Template Class NumberTheoreticTransformNat

Page Contents

Template Parameter Order

  1. typename VecType

Class Documentation

template<typename VecType>
class intnat::NumberTheoreticTransformNat

Number Theoretic Transform implementation.

Public Functions

void ForwardTransformIterative(const VecType &element, const VecType &rootOfUnityTable, VecType *result)

Forward transform in the ring Z_q[X]/(X^n-1).

Parameters

  • &element – is the input to the transform of type VecType and length n s.t. n|q-1.

  • &rootOfUnityTable – is the table with the root of unity powers.

Returns

is the result of the transform, a VecType should be of the same size as input or a throw if an error occurs.

void InverseTransformIterative(const VecType &element, const VecType &rootOfUnityInverseTable, VecType *result)

Inverse transform in the ring Z_q[X]/(X^n-1) with prime q and power-of-two n s.t. n|q-1.

Parameters

  • &element – [inout] is the input and output to the transform of type VecType and length n.

  • &rootOfUnityTable – is the table with the inverse n-th root of unity powers.

Returns

is the result of the transform, a VecType should be of the same size as input or a throw if an error occurs.

void ForwardTransformToBitReverse(const VecType &element, const VecType &rootOfUnityTable, VecType *result)

Copies element into result and calls ForwardTransformToBitReverseInPlace()

Forward transform in the ring Z_q[X]/(X^n+1) with prime q and power-of-two n s.t. 2n|q-1. Bit reversing indexes. [Algorithm 1 in https://eprint.iacr.org/2016/504.pdf]

See also

ForwardTransformToBitReverseInPlace()

Parameters

  • &element – [in] is the input to the transform of type VecType and length n.

  • &rootOfUnityTable – is the table with the n-th root of unity powers in bit reverse order.

  • *result – [out] is the result of the transform, a VecType should be of the same size as input or a throw if an error occurs.

void ForwardTransformToBitReverseInPlace(const VecType &rootOfUnityTable, VecType *element)

In-place forward transform in the ring Z_q[X]/(X^n+1) with prime q and power-of-two n s.t. 2n|q-1. Bit reversing indexes. [Algorithm 1 in https://eprint.iacr.org/2016/504.pdf]

Parameters

  • &rootOfUnityTable – is the table with the n-th root of unity powers in bit reverse order.

  • &element[in, out] – is the input/output of the transform of type VecType and length n.

Returns

none

void ForwardTransformToBitReverse(const VecType &element, const VecType &rootOfUnityTable, const VecType &preconRootOfUnityTable, VecType *result)

Copies element into result and calls ForwardTransformToBitReverseInPlace()

Forward transform in the ring Z_q[X]/(X^n+1) with prime q and power-of-two n s.t. 2n|q-1. Bit reversing indexes. The method works for the NativeInteger case based on NTL’s modular multiplication. [Algorithm 1 in https://eprint.iacr.org/2016/504.pdf]

See also

ForwardTransformToBitReverseInPlace()

Parameters

  • &element – is the input to the transform of type VecType and length n.

  • &rootOfUnityTable – is the table with the root of unity powers in bit reverse order.

  • &preconRootOfUnityTable – is NTL-specific precomputations for optimized NativeInteger modulo multiplications.

  • *result – [out] is the result of the transform, a VecType should be of the same size as input or a throw if an error occurs.

Returns

none

void ForwardTransformToBitReverseInPlace(const VecType &rootOfUnityTable, const VecType &preconRootOfUnityTable, VecType *element)

In-place forward transform in the ring Z_q[X]/(X^n+1) with prime q and power-of-two n s.t. 2n|q-1. Bit reversing indexes. The method works for the NativeInteger case based on NTL’s modular multiplication. [Algorithm 1 in https://eprint.iacr.org/2016/504.pdf]

Parameters

  • &rootOfUnityTable – is the table with the root of unity powers in bit reverse order.

  • &preconRootOfUnityTable – is NTL-specific precomputations for optimized NativeInteger modulo multiplications.

  • &element – [inout] is the input/output of the transform of type VecType and length n.

Returns

none

void InverseTransformFromBitReverse(const VecType &element, const VecType &rootOfUnityInverseTable, const IntType &cycloOrderInv, VecType *result)

Copies element into result and calls InverseTransformFromBitReverseInPlace()

Inverse transform in the ring Z_q[X]/(X^n+1) with prime q and power-of-two n s.t. 2n|q-1. Bit reversing indexes. [Algorithm 2 in https://eprint.iacr.org/2016/504.pdf]

See also

InverseTransformFromBitReverseInPlace()

Parameters

  • &element – is the input to the transform of type VecType and length n.

  • &rootOfUnityInverseTable – is the table with the inverse 2n-th root of unity powers in bit reverse order.

  • &cycloOrderInv – is inverse of n modulo q

  • *result – [out] is the result of the transform, a VecType should be of the same size as input or a throw if an error occurs.

Returns

none

void InverseTransformFromBitReverseInPlace(const VecType &rootOfUnityInverseTable, const IntType &cycloOrderInv, VecType *element)

In-place inverse transform in the ring Z_q[X]/(X^n+1) with prime q and power-of-two n s.t. 2n|q-1. Bit reversing indexes. [Algorithm 2 in https://eprint.iacr.org/2016/504.pdf]

Parameters

  • &rootOfUnityInverseTable – is the table with the inverse 2n-th root of unity powers in bit reverse order.

  • &cycloOrderInv – is inverse of n modulo q

  • &element – [inout] is the input/output of the transform of type VecType and length n.

Returns

none

void InverseTransformFromBitReverse(const VecType &element, const VecType &rootOfUnityInverseTable, const VecType &preconRootOfUnityInverseTable, const IntType &cycloOrderInv, const IntType &preconCycloOrderInv, VecType *result)

Copies element into result and calls InverseTransformFromBitReverseInPlace()

Inverse transform in the ring Z_q[X]/(X^n+1) with prime q and power-of-two n s.t. 2n|q-1. Bit reversing indexes. The method works for the NativeInteger case based on NTL’s modular multiplication. [Algorithm 2 in https://eprint.iacr.org/2016/504.pdf]

See also

InverseTransformFromBitReverseInPlace()

Parameters

  • &element – is the input to the transform of type VecType and length n.

  • &rootOfUnityInverseTable – is the table with the inverse 2n-th root of unity powers in bit reverse order.

  • &preconRootOfUnityInverseTable – is NTL-specific precomputations for optimized NativeInteger modulo multiplications.

  • &cycloOrderInv – is inverse of n modulo q

  • &preconCycloOrderInv – is NTL-specific precomputations for optimized NativeInteger modulo multiplications.

  • *result – is the result of the transform, a VecType should be of the same size as input or a throw if an error occurs.

Returns

none.

void InverseTransformFromBitReverseInPlace(const VecType &rootOfUnityInverseTable, const VecType &preconRootOfUnityInverseTable, const IntType &cycloOrderInv, const IntType &preconCycloOrderInv, VecType *element)

In-place Inverse transform in the ring Z_q[X]/(X^n+1) with prime q and power-of-two n s.t. 2n|q-1. Bit reversing indexes. The method works for the NativeInteger case based on NTL’s modular multiplication. [Algorithm 2 in https://eprint.iacr.org/2016/504.pdf]

Parameters

  • &rootOfUnityInverseTable – is the table with the inverse 2n-th root of unity powers in bit reverse order.

  • &preconRootOfUnityInverseTable – is NTL-specific precomputations for optimized NativeInteger modulo multiplications.

  • &cycloOrderInv – is inverse of n modulo q

  • &preconCycloOrderInv – is NTL-specific precomputations for optimized NativeInteger modulo multiplications.

  • &element[in, out] – is the input/output of the transform of type VecType and length n.

Returns

none