# 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.rsuse 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.