Negating a value means taking its opposite. The opposite of a ciphertext representing a message$m$ in the interval $[min, max]$ is a ciphertext representing $-m$ in the interval $[-max, -min]$. This operation does not consume padding nor add noise but it modifies the interval of the encoder.

Computing an LWE opposite

To compute the opposite of an LWE, simply use the opposite method, which will return a new ciphertext with the modified value. The method exists in a mutable opposite_inplace form as well, which modifies the ciphertext itself. All operations in concrete are implemented in immutable and mutable forms, with mutable forms always postfixed with _inplace.

Here is a complete example for a single LWE:

/// file: main.rs
use concrete::*;
​
fn main() -> Result<(), CryptoAPIError> {
    // encoder
    let encoder = Encoder::new(50., 100., 8, 2)?;
​
    // generate a secret key
    let secret_key = LWESecretKey::new(&LWE128_1024);
​
    // the message to negate
    let message: f64 = 95.46;
​
    // encode and encrypt
    let mut ciphertext = LWE::encode_encrypt(&secret_key, message, &encoder)?;
​
    // compute the opposite of the ciphertext
    ciphertext.opposite_inplace()?;
​
    // decryption
    let output: f64 = ciphertext.decrypt_decode(&secret_key)?;
​
    // check the value computed
    println!("opposite({}) = {}", message, output);
    Ok(())
}

As for all operations in Concrete, they can be applied to a vector of messages using the VectorLWE struct instead of LWE. The vectorized form has an additional method opposite_nth that enables negating a single value by passing its index to the function.