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FHE Dialect

High Level Fully Homomorphic Encryption dialect A dialect for representation of high level operation on fully homomorphic ciphertext.

Operation definition

FHE.add_eint_int (::mlir::concretelang::FHE::AddEintIntOp)

Adds an encrypted integer and a clear integer

The clear integer must have at most one more bit than the encrypted integer and the result must have the same width and the same signedness as the encrypted integer.

Example:

// ok
"FHE.add_eint_int"(%a, %i) : (!FHE.eint<2>, i3) -> !FHE.eint<2>
"FHE.add_eint_int"(%a, %i) : (!FHE.esint<2>, i3) -> !FHE.esint<2>

// error
"FHE.add_eint_int"(%a, %i) : (!FHE.eint<2>, i4) -> !FHE.eint<2>
"FHE.add_eint_int"(%a, %i) : (!FHE.eint<2>, i3) -> !FHE.eint<3>
"FHE.add_eint_int"(%a, %i) : (!FHE.eint<2>, i3) -> !FHE.esint<2>

Traits: AlwaysSpeculatableImplTrait

Interfaces: Binary, BinaryEintInt, ConditionallySpeculatable, NoMemoryEffect (MemoryEffectOpInterface)

Effects: MemoryEffects::Effect{}

Operands:

OperandDescription

a

b

integer

Results:

ResultDescription

«unnamed»

FHE.add_eint (::mlir::concretelang::FHE::AddEintOp)

Adds two encrypted integers

The encrypted integers and the result must have the same width and the same signedness.

Example:

// ok
"FHE.add_eint"(%a, %b): (!FHE.eint<2>, !FHE.eint<2>) -> (!FHE.eint<2>)
"FHE.add_eint"(%a, %b): (!FHE.esint<2>, !FHE.esint<2>) -> (!FHE.esint<2>)

// error
"FHE.add_eint"(%a, %b): (!FHE.eint<2>, !FHE.eint<3>) -> (!FHE.eint<2>)
"FHE.add_eint"(%a, %b): (!FHE.eint<2>, !FHE.eint<2>) -> (!FHE.eint<3>)
"FHE.add_eint"(%a, %b): (!FHE.eint<2>, !FHE.eint<2>) -> (!FHE.esint<2>)
"FHE.add_eint"(%a, %b): (!FHE.esint<2>, !FHE.eint<2>) -> (!FHE.eint<2>)

Traits: AlwaysSpeculatableImplTrait

Interfaces: BinaryEint, ConditionallySpeculatable, NoMemoryEffect (MemoryEffectOpInterface)

Effects: MemoryEffects::Effect{}

Operands:

OperandDescription

a

b

Results:

ResultDescription

«unnamed»

FHE.apply_lookup_table (::mlir::concretelang::FHE::ApplyLookupTableEintOp)

Applies a clear lookup table to an encrypted integer

The width of the result can be different than the width of the operand. The lookup table must be a tensor of size 2^p where p is the width of the encrypted integer.

Example:

// ok
"FHE.apply_lookup_table"(%a, %lut): (!FHE.eint<2>, tensor<4xi64>) -> (!FHE.eint<2>)
"FHE.apply_lookup_table"(%a, %lut): (!FHE.eint<2>, tensor<4xi64>) -> (!FHE.eint<3>)
"FHE.apply_lookup_table"(%a, %lut): (!FHE.eint<3>, tensor<4xi64>) -> (!FHE.eint<2>)

// error
"FHE.apply_lookup_table"(%a, %lut): (!FHE.eint<2>, tensor<8xi64>) -> (!FHE.eint<2>)

Traits: AlwaysSpeculatableImplTrait

Interfaces: ConditionallySpeculatable, ConstantNoise, NoMemoryEffect (MemoryEffectOpInterface)

Effects: MemoryEffects::Effect{}

Operands:

OperandDescription

a

lut

tensor of integer values

Results:

ResultDescription

«unnamed»

FHE.and (::mlir::concretelang::FHE::BoolAndOp)

Applies an AND gate to two encrypted boolean values

Example:

"FHE.and"(%a, %b): (!FHE.ebool, !FHE.ebool) -> (!FHE.ebool)

Traits: AlwaysSpeculatableImplTrait

Interfaces: ConditionallySpeculatable, NoMemoryEffect (MemoryEffectOpInterface)

Effects: MemoryEffects::Effect{}

Operands:

OperandDescription

left

An encrypted boolean

right

An encrypted boolean

Results:

ResultDescription

«unnamed»

An encrypted boolean

FHE.nand (::mlir::concretelang::FHE::BoolNandOp)

Applies a NAND gate to two encrypted boolean values

Example:

"FHE.nand"(%a, %b): (!FHE.ebool, !FHE.ebool) -> (!FHE.ebool)

Traits: AlwaysSpeculatableImplTrait

Interfaces: ConditionallySpeculatable, NoMemoryEffect (MemoryEffectOpInterface)

Effects: MemoryEffects::Effect{}

Operands:

OperandDescription

left

An encrypted boolean

right

An encrypted boolean

Results:

ResultDescription

«unnamed»

An encrypted boolean

FHE.not (::mlir::concretelang::FHE::BoolNotOp)

Applies a NOT gate to an encrypted boolean value

Example:

"FHE.not"(%a): (!FHE.ebool) -> (!FHE.ebool)

Traits: AlwaysSpeculatableImplTrait

Interfaces: ConditionallySpeculatable, NoMemoryEffect (MemoryEffectOpInterface), UnaryEint

Effects: MemoryEffects::Effect{}

Operands:

OperandDescription

value

An encrypted boolean

Results:

ResultDescription

«unnamed»

An encrypted boolean

FHE.or (::mlir::concretelang::FHE::BoolOrOp)

Applies an OR gate to two encrypted boolean values

Example:

"FHE.or"(%a, %b): (!FHE.ebool, !FHE.ebool) -> (!FHE.ebool)

Traits: AlwaysSpeculatableImplTrait

Interfaces: ConditionallySpeculatable, NoMemoryEffect (MemoryEffectOpInterface)

Effects: MemoryEffects::Effect{}

Operands:

OperandDescription

left

An encrypted boolean

right

An encrypted boolean

Results:

ResultDescription

«unnamed»

An encrypted boolean

FHE.xor (::mlir::concretelang::FHE::BoolXorOp)

Applies an XOR gate to two encrypted boolean values

Example:

"FHE.xor"(%a, %b): (!FHE.ebool, !FHE.ebool) -> (!FHE.ebool)

Traits: AlwaysSpeculatableImplTrait

Interfaces: ConditionallySpeculatable, NoMemoryEffect (MemoryEffectOpInterface)

Effects: MemoryEffects::Effect{}

Operands:

OperandDescription

left

An encrypted boolean

right

An encrypted boolean

Results:

ResultDescription

«unnamed»

An encrypted boolean

FHE.from_bool (::mlir::concretelang::FHE::FromBoolOp)

Cast a boolean to an unsigned integer

Examples:

"FHE.from_bool"(%x) : (!FHE.ebool) -> !FHE.eint<1>
"FHE.from_bool"(%x) : (!FHE.ebool) -> !FHE.eint<2>
"FHE.from_bool"(%x) : (!FHE.ebool) -> !FHE.eint<4>

Traits: AlwaysSpeculatableImplTrait

Interfaces: ConditionallySpeculatable, NoMemoryEffect (MemoryEffectOpInterface), UnaryEint

Effects: MemoryEffects::Effect{}

Operands:

OperandDescription

input

An encrypted boolean

Results:

ResultDescription

«unnamed»

An encrypted unsigned integer

FHE.gen_gate (::mlir::concretelang::FHE::GenGateOp)

Applies a truth table based on two boolean inputs

Truth table must be a tensor of four boolean values.

Example:

// ok
"FHE.gen_gate"(%a, %b, %ttable): (!FHE.ebool, !FHE.ebool, tensor<4xi64>) -> (!FHE.ebool)

// error
"FHE.gen_gate"(%a, %b, %ttable): (!FHE.ebool, !FHE.ebool, tensor<7xi64>) -> (!FHE.ebool)

Traits: AlwaysSpeculatableImplTrait

Interfaces: ConditionallySpeculatable, NoMemoryEffect (MemoryEffectOpInterface)

Effects: MemoryEffects::Effect{}

Operands:

OperandDescription

left

An encrypted boolean

right

An encrypted boolean

truth_table

tensor of integer values

Results:

ResultDescription

«unnamed»

An encrypted boolean

FHE.max_eint (::mlir::concretelang::FHE::MaxEintOp)

Retrieve the maximum of two encrypted integers.

Retrieve the maximum of two encrypted integers using the formula, 'max(x, y) == max(x - y, 0) + y'. The input and output types should be the same.

If `x - y`` inside the max overflows or underflows, the behavior is undefined. To support the full range, you should increase the bit-width by 1 manually.

Example:

// ok
"FHE.max_eint"(%x, %y) : (!FHE.eint<2>, !FHE.eint<2>) -> !FHE.eint<2>
"FHE.max_eint"(%x, %y) : (!FHE.esint<3>, !FHE.esint<3>) -> !FHE.esint<3>

// error
"FHE.max_eint"(%x, %y) : (!FHE.eint<2>, !FHE.eint<3>) -> !FHE.eint<2>
"FHE.max_eint"(%x, %y) : (!FHE.eint<2>, !FHE.eint<2>) -> !FHE.esint<2>
"FHE.max_eint"(%x, %y) : (!FHE.esint<2>, !FHE.eint<2>) -> !FHE.eint<2>

Traits: AlwaysSpeculatableImplTrait

Interfaces: BinaryEint, ConditionallySpeculatable, NoMemoryEffect (MemoryEffectOpInterface)

Effects: MemoryEffects::Effect{}

Operands:

OperandDescription

x

y

Results:

ResultDescription

«unnamed»

FHE.mul_eint_int (::mlir::concretelang::FHE::MulEintIntOp)

Multiply an encrypted integer with a clear integer

The clear integer must have one more bit than the encrypted integer and the result must have the same width and the same signedness as the encrypted integer.

Example:

// ok
"FHE.mul_eint_int"(%a, %i) : (!FHE.eint<2>, i3) -> !FHE.eint<2>
"FHE.mul_eint_int"(%a, %i) : (!FHE.esint<2>, i3) -> !FHE.esint<2>

// error
"FHE.mul_eint_int"(%a, %i) : (!FHE.eint<2>, i4) -> !FHE.eint<2>
"FHE.mul_eint_int"(%a, %i) : (!FHE.eint<2>, i3) -> !FHE.eint<3>
"FHE.mul_eint_int"(%a, %i) : (!FHE.eint<2>, i3) -> !FHE.esint<2>

Traits: AlwaysSpeculatableImplTrait

Interfaces: Binary, BinaryEintInt, ConditionallySpeculatable, NoMemoryEffect (MemoryEffectOpInterface)

Effects: MemoryEffects::Effect{}

Operands:

OperandDescription

a

b

integer

Results:

ResultDescription

«unnamed»

FHE.mul_eint (::mlir::concretelang::FHE::MulEintOp)

Multiplies two encrypted integers

The encrypted integers and the result must have the same width and signedness. Also, due to the current implementation, one supplementary bit of width must be provided, in addition to the number of bits needed to encode the largest output value.

Example:

// ok
"FHE.mul_eint"(%a, %b): (!FHE.eint<2>, !FHE.eint<2>) -> (!FHE.eint<2>)
"FHE.mul_eint"(%a, %b): (!FHE.eint<3>, !FHE.eint<3>) -> (!FHE.eint<3>)
"FHE.mul_eint"(%a, %b): (!FHE.esint<3>, !FHE.esint<3>) -> (!FHE.esint<3>)

// error
"FHE.mul_eint"(%a, %b): (!FHE.eint<2>, !FHE.eint<3>) -> (!FHE.eint<2>)
"FHE.mul_eint"(%a, %b): (!FHE.eint<2>, !FHE.eint<2>) -> (!FHE.eint<3>)
"FHE.mul_eint"(%a, %b): (!FHE.eint<2>, !FHE.eint<2>) -> (!FHE.esint<2>)
"FHE.mul_eint"(%a, %b): (!FHE.esint<2>, !FHE.eint<2>) -> (!FHE.eint<2>)

Traits: AlwaysSpeculatableImplTrait

Interfaces: BinaryEint, ConditionallySpeculatable, NoMemoryEffect (MemoryEffectOpInterface)

Effects: MemoryEffects::Effect{}

Operands:

OperandDescription

rhs

lhs

Results:

ResultDescription

«unnamed»

FHE.mux (::mlir::concretelang::FHE::MuxOp)

Multiplexer for two encrypted boolean inputs, based on an encrypted condition

Example:

"FHE.mux"(%cond, %c1, %c2): (!FHE.ebool, !FHE.ebool, !FHE.ebool) -> (!FHE.ebool)

Traits: AlwaysSpeculatableImplTrait

Interfaces: ConditionallySpeculatable, NoMemoryEffect (MemoryEffectOpInterface)

Effects: MemoryEffects::Effect{}

Operands:

OperandDescription

cond

An encrypted boolean

c1

An encrypted boolean

c2

An encrypted boolean

Results:

ResultDescription

«unnamed»

An encrypted boolean

FHE.neg_eint (::mlir::concretelang::FHE::NegEintOp)

Negates an encrypted integer

The result must have the same width and the same signedness as the encrypted integer.

Example:

// ok
"FHE.neg_eint"(%a): (!FHE.eint<2>) -> (!FHE.eint<2>)
"FHE.neg_eint"(%a): (!FHE.esint<2>) -> (!FHE.esint<2>)

// error
"FHE.neg_eint"(%a): (!FHE.eint<2>) -> (!FHE.eint<3>)
"FHE.neg_eint"(%a): (!FHE.eint<2>) -> (!FHE.esint<2>)

Traits: AlwaysSpeculatableImplTrait

Interfaces: ConditionallySpeculatable, NoMemoryEffect (MemoryEffectOpInterface), UnaryEint

Effects: MemoryEffects::Effect{}

Operands:

OperandDescription

a

Results:

ResultDescription

«unnamed»

FHE.round (::mlir::concretelang::FHE::RoundEintOp)

Rounds a ciphertext to a smaller precision.

Assuming a ciphertext whose message is implemented over p bits, this operation rounds it to fit to q bits with p>q.

Example:

 // ok
 "FHE.round"(%a): (!FHE.eint<6>) -> (!FHE.eint<5>)
 "FHE.round"(%a): (!FHE.eint<5>) -> (!FHE.eint<3>)
 "FHE.round"(%a): (!FHE.eint<3>) -> (!FHE.eint<2>)
 "FHE.round"(%a): (!FHE.esint<3>) -> (!FHE.esint<2>)

// error
 "FHE.round"(%a): (!FHE.eint<6>) -> (!FHE.eint<6>)
 "FHE.round"(%a): (!FHE.eint<4>) -> (!FHE.eint<5>)
 "FHE.round"(%a): (!FHE.eint<4>) -> (!FHE.esint<5>)

Traits: AlwaysSpeculatableImplTrait

Interfaces: ConditionallySpeculatable, NoMemoryEffect (MemoryEffectOpInterface), UnaryEint

Effects: MemoryEffects::Effect{}

Operands:

OperandDescription

input

Results:

ResultDescription

«unnamed»

FHE.sub_eint_int (::mlir::concretelang::FHE::SubEintIntOp)

Subtract a clear integer from an encrypted integer

The clear integer must have one more bit than the encrypted integer and the result must have the same width and the same signedness as the encrypted integer.

Example:

// ok
"FHE.sub_eint_int"(%i, %a) : (!FHE.eint<2>, i3) -> !FHE.eint<2>
"FHE.sub_eint_int"(%i, %a) : (!FHE.esint<2>, i3) -> !FHE.esint<2>

// error
"FHE.sub_eint_int"(%i, %a) : (!FHE.eint<2>, i4) -> !FHE.eint<2>
"FHE.sub_eint_int"(%i, %a) : (!FHE.eint<2>, i3) -> !FHE.eint<3>
"FHE.sub_eint_int"(%i, %a) : (!FHE.eint<2>, i3) -> !FHE.esint<2>

Traits: AlwaysSpeculatableImplTrait

Interfaces: Binary, BinaryEintInt, ConditionallySpeculatable, NoMemoryEffect (MemoryEffectOpInterface)

Effects: MemoryEffects::Effect{}

Operands:

OperandDescription

a

b

integer

Results:

ResultDescription

«unnamed»

FHE.sub_eint (::mlir::concretelang::FHE::SubEintOp)

Subtract an encrypted integer from an encrypted integer

The encrypted integers and the result must have the same width and the same signedness.

Example:

// ok
"FHE.sub_eint"(%a, %b): (!FHE.eint<2>, !FHE.eint<2>) -> (!FHE.eint<2>)
"FHE.sub_eint"(%a, %b): (!FHE.esint<2>, !FHE.esint<2>) -> (!FHE.esint<2>)

// error
"FHE.sub_eint"(%a, %b): (!FHE.eint<2>, !FHE.eint<3>) -> (!FHE.eint<2>)
"FHE.sub_eint"(%a, %b): (!FHE.eint<2>, !FHE.eint<2>) -> (!FHE.eint<3>)
"FHE.sub_eint"(%a, %b): (!FHE.eint<2>, !FHE.esint<2>) -> (!FHE.esint<2>)
"FHE.sub_eint"(%a, %b): (!FHE.eint<2>, !FHE.eint<2>) -> (!FHE.esint<2>)

Traits: AlwaysSpeculatableImplTrait

Interfaces: BinaryEint, ConditionallySpeculatable, NoMemoryEffect (MemoryEffectOpInterface)

Effects: MemoryEffects::Effect{}

Operands:

OperandDescription

a

b

Results:

ResultDescription

«unnamed»

FHE.sub_int_eint (::mlir::concretelang::FHE::SubIntEintOp)

Subtract an encrypted integer from a clear integer

The clear integer must have one more bit than the encrypted integer and the result must have the same width and the same signedness as the encrypted integer.

Example:

// ok
"FHE.sub_int_eint"(%i, %a) : (i3, !FHE.eint<2>) -> !FHE.eint<2>
"FHE.sub_int_eint"(%i, %a) : (i3, !FHE.esint<2>) -> !FHE.esint<2>

// error
"FHE.sub_int_eint"(%i, %a) : (i4, !FHE.eint<2>) -> !FHE.eint<2>
"FHE.sub_int_eint"(%i, %a) : (i3, !FHE.eint<2>) -> !FHE.eint<3>
"FHE.sub_int_eint"(%i, %a) : (i3, !FHE.eint<2>) -> !FHE.esint<2>

Traits: AlwaysSpeculatableImplTrait

Interfaces: Binary, BinaryIntEint, ConditionallySpeculatable, NoMemoryEffect (MemoryEffectOpInterface)

Effects: MemoryEffects::Effect{}

Operands:

OperandDescription

a

integer

b

Results:

ResultDescription

«unnamed»

FHE.to_bool (::mlir::concretelang::FHE::ToBoolOp)

Cast an unsigned integer to a boolean

The input must be of width one or two. Two being the current representation of an encrypted boolean, leaving one bit for the carry.

Examples:

// ok
"FHE.to_bool"(%x) : (!FHE.eint<1>) -> !FHE.ebool
"FHE.to_bool"(%x) : (!FHE.eint<2>) -> !FHE.ebool

// error
"FHE.to_bool"(%x) : (!FHE.eint<3>) -> !FHE.ebool

Traits: AlwaysSpeculatableImplTrait

Interfaces: ConditionallySpeculatable, NoMemoryEffect (MemoryEffectOpInterface), UnaryEint

Effects: MemoryEffects::Effect{}

Operands:

OperandDescription

input

An encrypted unsigned integer

Results:

ResultDescription

«unnamed»

An encrypted boolean

FHE.to_signed (::mlir::concretelang::FHE::ToSignedOp)

Cast an unsigned integer to a signed one

The result must have the same width as the input.

The behavior is undefined on overflow/underflow.

Examples:

// ok
"FHE.to_signed"(%x) : (!FHE.eint<2>) -> !FHE.esint<2>

// error
"FHE.to_signed"(%x) : (!FHE.eint<2>) -> !FHE.esint<3>

Traits: AlwaysSpeculatableImplTrait

Interfaces: ConditionallySpeculatable, NoMemoryEffect (MemoryEffectOpInterface), UnaryEint

Effects: MemoryEffects::Effect{}

Operands:

OperandDescription

input

An encrypted unsigned integer

Results:

ResultDescription

«unnamed»

An encrypted signed integer

FHE.to_unsigned (::mlir::concretelang::FHE::ToUnsignedOp)

Cast a signed integer to an unsigned one

The result must have the same width as the input.

The behavior is undefined on overflow/underflow.

Examples:

// ok
"FHE.to_unsigned"(%x) : (!FHE.esint<2>) -> !FHE.eint<2>

// error
"FHE.to_unsigned"(%x) : (!FHE.esint<2>) -> !FHE.eint<3>

Traits: AlwaysSpeculatableImplTrait

Interfaces: ConditionallySpeculatable, NoMemoryEffect (MemoryEffectOpInterface), UnaryEint

Effects: MemoryEffects::Effect{}

Operands:

OperandDescription

input

An encrypted signed integer

Results:

ResultDescription

«unnamed»

An encrypted unsigned integer

FHE.zero (::mlir::concretelang::FHE::ZeroEintOp)

Returns a trivial encrypted integer of 0

Example:

"FHE.zero"() : () -> !FHE.eint<2>
"FHE.zero"() : () -> !FHE.esint<2>

Traits: AlwaysSpeculatableImplTrait

Interfaces: ConditionallySpeculatable, ConstantNoise, NoMemoryEffect (MemoryEffectOpInterface)

Effects: MemoryEffects::Effect{}

Results:

ResultDescription

out

FHE.zero_tensor (::mlir::concretelang::FHE::ZeroTensorOp)

Creates a new tensor with all elements initialized to an encrypted zero.

Creates a new tensor with the shape specified in the result type and initializes its elements with an encrypted zero.

Example:

%tensor = "FHE.zero_tensor"() : () -> tensor<5x!FHE.eint<4>>
%tensor = "FHE.zero_tensor"() : () -> tensor<5x!FHE.esint<4>>

Traits: AlwaysSpeculatableImplTrait

Interfaces: ConditionallySpeculatable, ConstantNoise, NoMemoryEffect (MemoryEffectOpInterface)

Effects: MemoryEffects::Effect{}

Results:

ResultDescription

tensor

Type definition

EncryptedBooleanType

An encrypted boolean

Syntax: !FHE.ebool

An encrypted boolean.

EncryptedSignedIntegerType

An encrypted signed integer

An encrypted signed integer with width bits to performs FHE Operations.

Examples:

!FHE.esint<7>
!FHE.esint<6>

Parameters:

ParameterC++ typeDescription

width

unsigned

EncryptedUnsignedIntegerType

An encrypted unsigned integer

An encrypted unsigned integer with width bits to performs FHE Operations.

Examples:

!FHE.eint<7>
!FHE.eint<6>

Parameters:

ParameterC++ typeDescription

width

unsigned

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