Negating a ciphertext

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.

Operation	$opposite(E[m]) = E[-m]$
Type	Noiseless
Side effects	Modifies encoding

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.