fhelium.engine.rns.montgomery

MontgomeryParameters

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MontgomeryParameters(ckks_config: CkksConfig)

Host-side constants for per-prime Montgomery arithmetic.

Let $R=2^w$, where $w=\mathtt{buffer}\mathtt{\_}\mathtt{bit}\mathtt{\_}\mathtt{length}$. For every odd modulus $q_i$ in canonical level-zero [Q | P] order, standard residue $x_i$ is stored in Montgomery representation as $x_{i}Rmod{q}_i$. The native reduction

$${\mathrm{REDC}}_{q_i}(t)=(t+m{q}_i)/R,m=t(-q_i^{-1})modR,$$

therefore maps a product of two Montgomery residues back to Montgomery form. Native kernels accept lazy representatives in $[0,2q_i)$ and rely on $4q_i<R$ for signed-word overflow safety. This object stores Python integers only; RnsRuntime materializes exact integral row tables.

moduli

property

moduli: list[int]

Canonical modulus order [Q | P].

twice_modulus

property

twice_modulus: list[int]

Return $2q_i$ for lazy-range corrections, in prime-id order.

buffer_bit_length

property

buffer_bit_length: int

Bit-length of the buffer type (30 or 62).

half_buffer_bit_length

property

half_buffer_bit_length: int

Return $w/2$ for the native split-word implementation.

lower_bits_mask

property

lower_bits_mask: int

Return the lower-half mask $2^{w/2}-1$.

full_bits_mask

property

full_bits_mask: int

Return the radix mask $R-1=2^w-1$.

R

property

R: int

Return Montgomery radix $R=2^w$.

montgomery_r2

property

montgomery_r2: list[int]

Return $R^{2}mod{q}_i$ used by REDC to map $x_i$ to $x_{i}R$.

montgomery_r_inverse

property

montgomery_r_inverse: list[int]

Return $R^{-1}mod{q}_i$ in canonical prime-id order.

neg_inv_modulus

property

neg_inv_modulus: list[int]

Return $-q_i^{-1}modR$ for Montgomery reduction.

neg_inv_modulus_lower_bits

property

neg_inv_modulus_lower_bits: list[int]

Return the lower $w/2$ bits of $-q_i^{-1}modR$.

neg_inv_modulus_higher_bits

property

neg_inv_modulus_higher_bits: list[int]

Return the higher $w/2$ bits of $-q_i^{-1}modR$.

modulus_lower_bits

property

modulus_lower_bits: list[int]

Return the lower $w/2$ bits of each $q_i$.

modulus_higher_bits

property

modulus_higher_bits: list[int]

Return the higher $w/2$ bits of each $q_i$.