> ## Documentation Index
> Fetch the complete documentation index at: https://docs.inco.org/llms.txt
> Use this file to discover all available pages before exploring further.

# Operations

> Operations available on encrypted data

# Operations

Inco Lightning provides arithmetic, comparison, and bitwise operations on encrypted values.

## Arithmetic Operations

All arithmetic operations return an `Euint128`.

| Function | Description    | Signature                          |
| -------- | -------------- | ---------------------------------- |
| `e_add`  | Addition       | `(Euint128, Euint128) -> Euint128` |
| `e_sub`  | Subtraction    | `(Euint128, Euint128) -> Euint128` |
| `e_mul`  | Multiplication | `(Euint128, Euint128) -> Euint128` |
| `e_rem`  | Remainder      | `(Euint128, Euint128) -> Euint128` |

### Example: Encrypted Addition

```rust theme={null}
pub fn add_balances(
    ctx: Context<AddBalances>,
    amount_a: Euint128,
    amount_b: Euint128,
) -> Result<()> {
    let cpi_ctx = CpiContext::new(
        ctx.accounts.inco_lightning_program.to_account_info(),
        Operation {
            signer: ctx.accounts.authority.to_account_info(),
        },
    );

    // Add two encrypted values
    let result: Euint128 = e_add(cpi_ctx, amount_a, amount_b, 0)?;

    ctx.accounts.account.total = result;

    // IMPORTANT: After storing the result handle, grant decryption access
    // to the appropriate address (e.g., owner) using the `allow` function.
    // See the Access Control guide for details.

    Ok(())
}
```

## Comparison Operations

Comparison operations return an `Ebool`.

| Function | Description           | Signature                       |
| -------- | --------------------- | ------------------------------- |
| `e_ge`   | Greater than or equal | `(Euint128, Euint128) -> Ebool` |
| `e_gt`   | Greater than          | `(Euint128, Euint128) -> Ebool` |
| `e_le`   | Less than or equal    | `(Euint128, Euint128) -> Ebool` |
| `e_lt`   | Less than             | `(Euint128, Euint128) -> Ebool` |
| `e_eq`   | Equal                 | `(Euint128, Euint128) -> Ebool` |

## Bitwise Operations

| Function | Description | Signature                          |
| -------- | ----------- | ---------------------------------- |
| `e_and`  | Bitwise AND | `(Euint128, Euint128) -> Euint128` |
| `e_or`   | Bitwise OR  | `(Euint128, Euint128) -> Euint128` |
| `e_not`  | Bitwise NOT | `(Euint128) -> Euint128`           |
| `e_shl`  | Shift left  | `(Euint128, Euint128) -> Euint128` |
| `e_shr`  | Shift right | `(Euint128, Euint128) -> Euint128` |

## CPI Context Pattern

All operations require a CPI context with the Inco Lightning program:

```rust theme={null}
let cpi_ctx = CpiContext::new(
    ctx.accounts.inco_lightning_program.to_account_info(),
    Operation {
        signer: ctx.accounts.authority.to_account_info(),
    },
);

let result = e_add(cpi_ctx, a, b, 0)?;

// IMPORTANT: Define allowance rules after each operation that produces
// a handle you want to decrypt later. See Access Control guide.
```

<Note>
  The last parameter in operation calls identifies whether the left-hand side operand is ciphertext (`0`) or plaintext (`1`). Always pass `0` when working with encrypted handles.
</Note>