FHElium

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fhelium.config ​

CKKS parameter, NTT-policy, and security-assessment interfaces.

Public modules are named for the configured subject: ckks owns the CKKS parameter model, ntt owns NTT execution policies, and security assesses complete modulus sets against the published table built into FHElium. Private resource mechanisms use a leading underscore, as in _prime_catalog.

DEFAULT_CPU_NTT_BACKEND ​

constant View source

python
DEFAULT_CPU_NTT_BACKEND: Final[str] = 'radix2_indexed'

DEFAULT_NTT_BACKEND ​

constant View source

python
DEFAULT_NTT_BACKEND: Final[str] = 'radix2_compact_group8_smem8'

SUPPORTED_NTT_BACKENDS ​

constant View source

python
SUPPORTED_NTT_BACKENDS: Final = tuple(NTT_BACKEND_POLICIES)

CkksConfig ​

class View source

python
CkksConfig(*, default_scale: float, q_depth_groups: tuple[tuple[int, ...], ...], p_moduli: tuple[int, ...], logN: int, sigma: float=3.19, security_bits: int=128, enforce_security_budget: bool=True, galois_generator: int=3)

Immutable CKKS mathematical and security parameters.

The configuration defines CKKS over R=Z[X]/(XN+1), where N=2logN, together with the exact ciphertext-modulus chain and hybrid key-switch modulus.

q_depth_groups contains ordered Q groups. At depth d, the active Q basis is the concatenation of groups d:. A rescale removes group d and advances to d + 1. The last group is the terminal basis: max_depth == len(q_depth_groups) - 1 and no further rescale exists there. Depth identifies the active basis; it does not count multiplications or record how the value reached that basis.

p_moduli contains the special primes whose product is the key-switch modulus P. default_scale is used only when value creation omits a scale; every live plaintext and ciphertext carries its own actual scale. The Engine selects the residue dtype and Montgomery radix from these exact primes, and each device-local RNS context materializes the corresponding arithmetic tables.

parse ​

method

python
def parse(src: Mapping[str, Any] | Preset, **overrides: Any) -> 'CkksConfig': ...

Resolve a preset or a serialized exact configuration.

dumps ​

method

python
def dumps() -> dict[str, object]: ...

Return a versioned dictionary containing the exact parameter set.

N ​

property

python
N: int

Polynomial ring dimension.

num_slots ​

property

python
num_slots: int

Number of complex CKKS slots, N/2.

max_depth ​

property

python
max_depth: int

Greatest public CKKS depth represented by this Q chain.

depth_remaining ​

method

python
def depth_remaining(depth: int) -> int: ...

Return the public rescale transitions remaining at depth.

q_moduli ​

property

python
q_moduli: tuple[int, ...]

Q primes in depth-group and within-group order.

moduli ​

property

python
moduli: tuple[int, ...]

Complete QP prime sequence used by RNS resources.

num_q_primes ​

property

python
num_q_primes: int

Number of prime rows in the complete Q chain.

num_p_primes ​

property

python
num_p_primes: int

Number of special-prime rows in P.

total_num_primes ​

property

python
total_num_primes: int

Number of prime rows in the complete QP basis.

rescale_divisor ​

method

python
def rescale_divisor(depth: int) -> int: ...

Return the Q-group product removed at one public depth.

q_row_start ​

method

python
def q_row_start(depth: int) -> int: ...

Return the first Q row active at depth.

active_q_moduli ​

method

python
def active_q_moduli(depth: int) -> tuple[int, ...]: ...

Return the ordered Q primes active at depth.

inverse_ntt_scale ​

property

python
inverse_ntt_scale: tuple[int, ...]

Return N−1modm in complete QP prime order.

total_modulus_bits ​

property

python
total_modulus_bits: int

Bit width of the complete QP product.

maximum_modulus_bits ​

property

python
maximum_modulus_bits: int

Built-in complete-QP budget for the selected security category.

security_assessment ​

property

python
security_assessment: SecurityAssessment

Return the built-in assessment of the complete QP product.

validate_security_budget ​

method

python
def validate_security_budget() -> SecurityAssessment: ...

Require the complete QP product to meet the configured budget.

Preset ​

class View source

python
Preset()

Bases: Enum

Built-in CKKS parameter presets.

Each member name records the complex slot capacity, default scale bits, maximum public depth, and the Engine's selected residue dtype for its prime set. All baselines select the 128-bit classical security category, Gaussian error standard deviation 3.19, uniform-ternary secret sampling, and a ring-specific P-prime count. CkksConfig.parse accepts keyword overrides when an application needs a derived configuration.

Attributes ​

NameTypeDefault/value
slots8192_scale30_depth9_int64'slots8192-scale30-depth9-int64'
slots8192_scale40_depth7_int64'slots8192-scale40-depth7-int64'
slots8192_scale50_depth5_int64'slots8192-scale50-depth5-int64'
slots16384_scale30_depth21_int64'slots16384-scale30-depth21-int64'
slots16384_scale40_depth16_int64'slots16384-scale40-depth16-int64'
slots16384_scale50_depth12_int64'slots16384-scale50-depth12-int64'
slots32768_scale30_depth45_int64'slots32768-scale30-depth45-int64'
slots32768_scale40_depth34_int64'slots32768-scale40-depth34-int64'
slots32768_scale50_depth27_int64'slots32768-scale50-depth27-int64'
slots32768_scale50_depth29_int64'slots32768-scale50-depth29-int64'
slots65536_scale30_depth95_int64'slots65536-scale30-depth95-int64'
slots65536_scale40_depth72_int64'slots65536-scale40-depth72-int64'
slots65536_scale50_depth58_int64'slots65536-scale50-depth58-int64'
slots8192_scale25_depth14_int32'slots8192-scale25-depth14-int32'
slots16384_scale25_depth29_int32'slots16384-scale25-depth29-int32'
slots32768_scale25_depth24_int32'slots32768-scale25-depth24-int32'
slots65536_scale25_depth14_int32'slots65536-scale25-depth14-int32'

SecurityAssessment ​

class View source

python
SecurityAssessment(status: Literal['meets', 'exceeds', 'unsupported'], ring_dimension: int, target_bits: int, secret_distribution: str, error_stddev: float, modulus_bits: int, maximum_modulus_bits: int | None, modulus_margin_bits: int | None, reason: str | None)

Immutable result of a built-in parameter assessment.

status is "meets" when ⌈log2⁡q⌉ is at most the table budget, "exceeds" when it is larger, and "unsupported" when no table row matches the assumptions. An unsupported result has None for maximum_modulus_bits and modulus_margin_bits. A negative modulus margin reports how far a supported parameter tuple exceeds its modulus budget; it is not a bit-security margin.

Attributes ​

NameTypeDefault/value
statusLiteral['meets', 'exceeds', 'unsupported']
ring_dimensionint
target_bitsint
secret_distributionstr
error_stddevfloat
modulus_bitsint
maximum_modulus_bitsint | None
modulus_margin_bitsint | None
reasonstr | None

assess_config_security ​

function View source

python
def assess_config_security(config: CkksConfig) -> SecurityAssessment: ...

Assess a fhelium.config.CkksConfig complete QP modulus.

assess_security ​

function View source

python
def assess_security(ring_dimension: int, *, modulus: int | None=None, moduli: Sequence[int] | None=None, target_bits: int=128, secret_distribution: str='ternary', error_stddev: float=_TABLE_ERROR_STANDARD_DEVIATION) -> SecurityAssessment: ...

Assess a complete modulus against one built-in budget row.

Parameters

  • ring_dimension: Polynomial-ring dimension N.
  • modulus: Complete parameter modulus q. For CKKS hybrid key switching this is Q * P.
  • moduli: Factors of the complete parameter modulus. Specify this or modulus, but not both.
  • target_bits: Classical security category.
  • secret_distribution: Table secret distribution, "ternary" or "gaussian".
  • error_stddev: Gaussian error standard deviation. The built-in budgets support exactly 3.19.

Returns

A structured assessment with status, modulus-bit width, budget, margin, and an unsupported reason when applicable. Parameters without a matching row return status="unsupported"; this function never interpolates or extrapolates.

Raises

  • TypeError: If an input has the wrong structural type.
  • ValueError: If a numeric input is non-positive or non-finite, or the modulus inputs are missing or ambiguous.

compatible_ntt_backends ​

function View source

python
def compatible_ntt_backends(log_ring_dimension: int) -> tuple[str, ...]: ...

Return registered policy names executable for one logN.

Names retain registry order. Strict fixed-radix policies whose digit width does not divide log_ring_dimension are omitted; grouped radix-2 policies remain available for every supported ring dimension. A non-positive dimension raises ValueError.