Negating a ciphertext

Negating a value means taking its opposite. The opposite of a ciphertext representing a messagemm in the interval [min,max][min, max] is a ciphertext representing m-m in the interval [max,min][-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]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.