BGV

‘bgv’ Dialect

The BGV dialect defines the types and operations of the BGV and B/FV cryptosystem.

Due to similarity with the BFV scheme, BGV dialect also represents the B/FV scheme.

The semantics of bgv dialect operations are determined by the scheme.bgv or scheme.bfv annotation at the module level.

In B/FV mode, bgv.modulus_switch is an no-op.

BGV attributes

SchemeParamAttr

BGV Scheme Parameters

Syntax:

#bgv.scheme_param<
  int,   # logN
  DenseI64ArrayAttr,   # Q
  DenseI64ArrayAttr,   # P
  int64_t,   # plaintextModulus
  BGVEncryptionType,   # encryptionType
  BGVEncryptionTechnique   # encryptionTechnique
>

This attribute is used for recording the scheme parameters for CKKS.

The attribute is a struct with the following fields:

• int logN: The log of the degree of the polynomial modulus.
• DenseI64ArrayAttr Q: The array of primes in the ciphertext modulus.
• DenseI64ArrayAttr P: The array of primes in the special modulus, used for key switching.
• int64_t plaintextModulus: The plaintext modulus.

Parameters:

BGV ops

bgv.add (heir::bgv::AddOp)

Addition operation between ciphertexts.

Syntax:

operation ::= `bgv.add` operands attr-dict `:`  functional-type(operands, results)

Traits: AlwaysSpeculatableImplTrait, Commutative, InferTypeOpAdaptor, SameOperandsAndResultPlaintextTypes, SameOperandsAndResultRings

Interfaces: ConditionallySpeculatable, InferTypeOpInterface, NoMemoryEffect (MemoryEffectOpInterface)

Effects: MemoryEffects::Effect{}

Operands:

Results:

bgv.add_plain (heir::bgv::AddPlainOp)

Addition operation between ciphertext-plaintext.

Syntax:

operation ::= `bgv.add_plain` operands attr-dict `:`  functional-type(operands, results)

Traits: AlwaysSpeculatableImplTrait, SameOperandsAndResultPlaintextTypes

Interfaces: ConditionallySpeculatable, InferTypeOpInterface, NoMemoryEffect (MemoryEffectOpInterface)

Effects: MemoryEffects::Effect{}

Operands:

Results:

bgv.extract (heir::bgv::ExtractOp)

Extract the i-th element of a ciphertext.

Syntax:

operation ::= `bgv.extract` operands attr-dict `:`  functional-type(operands, results)

While this operation is costly to compute in FHE, we represent it so we can implement efficient lowerings and folders.

This op can be implemented as a plaintext multiplication with a one-hot vector and a rotate into the zero-th index.

An extraction op’s input ciphertext type is asserted to have an underlying_type corresponding to a ranked tensor type, and this op’s return type is inferred to have the underlying_type corresponding to the element type of that tensor type.

Traits: AlwaysSpeculatableImplTrait, SameOperandsAndResultRings

Interfaces: ConditionallySpeculatable, NoMemoryEffect (MemoryEffectOpInterface)

Effects: MemoryEffects::Effect{}

Operands:

Results:

bgv.level_reduce (heir::bgv::LevelReduceOp)

Lower the modulus level of the ciphertext via dropping RNS limbs.

Syntax:

operation ::= `bgv.level_reduce` operands attr-dict `:` qualified(type($input)) `->` qualified(type($output))

Traits: AlwaysSpeculatableImplTrait, SameOperandsAndResultPlaintextTypes

Interfaces: ConditionallySpeculatable, NoMemoryEffect (MemoryEffectOpInterface)

Effects: MemoryEffects::Effect{}

Attributes:

Operands:

Results:

bgv.modulus_switch (heir::bgv::ModulusSwitchOp)

Lower the modulus level of the ciphertext via modulus switching.

Syntax:

operation ::= `bgv.modulus_switch` operands attr-dict `:` qualified(type($input)) `->` qualified(type($output))

Traits: AlwaysSpeculatableImplTrait

Interfaces: ConditionallySpeculatable, NoMemoryEffect (MemoryEffectOpInterface)

Effects: MemoryEffects::Effect{}

Attributes:

Operands:

Results:

bgv.mul (heir::bgv::MulOp)

Multiplication operation between ciphertexts.

Syntax:

operation ::= `bgv.mul` operands attr-dict `:`  functional-type(operands, results)

Traits: AlwaysSpeculatableImplTrait, Commutative, InferTypeOpAdaptor, SameOperandsAndResultRings

Interfaces: ConditionallySpeculatable, InferTypeOpInterface, NoMemoryEffect (MemoryEffectOpInterface)

Effects: MemoryEffects::Effect{}

Operands:

Results:

bgv.mul_plain (heir::bgv::MulPlainOp)

Multiplication operation between ciphertext-plaintext.

Syntax:

operation ::= `bgv.mul_plain` operands attr-dict `:`  functional-type(operands, results)

Traits: AlwaysSpeculatableImplTrait, InferTypeOpAdaptor

Interfaces: ConditionallySpeculatable, InferTypeOpInterface, NoMemoryEffect (MemoryEffectOpInterface)

Effects: MemoryEffects::Effect{}

Operands:

Results:

bgv.negate (heir::bgv::NegateOp)

Negate the coefficients of the ciphertext.

Syntax:

operation ::= `bgv.negate` operands attr-dict `:` qualified(type($output))

Traits: AlwaysSpeculatableImplTrait, Involution, SameOperandsAndResultType

Interfaces: ConditionallySpeculatable, InferTypeOpInterface, NoMemoryEffect (MemoryEffectOpInterface)

Effects: MemoryEffects::Effect{}

Operands:

Results:

bgv.relinearize (heir::bgv::RelinearizeOp)

Relinearize the ciphertext.

Syntax:

operation ::= `bgv.relinearize` operands attr-dict `:` qualified(type($input)) `->` qualified(type($output))

This op takes integer array attributes from_basis and to_basis that are used to indicate the key basis from which and to which the ciphertext is encrypted against. A ciphertext is canonically encrypted against key basis (1, s). After a multiplication, its size will increase and the basis will be (1, s, s^2). The array that represents the key basis is constructed by listing the powers of s at each position of the array. For example, (1, s, s^2) corresponds to [0, 1, 2], while (1, s^2) corresponds to [0, 2].

Traits: AlwaysSpeculatableImplTrait, InferTypeOpAdaptor, SameOperandsAndResultPlaintextTypes, SameOperandsAndResultRings

Interfaces: ConditionallySpeculatable, InferTypeOpInterface, NoMemoryEffect (MemoryEffectOpInterface)

Effects: MemoryEffects::Effect{}

Attributes:

Operands:

Results:

bgv.rotate_cols (heir::bgv::RotateColumnsOp)

Rotate the columns of the coefficients of the ciphertext using a Galois automorphism.

Syntax:

operation ::= `bgv.rotate_cols` operands attr-dict `:` qualified(type($input))

This operation rotates the columns of the coefficients of the ciphertext using a Galois automorphism.

Often BGV scheme is instantiated with a ring of the form Z_q[X]/(X^N + 1) and plaintext modulus t where N is a power of 2 and t is a prime number. In this case, the plaintext slots can be viewed as a 2 x N/2 matrix where N/2 is the number of columns and 2 is the number of rows.

Traits: AlwaysSpeculatableImplTrait

Interfaces: ConditionallySpeculatable, InferTypeOpInterface, NoMemoryEffect (MemoryEffectOpInterface)

Effects: MemoryEffects::Effect{}

Attributes:

Operands:

Results:

bgv.rotate_rows (heir::bgv::RotateRowsOp)

Rotate the rows of the coefficients of the ciphertext using a Galois automorphism.

Syntax:

operation ::= `bgv.rotate_rows` operands attr-dict `:` qualified(type($input))

This operation rotates the rows of the coefficients of the ciphertext using a Galois automorphism.

Often BGV scheme is instantiated with a ring of the form Z_q[X]/(X^N + 1) and plaintext modulus t where N is a power of 2 and t is a prime number. In this case, the plaintext slots can be viewed as a 2 x N/2 matrix where N/2 is the number of columns and 2 is the number of rows.

Traits: AlwaysSpeculatableImplTrait

Interfaces: ConditionallySpeculatable, InferTypeOpInterface, NoMemoryEffect (MemoryEffectOpInterface)

Effects: MemoryEffects::Effect{}

Attributes:

Operands:

Results:

bgv.sub (heir::bgv::SubOp)

Subtraction operation between ciphertexts.

Syntax:

operation ::= `bgv.sub` operands attr-dict `:`  functional-type(operands, results)

Traits: AlwaysSpeculatableImplTrait, InferTypeOpAdaptor, SameOperandsAndResultPlaintextTypes, SameOperandsAndResultRings

Interfaces: ConditionallySpeculatable, InferTypeOpInterface, NoMemoryEffect (MemoryEffectOpInterface)

Effects: MemoryEffects::Effect{}

Operands:

Results:

bgv.sub_plain (heir::bgv::SubPlainOp)

Subtraction operation between ciphertext-plaintext.

Syntax:

operation ::= `bgv.sub_plain` operands attr-dict `:`  functional-type(operands, results)

Traits: AlwaysSpeculatableImplTrait, SameOperandsAndResultPlaintextTypes

Interfaces: ConditionallySpeculatable, InferTypeOpInterface, NoMemoryEffect (MemoryEffectOpInterface)

Effects: MemoryEffects::Effect{}

Operands:

Results:

BGV additional definitions

BGVEncryptionTechnique

An enum attribute representing an encryption technique

Cases:

BGVEncryptionType

An enum attribute representing an encryption method

Cases: