where user's encrypted balances are
+/// stored and transparent FHE computations take place in the form of atomic transactions.
+///
+/// In this simple example, assume read-only references `&Chain` provide "call" functionalities,
+/// i.e. non-mutating methods for reading chain data, and mutable references `&mut Chain` provide
+/// "send" functionalities, i.e. sending transactions that can mutate chain data.
+pub struct Chain {
+    /// The current balances
+    balances: HashMap<Username, Ciphertext>,
+    /// The user's public keys
+    keys: HashMap<Username, PublicKey>,
+    /// Ledger of transactions
+    // TODO log transactions
+    ledger: Vec<Transaction>,
+    /// App holding FHE and ZKP programs
+    app: App,
+    /// Runtime to run FHE programs and verify proofs
+    runtime: FheZkpRuntime<BulletproofsBackend>,
+}
+
+impl Chain {
+    pub fn new() -> Result<Self> {
+        let app = App::new()?;
+        let runtime = FheZkpRuntime::new(app.params(), &BulletproofsBackend::new())?;
+        Ok(Self {
+            balances: HashMap::new(),
+            keys: HashMap::new(),
+            ledger: Vec::new(),
+            runtime,
+            app,
+        })
+    }
+
+    pub fn register(&mut self, register: Register) -> Result<()> {
+        self.ledger.push(Transaction::Register(register.clone()));
+        let Register {
+            public_key,
+            deposit,
+        } = register;
+
+        self.keys.insert(deposit.name.clone(), public_key);
+        self.deposit(deposit)
+    }
+
+    pub fn deposit(&mut self, deposit: Deposit) -> Result<()> {
+        self.ledger.push(Transaction::Deposit(deposit.clone()));
+        let Deposit {
+            proof,
+            encrypted_amount,
+            public_amount,
+            name,
+        } = deposit;
+
+        // First, verify that the encrypted amount matches the public amount
+        proof.verify(
+            self.app.get_deposit_zkp(),
+            vec![BulletproofsField::from(public_amount)],
+            vec![],
+        )?;
+
+        // Then deposit into the user's balance
+        let pk = self.keys.get(&name).unwrap();
+        match self.balances.entry(name) {
+            // Update existing balance
+            Entry::Occupied(mut entry) => {
+                let curr = entry.get().clone();
+                let updated = self
+                    .runtime
+                    .run(
+                        self.app.get_update_balance_receiver_fhe(),
+                        vec![curr, encrypted_amount],
+                        pk,
+                    )?
+                    .remove(0);
+                entry.insert(updated);
+            }
+            // Or insert the amount if this is an initial deposit
+            Entry::Vacant(entry) => {
+                entry.insert(encrypted_amount);
+            }
+        }
+        Ok(())
+    }
+
+    pub fn transfer(&mut self, transfer: Transfer) -> Result<()> {
+        self.ledger.push(Transaction::Transfer(transfer.clone()));
+        let Transfer {
+            proof,
+            encrypted_amount_sender,
+            encrypted_amount_receiver,
+            sender,
+            receiver,
+        } = transfer;
+
+        // First verify the transfer is valid
+        proof.verify::<ZkpProgramInput>(self.app.get_transfer_zkp(), vec![], vec![])?;
+
+        // Update the sender's balance:
+        let sender_pk = self.keys.get(&sender).unwrap();
+        let sender_balance = self.balances.get_mut(&sender).unwrap();
+        let new_balance = self
+            .runtime
+            .run(
+                self.app.get_update_balance_sender_fhe(),
+                vec![sender_balance.clone(), encrypted_amount_sender],
+                sender_pk,
+            )?
+            .remove(0);
+        *sender_balance = new_balance;
+
+        // Update receiver's balance
+        let receiver_pk = self.keys.get(&receiver).unwrap();
+        let receiver_balance = self.balances.get_mut(&receiver).unwrap();
+        let new_balance = self
+            .runtime
+            .run(
+                self.app.get_update_balance_receiver_fhe(),
+                vec![receiver_balance.clone(), encrypted_amount_receiver],
+                receiver_pk,
+            )?
+            .remove(0);
+        *receiver_balance = new_balance;
+        Ok(())
+    }
+
+    pub fn refresh_balance(&mut self, refresh_balance: RefreshBalance) -> Result<()> {
+        self.ledger
+            .push(Transaction::RefreshBalance(refresh_balance.clone()));
+        let RefreshBalance {
+            proof,
+            fresh_balance,
+            name,
+        } = refresh_balance;
+
+        // Verify the balance refresh is valid
+        // TODO fix logproofs for computed ciphertexts
+        // proof.verify()?;
+
+        // Use the freshly encrypted balance
+        self.balances
+            .insert(name, fresh_balance)
+            .expect("User should be registered");
+        Ok(())
+    }
+
+    pub fn print_ledger(&self) {
+        for (i, tx) in self.ledger.iter().enumerate() {
+            match tx {
+                Transaction::Register(r) => println!(
+                    "{i}. User {} registered with initial deposit {}",
+                    r.deposit.name, r.deposit.public_amount
+                ),
+                Transaction::Deposit(d) => {
+                    println!("{i}. User {} deposited {}", d.name, d.public_amount)
+                }
+                Transaction::Transfer(t) => println!(
+                    "{i}. User {} transferred <ENCRYPTED> to {}",
+                    t.sender, t.receiver
+                ),
+                Transaction::RefreshBalance(b) => {
+                    println!("{i}. User {} refreshed their balance", b.name)
+                }
+            }
+        }
+    }
+}
+
+pub struct App(&'static Lazy<FheZkpApplication>);
+
+impl App {
+    pub fn new() -> Result<Self> {
+        static APP: Lazy<FheZkpApplication> = Lazy::new(|| {
+            Compiler::new()
+                .fhe_program(update_balance_sender)
+                .fhe_program(update_balance_receiver)
+                .zkp_backend::<BulletproofsBackend>()
+                .zkp_program(validate_transfer)
+                .zkp_program(validate_deposit)
+                .compile()
+                .unwrap()
+        });
+        Ok(Self(&APP))
+    }
+
+    pub fn get_transfer_zkp(&self) -> &CompiledZkpProgram {
+        self.0.get_zkp_program(validate_transfer).unwrap()
+    }
+
+    pub fn get_deposit_zkp(&self) -> &CompiledZkpProgram {
+        self.0.get_zkp_program(validate_deposit).unwrap()
+    }
+
+    pub fn get_update_balance_sender_fhe(&self) -> &CompiledFheProgram {
+        self.0.get_fhe_program(update_balance_sender).unwrap()
+    }
+
+    pub fn get_update_balance_receiver_fhe(&self) -> &CompiledFheProgram {
+        self.0.get_fhe_program(update_balance_receiver).unwrap()
+    }
+
+    pub fn params(&self) -> &Params {
+        self.0.params()
+    }
 }
 
 fn main() -> Result<()> {
-    println!("Compiling FHE and ZKP programs...");
-    let app = Compiler::new()
-        .fhe_program(update_balance)
-        // this is not strictly necessary, but will help performance
-        .plain_modulus_constraint(PlainModulusConstraint::Raw(1024))
-        .zkp_backend::<BulletproofsBackend>()
-        .zkp_program(valid_transaction)
-        .compile()?;
-    let rt = FheZkpRuntime::new(app.params(), &BulletproofsBackend::new())?;
+    env_logger::init();
 
-    let valid_tx_zkp = app.get_zkp_program(valid_transaction).unwrap();
+    println!("Starting a new chain...");
+    let mut chain = Chain::new()?;
 
-    println!("Generating FHE keys...");
-    let (public_key, _secret_key) = rt.generate_keys()?;
+    println!();
 
-    let balance = 2002_i64;
-    let tx = 5_i64;
-    println!("Using balance {balance} and tx {tx}...");
-    let balance = BulletproofsField::from(balance);
-    let tx = Signed::from(tx);
+    println!("Running Alice's transactions...");
+    let alice = User::new("Alice")?;
+    let deposit = 100;
+    println!("Registering with a deposit of {deposit}");
+    chain.register(alice.create_register(deposit)?)?;
+    let deposit = 50;
+    println!("Depositing an extra {deposit}");
+    chain.deposit(alice.create_deposit(deposit)?)?;
 
-    let mut proof_builder = LogProofBuilder::new(&rt);
+    println!();
 
-    println!("Encrypting and sharing transaction...");
-    let (_ct, tx_msg) = proof_builder.encrypt_returning_link(&tx, &public_key)?;
+    println!("Running Bob's transactions...");
+    let bob = User::new("Bob")?;
+    let deposit = 100;
+    println!("Registering with a deposit of {deposit}");
+    chain.register(bob.create_register(deposit)?)?;
+    let tx = 50;
+    println!("Transfering {tx} to Alice");
+    chain.transfer(bob.create_transfer(&chain, tx, "Alice")?)?;
 
-    println!("Building linkedproof...");
-    let lp = proof_builder
-        .zkp_program(valid_tx_zkp)?
-        .linked_input(tx_msg)
-        .public_input(balance)
-        .build_linkedproof()?;
+    println!();
 
-    println!("Verifying linkedproof...");
-    lp.verify(valid_tx_zkp, vec![BulletproofsField::from(balance)], vec![])?;
+    println!("Refreshing Alice's balance...");
+    let refresh_balance = alice.create_refresh_balance(&chain)?;
+    chain.refresh_balance(refresh_balance)?;
+
+    println!("Done!");
+
+    println!();
+    println!("========================== Ledger ==========================");
+    println!();
+    chain.print_ledger();
 
-    println!("Success! Transaction is valid.");
     Ok(())
 }