Trait CrtGadgets

pub trait CrtGadgets:
    FancyArithmetic
    + FancyBinary
    + ArithmeticBundleGadgets
    + BundleGadgets {
    // Provided methods
    fn crt_constant_bundle(
        &mut self,
        x: u128,
        q: u128,
    ) -> Result<CrtBundle<Self::Item>, Self::Error> { ... }
    fn crt_output(
        &mut self,
        x: &CrtBundle<Self::Item>,
    ) -> Result<Option<u128>, Self::Error> { ... }
    fn crt_outputs(
        &mut self,
        xs: &[CrtBundle<Self::Item>],
    ) -> Result<Option<Vec<u128>>, Self::Error> { ... }
    fn crt_add(
        &mut self,
        x: &CrtBundle<Self::Item>,
        y: &CrtBundle<Self::Item>,
    ) -> Result<CrtBundle<Self::Item>, Self::Error> { ... }
    fn crt_sub(
        &mut self,
        x: &CrtBundle<Self::Item>,
        y: &CrtBundle<Self::Item>,
    ) -> Result<CrtBundle<Self::Item>, Self::Error> { ... }
    fn crt_cmul(
        &mut self,
        x: &CrtBundle<Self::Item>,
        c: u128,
    ) -> Result<CrtBundle<Self::Item>, Self::Error> { ... }
    fn crt_mul(
        &mut self,
        x: &CrtBundle<Self::Item>,
        y: &CrtBundle<Self::Item>,
    ) -> Result<CrtBundle<Self::Item>, Self::Error> { ... }
    fn crt_cexp(
        &mut self,
        x: &CrtBundle<Self::Item>,
        c: u16,
    ) -> Result<CrtBundle<Self::Item>, Self::Error> { ... }
    fn crt_rem(
        &mut self,
        x: &CrtBundle<Self::Item>,
        p: u16,
    ) -> Result<CrtBundle<Self::Item>, Self::Error> { ... }
    fn crt_fractional_mixed_radix(
        &mut self,
        bun: &CrtBundle<Self::Item>,
        ms: &[u16],
    ) -> Result<Self::Item, Self::Error> { ... }
    fn crt_relu(
        &mut self,
        x: &CrtBundle<Self::Item>,
        accuracy: &str,
        output_moduli: Option<&[u16]>,
    ) -> Result<CrtBundle<Self::Item>, Self::Error> { ... }
    fn crt_sign(
        &mut self,
        x: &CrtBundle<Self::Item>,
        accuracy: &str,
    ) -> Result<Self::Item, Self::Error> { ... }
    fn crt_sgn(
        &mut self,
        x: &CrtBundle<Self::Item>,
        accuracy: &str,
        output_moduli: Option<&[u16]>,
    ) -> Result<CrtBundle<Self::Item>, Self::Error> { ... }
    fn crt_lt(
        &mut self,
        x: &CrtBundle<Self::Item>,
        y: &CrtBundle<Self::Item>,
        accuracy: &str,
    ) -> Result<Self::Item, Self::Error> { ... }
    fn crt_geq(
        &mut self,
        x: &CrtBundle<Self::Item>,
        y: &CrtBundle<Self::Item>,
        accuracy: &str,
    ) -> Result<Self::Item, Self::Error> { ... }
    fn crt_max(
        &mut self,
        xs: &[CrtBundle<Self::Item>],
        accuracy: &str,
    ) -> Result<CrtBundle<Self::Item>, Self::Error> { ... }
    fn crt_to_pmr(
        &mut self,
        xs: &CrtBundle<Self::Item>,
    ) -> Result<Bundle<Self::Item>, Self::Error> { ... }
    fn pmr_lt(
        &mut self,
        x: &CrtBundle<Self::Item>,
        y: &CrtBundle<Self::Item>,
    ) -> Result<Self::Item, Self::Error> { ... }
    fn pmr_geq(
        &mut self,
        x: &CrtBundle<Self::Item>,
        y: &CrtBundle<Self::Item>,
    ) -> Result<Self::Item, Self::Error> { ... }
    fn crt_div(
        &mut self,
        x: &CrtBundle<Self::Item>,
        y: &CrtBundle<Self::Item>,
    ) -> Result<CrtBundle<Self::Item>, Self::Error> { ... }
}

Extension trait for Fancy providing advanced CRT gadgets based on bundles of wires.

Provided Methods

fn crt_constant_bundle( &mut self, x: u128, q: u128, ) -> Result<CrtBundle<Self::Item>, Self::Error>

Creates a bundle of constant wires for the CRT representation of x under composite modulus q.

fn crt_output( &mut self, x: &CrtBundle<Self::Item>, ) -> Result<Option<u128>, Self::Error>

Output a CRT bundle and interpret it mod Q.

fn crt_outputs( &mut self, xs: &[CrtBundle<Self::Item>], ) -> Result<Option<Vec<u128>>, Self::Error>

Output a slice of CRT bundles and interpret the outputs mod Q.

fn crt_add( &mut self, x: &CrtBundle<Self::Item>, y: &CrtBundle<Self::Item>, ) -> Result<CrtBundle<Self::Item>, Self::Error>

Add two CRT bundles.

fn crt_sub( &mut self, x: &CrtBundle<Self::Item>, y: &CrtBundle<Self::Item>, ) -> Result<CrtBundle<Self::Item>, Self::Error>

Subtract two CRT bundles.

fn crt_cmul( &mut self, x: &CrtBundle<Self::Item>, c: u128, ) -> Result<CrtBundle<Self::Item>, Self::Error>

Multiplies each wire in x by the corresponding residue of c.

fn crt_mul( &mut self, x: &CrtBundle<Self::Item>, y: &CrtBundle<Self::Item>, ) -> Result<CrtBundle<Self::Item>, Self::Error>

Multiply x with y.

fn crt_cexp( &mut self, x: &CrtBundle<Self::Item>, c: u16, ) -> Result<CrtBundle<Self::Item>, Self::Error>

Exponentiate x by the constant c.

fn crt_rem( &mut self, x: &CrtBundle<Self::Item>, p: u16, ) -> Result<CrtBundle<Self::Item>, Self::Error>

Compute the remainder with respect to modulus p.

fn crt_fractional_mixed_radix( &mut self, bun: &CrtBundle<Self::Item>, ms: &[u16], ) -> Result<Self::Item, Self::Error>

Helper function for advanced gadgets, returns the MSB of the fractional part of X/M where M=product(ms).

fn crt_relu( &mut self, x: &CrtBundle<Self::Item>, accuracy: &str, output_moduli: Option<&[u16]>, ) -> Result<CrtBundle<Self::Item>, Self::Error>

Compute max(x,0).

Optional output moduli.

fn crt_sign( &mut self, x: &CrtBundle<Self::Item>, accuracy: &str, ) -> Result<Self::Item, Self::Error>

Return 0 if x is positive and 1 if x is negative.

fn crt_sgn( &mut self, x: &CrtBundle<Self::Item>, accuracy: &str, output_moduli: Option<&[u16]>, ) -> Result<CrtBundle<Self::Item>, Self::Error>

Return if x >= 0 then 1 else -1, where -1 is interpreted as Q-1.

If provided, will produce a bundle under output_moduli instead of x.moduli()

fn crt_lt( &mut self, x: &CrtBundle<Self::Item>, y: &CrtBundle<Self::Item>, accuracy: &str, ) -> Result<Self::Item, Self::Error>

Returns 1 if x < y.

fn crt_geq( &mut self, x: &CrtBundle<Self::Item>, y: &CrtBundle<Self::Item>, accuracy: &str, ) -> Result<Self::Item, Self::Error>

Returns 1 if x >= y.

fn crt_max( &mut self, xs: &[CrtBundle<Self::Item>], accuracy: &str, ) -> Result<CrtBundle<Self::Item>, Self::Error>

Compute the maximum bundle in xs.

fn crt_to_pmr( &mut self, xs: &CrtBundle<Self::Item>, ) -> Result<Bundle<Self::Item>, Self::Error>

Convert the xs bundle to PMR representation. Useful for extracting out of CRT.

fn pmr_lt( &mut self, x: &CrtBundle<Self::Item>, y: &CrtBundle<Self::Item>, ) -> Result<Self::Item, Self::Error>

Comparison based on PMR, more expensive than crt_lt but works on more things. For it to work, there must be an extra modulus in the CRT that is not necessary to represent the values. This ensures that if x < y, the most significant PMR digit is nonzero after subtracting them. You could add a prime to your CrtBundles right before using this gadget.

fn pmr_geq( &mut self, x: &CrtBundle<Self::Item>, y: &CrtBundle<Self::Item>, ) -> Result<Self::Item, Self::Error>

Comparison based on PMR, more expensive than crt_lt but works on more things. For it to work, there must be an extra modulus in the CRT that is not necessary to represent the values. This ensures that if x < y, the most significant PMR digit is nonzero after subtracting them. You could add a prime to your CrtBundles right before using this gadget.

fn crt_div( &mut self, x: &CrtBundle<Self::Item>, y: &CrtBundle<Self::Item>, ) -> Result<CrtBundle<Self::Item>, Self::Error>

Generic, and expensive, CRT-based addition for two ciphertexts. Uses PMR comparison repeatedly. Requires an extra unused prime in both inputs.

Implementors

impl<F: FancyArithmetic + FancyBinary> CrtGadgets for F