Tracing dialect A dialect to print program values at runtime.

Operation definition

Tracing.trace_ciphertext (::mlir::concretelang::Tracing::TraceCiphertextOp)

Prints a ciphertext.

Attributes:

Operands:

Tracing.trace_message (::mlir::concretelang::Tracing::TraceMessageOp)

Prints a message.

Attributes:

Tracing.trace_plaintext (::mlir::concretelang::Tracing::TracePlaintextOp)

Prints a plaintext.

Attributes:

Operands:

Introduction

Compilation of a Python program starts with Concrete's Python frontend, which first traces and transforms it and then converts it into an intermediate representation (IR) that is further processed by Concrete Compiler. This IR is based on the MLIR subproject of the LLVM compiler infrastructure. This document provides an overview of Concrete's FHE-specific representations based on the MLIR framework.

In contrast to traditional infrastructure for compilers, the set of operations and data types that constitute the IR, as well as the level of abstraction that the IR represents, are not fixed in MLIR and can easily be extended. All operations and data types are grouped into dialects, with each dialect representing a specific domain or a specific level of abstraction. Mixing operations and types from different dialects within the same IR is allowed and even encouraged, with all dialects--builtin or developed as an extension--being first-class citizens.

Concrete compiler takes advantage of these concepts by defining a set of dialects, capable of representing an FHE program from an abstract specification that is independent of the actual cryptosystem down to a program that can easily be mapped to function calls of a cryptographic library. The dialects for the representation of an FHE program are:

• The FHELinalg Dialect (documentation, source)

• The FHE Dialect (documentation, source)

• The TFHE Dialect (documentation, source)

• The Concrete Dialect (documentation, source)

• and for debugging purposes, the Tracing Dialect (documentation, source).

In addition, the project further defines two dialects that help expose dynamic task-parallelism and static data-flow graphs in order to benefit from multi-core, multi-accelerator and distributed systems. These are:

• The RT Dialect (documentation, source) and

• The SDFG Dialect (documentation, source).

The figure below illustrates the relationship between the dialects and their embedding into the compilation pipeline.

The following sections focus on the FHE-related dialects, i.e., on the FHELinalg Dialect, the FHE Dialect, the TFHE Dialect and the Concrete Dialect.

The FHE and FHELinalg Dialects: An abstract specification of an FHE program

The top part of the figure shows the components which are involved in the generation of the initial IR, ending with the step labelled MLIR translation. When the initial IR is passed on to Concrete Compiler through its Python bindings, all FHE-related operations are specified using either the FHE or FHELinalg Dialect. Both of these dialects provide operations and data types for the abstract specification of an FHE program, completely independently of a cryptosystem. At this point, the IR simply indicates whether an operand is encrypted (via the type FHE.eint<n>, where n stands for the precision in bits) and what operations are applied to encrypted values. Plaintext values simply use MLIR's builtin integer type in (e.g., i3 or i64).

The FHE Dialect provides scalar operations on encrypted integers, such as additions (FHE.add_eint) or multiplications (FHE.mul_eint), while the FHELinalg Dialect offers operations on tensors of encrypted integers, e.g., matrix products (FHELinalg.matmul_eint_eint) or convolutions (FHELinalg.conv2d).

In a first lowering step of the pipeline, all FHELinalg operations are lowered to operations from MLIR's builtin Linalg Dialect using scalar operations from the FHE Dialect. Consider the following example, which consists of a function that performs a multiplication of a matrix of encrypted integers and a matrix of cleartext values:

func.func @main(%arg0: tensor<4x3x!FHE.eint<2>>, %arg1: tensor<3x2xi3>) -> tensor<4x2x!FHE.eint<2>> {
  %0 = "FHELinalg.matmul_eint_int"(%arg0, %arg1) : (tensor<4x3x!FHE.eint<2>>, tensor<3x2xi3>) -> tensor<4x2x!FHE.eint<2>>
  return %0 : tensor<4x2x!FHE.eint<2>>
}

Upon conversion, the FHELinalg.matmul operation is converted to a linalg.generic operation whose body contains a scalar multiplication (FHE.mul_eint_int) and a scalar addition (FHE.add_eint_int):

#map = affine_map<(d0, d1, d2) -> (d0, d2)>
#map1 = affine_map<(d0, d1, d2) -> (d2, d1)>
#map2 = affine_map<(d0, d1, d2) -> (d0, d1)>

func.func @main(%arg0: tensor<4x3x!FHE.eint<2>>, %arg1: tensor<3x2xi3>) -> tensor<4x2x!FHE.eint<2>> {
  %0 = "FHE.zero_tensor"() : () -> tensor<4x2x!FHE.eint<2>>
  %1 = linalg.generic {indexing_maps = [#map, #map1, #map2], iterator_types = ["parallel", "parallel", "reduction"]} ins(%arg0, %arg1 : tensor<4x3x!FHE.eint<2>>, tensor<3x2xi3>) outs(%0 : tensor<4x2x!FHE.eint<2>>) {
  ^bb0(%in: !FHE.eint<2>, %in_0: i3, %out: !FHE.eint<2>):
    %2 = "FHE.mul_eint_int"(%in, %in_0) : (!FHE.eint<2>, i3) -> !FHE.eint<2>
    %3 = "FHE.add_eint"(%out, %2) : (!FHE.eint<2>, !FHE.eint<2>) -> !FHE.eint<2>
    linalg.yield %3 : !FHE.eint<2>
  } -> tensor<4x2x!FHE.eint<2>>
  return %1 : tensor<4x2x!FHE.eint<2>>
}

This is then further lowered to a nest of loops from MLIR's SCF Dialect, implementing the parallel and reduction dimensions from the linalg.generic operation above:

func.func @main(%arg0: tensor<4x3x!FHE.eint<2>>, %arg1: tensor<3x2xi3>) -> tensor<4x2x!FHE.eint<2>> {
  %c0 = arith.constant 0 : index
  %c4 = arith.constant 4 : index
  %c1 = arith.constant 1 : index
  %c2 = arith.constant 2 : index
  %c3 = arith.constant 3 : index
  %0 = "FHE.zero_tensor"() : () -> tensor<4x2x!FHE.eint<2>>
  %1 = scf.for %arg2 = %c0 to %c4 step %c1 iter_args(%arg3 = %0) -> (tensor<4x2x!FHE.eint<2>>) {
    %2 = scf.for %arg4 = %c0 to %c2 step %c1 iter_args(%arg5 = %arg3) -> (tensor<4x2x!FHE.eint<2>>) {
      %3 = scf.for %arg6 = %c0 to %c3 step %c1 iter_args(%arg7 = %arg5) -> (tensor<4x2x!FHE.eint<2>>) {
        %extracted = tensor.extract %arg0[%arg2, %arg6] : tensor<4x3x!FHE.eint<2>>
        %extracted_0 = tensor.extract %arg1[%arg6, %arg4] : tensor<3x2xi3>
        %extracted_1 = tensor.extract %arg7[%arg2, %arg4] : tensor<4x2x!FHE.eint<2>>
        %4 = "FHE.mul_eint_int"(%extracted, %extracted_0) : (!FHE.eint<2>, i3) -> !FHE.eint<2>
        %5 = "FHE.add_eint"(%extracted_1, %4) : (!FHE.eint<2>, !FHE.eint<2>) -> !FHE.eint<2>
        %inserted = tensor.insert %5 into %arg7[%arg2, %arg4] : tensor<4x2x!FHE.eint<2>>
        scf.yield %inserted : tensor<4x2x!FHE.eint<2>>
      }
      scf.yield %3 : tensor<4x2x!FHE.eint<2>>
    }
    scf.yield %2 : tensor<4x2x!FHE.eint<2>>
  }
  return %1 : tensor<4x2x!FHE.eint<2>>
}

The TFHE Dialect: Binding to the TFHE cryptosystem and parametrization

In order to obtain an executable program at the end of the compilation pipeline, the abstract specification of the FHE program must at some point be bound to a specific cryptosystem. This is the role of the TFHE Dialect, whose purpose is:

• to indicate operations to be carried out using an implementation of the TFHE cryptosystem

• to parametrize the cryptosystem with key sizes, and

• to provide a mapping between keys and encrypted values

When lowering the IR based on the FHE Dialect to the TFHE Dialect, the compiler first generates a generic form, in which FHE operations are lowered to TFHE operations and where values are converted to unparametrized TFHE.glwe values. The unparametrized form TFHE.glwe<sk?> simply indicates that a TFHE.glwe value is to be used, but without any indication of the cryptographic parameters and the actual key.

The IR below shows the example program after lowering to unparametrized TFHE:

func.func @main(%arg0: tensor<4x3x!TFHE.glwe<sk?>>, %arg1: tensor<3x2xi3>) -> tensor<4x2x!TFHE.glwe<sk?>> {
  %c0 = arith.constant 0 : index
  %c4 = arith.constant 4 : index
  %c1 = arith.constant 1 : index
  %c2 = arith.constant 2 : index
  %c3 = arith.constant 3 : index
  %0 = "TFHE.zero_tensor"() : () -> tensor<4x2x!TFHE.glwe<sk?>>
  %1 = scf.for %arg2 = %c0 to %c4 step %c1 iter_args(%arg3 = %0) -> (tensor<4x2x!TFHE.glwe<sk?>>) {
    %2 = scf.for %arg4 = %c0 to %c2 step %c1 iter_args(%arg5 = %arg3) -> (tensor<4x2x!TFHE.glwe<sk?>>) {
      %3 = scf.for %arg6 = %c0 to %c3 step %c1 iter_args(%arg7 = %arg5) -> (tensor<4x2x!TFHE.glwe<sk?>>) {
        %extracted = tensor.extract %arg0[%arg2, %arg6] : tensor<4x3x!TFHE.glwe<sk?>>
        %extracted_0 = tensor.extract %arg1[%arg6, %arg4] : tensor<3x2xi3>
        %extracted_1 = tensor.extract %arg7[%arg2, %arg4] : tensor<4x2x!TFHE.glwe<sk?>>
        %4 = arith.extsi %extracted_0 : i3 to i64
        %5 = "TFHE.mul_glwe_int"(%extracted, %4) : (!TFHE.glwe<sk?>, i64) -> !TFHE.glwe<sk?>
        %6 = "TFHE.add_glwe"(%extracted_1, %5) : (!TFHE.glwe<sk?>, !TFHE.glwe<sk?>) -> !TFHE.glwe<sk?>
        %inserted = tensor.insert %6 into %arg7[%arg2, %arg4] : tensor<4x2x!TFHE.glwe<sk?>>
        scf.yield %inserted : tensor<4x2x!TFHE.glwe<sk?>>
      }
      scf.yield %3 : tensor<4x2x!TFHE.glwe<sk?>>
    }
    scf.yield %2 : tensor<4x2x!TFHE.glwe<sk?>>
  }
  return %1 : tensor<4x2x!TFHE.glwe<sk?>>
}

All operations from the FHE dialect have been replaced with corresponding operations from the TFHE Dialect.

During subsequent parametrization, the compiler can either use a set of default parameters or can obtain a set of parameters from Concrete's optimizer. Either way, an additional pass injects the parameters into the IR, replacing all TFHE.glwe<sk?> instances with TFHE.glwe<i,d,n>, where i is a sequential identifier for a key, d the number of GLWE dimensions and n the size of the GLWE polynomial.

The result of such a parametrization for the example is given below:

func.func @main(%arg0: tensor<4x3x!TFHE.glwe<sk<0,1,512>>>, %arg1: tensor<3x2xi3>) -> tensor<4x2x!TFHE.glwe<sk<0,1,512>>> {
  %c0 = arith.constant 0 : index
  %c4 = arith.constant 4 : index
  %c1 = arith.constant 1 : index
  %c2 = arith.constant 2 : index
  %c3 = arith.constant 3 : index
  %0 = "TFHE.zero_tensor"() : () -> tensor<4x2x!TFHE.glwe<sk<0,1,512>>>
  %1 = scf.for %arg2 = %c0 to %c4 step %c1 iter_args(%arg3 = %0) -> (tensor<4x2x!TFHE.glwe<sk<0,1,512>>>) {
    %2 = scf.for %arg4 = %c0 to %c2 step %c1 iter_args(%arg5 = %arg3) -> (tensor<4x2x!TFHE.glwe<sk<0,1,512>>>) {
      %3 = scf.for %arg6 = %c0 to %c3 step %c1 iter_args(%arg7 = %arg5) -> (tensor<4x2x!TFHE.glwe<sk<0,1,512>>>) {
        %extracted = tensor.extract %arg0[%arg2, %arg6] : tensor<4x3x!TFHE.glwe<sk<0,1,512>>>
        %extracted_0 = tensor.extract %arg1[%arg6, %arg4] : tensor<3x2xi3>
        %extracted_1 = tensor.extract %arg7[%arg2, %arg4] : tensor<4x2x!TFHE.glwe<sk<0,1,512>>>
        %4 = arith.extsi %extracted_0 : i3 to i64
        %5 = "TFHE.mul_glwe_int"(%extracted, %4) : (!TFHE.glwe<sk<0,1,512>>, i64) -> !TFHE.glwe<sk<0,1,512>>
        %6 = "TFHE.add_glwe"(%extracted_1, %5) : (!TFHE.glwe<sk<0,1,512>>, !TFHE.glwe<sk<0,1,512>>) -> !TFHE.glwe<sk<0,1,512>>
        %inserted = tensor.insert %6 into %arg7[%arg2, %arg4] : tensor<4x2x!TFHE.glwe<sk<0,1,512>>>
        scf.yield %inserted : tensor<4x2x!TFHE.glwe<sk<0,1,512>>>
      }
      scf.yield %3 : tensor<4x2x!TFHE.glwe<sk<0,1,512>>>
    }
    scf.yield %2 : tensor<4x2x!TFHE.glwe<sk<0,1,512>>>
  }
  return %1 : tensor<4x2x!TFHE.glwe<sk<0,1,512>>>
}

In this parametrization, a single key with the ID 0 is used, with a single dimension and a polynomial of size 512.

The Concrete Dialect: Preparing bindings with a crypto library

In the next step of the pipeline, operations and types are lowered to the Concrete Dialect. This dialect provides operations, which are implemented by one of Concrete's backend libraries, but still abstracts from any technical details required for interaction with an actual library. The goal is to maintain a high-level representation with value-based semantics and actual operations instead of buffer semantics and library calls, while ensuring that all operations an effectively be lowered to a library call later in the pipeline. However, the abstract types from TFHE are already lowered to tensors of integers with a suitable shape that will hold the binary data of the encrypted values.

The result of the lowering of the example to the Concrete Dialect is shown below:

func.func @main(%arg0: tensor<4x3x513xi64>, %arg1: tensor<3x2xi3>) -> tensor<4x2x513xi64> {
  %c0 = arith.constant 0 : index
  %c4 = arith.constant 4 : index
  %c1 = arith.constant 1 : index
  %c2 = arith.constant 2 : index
  %c3 = arith.constant 3 : index
  %generated = tensor.generate  {
  ^bb0(%arg2: index, %arg3: index, %arg4: index):
    %c0_i64 = arith.constant 0 : i64
    tensor.yield %c0_i64 : i64
  } : tensor<4x2x513xi64>
  %0 = scf.for %arg2 = %c0 to %c4 step %c1 iter_args(%arg3 = %generated) -> (tensor<4x2x513xi64>) {
    %1 = scf.for %arg4 = %c0 to %c2 step %c1 iter_args(%arg5 = %arg3) -> (tensor<4x2x513xi64>) {
      %2 = scf.for %arg6 = %c0 to %c3 step %c1 iter_args(%arg7 = %arg5) -> (tensor<4x2x513xi64>) {
        %extracted_slice = tensor.extract_slice %arg0[%arg2, %arg6, 0] [1, 1, 513] [1, 1, 1] : tensor<4x3x513xi64> to tensor<513xi64>
        %extracted = tensor.extract %arg1[%arg6, %arg4] : tensor<3x2xi3>
        %extracted_slice_0 = tensor.extract_slice %arg7[%arg2, %arg4, 0] [1, 1, 513] [1, 1, 1] : tensor<4x2x513xi64> to tensor<513xi64>
        %3 = arith.extsi %extracted : i3 to i64
        %4 = "Concrete.mul_cleartext_lwe_tensor"(%extracted_slice, %3) : (tensor<513xi64>, i64) -> tensor<513xi64>
        %5 = "Concrete.add_lwe_tensor"(%extracted_slice_0, %4) : (tensor<513xi64>, tensor<513xi64>) -> tensor<513xi64>
        %inserted_slice = tensor.insert_slice %5 into %arg7[%arg2, %arg4, 0] [1, 1, 513] [1, 1, 1] : tensor<513xi64> into tensor<4x2x513xi64>
        scf.yield %inserted_slice : tensor<4x2x513xi64>
      }
      scf.yield %2 : tensor<4x2x513xi64>
    }
    scf.yield %1 : tensor<4x2x513xi64>
  }
  return %0 : tensor<4x2x513xi64>
}

Bufferization and emitting library calls

The remaining stages of the pipeline are rather technical. Before any binding to an actual Concrete backend library, the compiler first invokes MLIR's bufferization infrastructure to convert the value-based IR into an IR with buffer semantics. In particular, this means that keys and encrypted values are no longer abstract values in a mathematical sense, but values backed by a memory location that holds the actual data. This form of IR is then suitable for a pass emitting actual library calls that implement the corresponding operations from the Concrete Dialect for a specific backend.

The result for the example is given below:

func.func @main(%arg0: memref<4x3x513xi64, strided<[?, ?, ?], offset: ?>>, %arg1: memref<3x2xi3, strided<[?, ?], offset: ?>>, %arg2: !Concrete.context) -> memref<4x2x513xi64> {
  %c0_i64 = arith.constant 0 : i64
  call @_dfr_start(%c0_i64, %arg2) : (i64, !Concrete.context) -> ()
  %c0 = arith.constant 0 : index
  %c4 = arith.constant 4 : index
  %c1 = arith.constant 1 : index
  %c2 = arith.constant 2 : index
  %c513 = arith.constant 513 : index
  %c0_i64_0 = arith.constant 0 : i64
  %c3 = arith.constant 3 : index
  %alloc = memref.alloc() {alignment = 64 : i64} : memref<4x2x513xi64>
  scf.for %arg3 = %c0 to %c4 step %c1 {
    scf.for %arg4 = %c0 to %c2 step %c1 {
      scf.for %arg5 = %c0 to %c513 step %c1 {
        memref.store %c0_i64_0, %alloc[%arg3, %arg4, %arg5] : memref<4x2x513xi64>
      }
    }
  }
  scf.for %arg3 = %c0 to %c4 step %c1 {
    scf.for %arg4 = %c0 to %c2 step %c1 {
      %subview = memref.subview %alloc[%arg3, %arg4, 0] [1, 1, 513] [1, 1, 1] : memref<4x2x513xi64> to memref<513xi64, strided<[1], offset: ?>>
      scf.for %arg5 = %c0 to %c3 step %c1 {
        %subview_1 = memref.subview %arg0[%arg3, %arg5, 0] [1, 1, 513] [1, 1, 1] : memref<4x3x513xi64, strided<[?, ?, ?], offset: ?>> to memref<513xi64, strided<[?], offset: ?>>
        %0 = memref.load %arg1[%arg5, %arg4] : memref<3x2xi3, strided<[?, ?], offset: ?>>
        %1 = arith.extsi %0 : i3 to i64
        %alloc_2 = memref.alloc() {alignment = 64 : i64} : memref<513xi64>
        %cast = memref.cast %alloc_2 : memref<513xi64> to memref<?xi64, #map>
        %cast_3 = memref.cast %subview_1 : memref<513xi64, strided<[?], offset: ?>> to memref<?xi64, #map>
        func.call @memref_mul_cleartext_lwe_ciphertext_u64(%cast, %cast_3, %1) : (memref<?xi64, #map>, memref<?xi64, #map>, i64) -> ()
        %alloc_4 = memref.alloc() {alignment = 64 : i64} : memref<513xi64>
        %cast_5 = memref.cast %alloc_4 : memref<513xi64> to memref<?xi64, #map>
        %cast_6 = memref.cast %subview : memref<513xi64, strided<[1], offset: ?>> to memref<?xi64, #map>
        %cast_7 = memref.cast %alloc_2 : memref<513xi64> to memref<?xi64, #map>
        func.call @memref_add_lwe_ciphertexts_u64(%cast_5, %cast_6, %cast_7) : (memref<?xi64, #map>, memref<?xi64, #map>, memref<?xi64, #map>) -> ()
        memref.dealloc %alloc_2 : memref<513xi64>
        memref.copy %alloc_4, %subview : memref<513xi64> to memref<513xi64, strided<[1], offset: ?>>
        memref.dealloc %alloc_4 : memref<513xi64>
      }
    }
  }
  call @_dfr_stop(%c0_i64) : (i64) -> ()
  return %alloc : memref<4x2x513xi64>
}

At this stage, the IR is only composed of operations from builtin Dialects and thus amenable to lowering to LLVM-IR using the lowering passes provided by MLIR.

High Level Fully Homomorphic Encryption Linalg dialect A dialect for representation of high level linalg operations on fully homomorphic ciphertexts.

Operation definition

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

Returns a tensor that contains the addition of a tensor of encrypted integers and a tensor of clear integers.

Performs an addition following the broadcasting rules between a tensor of encrypted integers and a tensor of clear integers. The width of the clear integers must be less than or equal to the width of encrypted integers.

Examples:

Traits: AlwaysSpeculatableImplTrait, TensorBinaryEintInt, TensorBroadcastingRules

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

Effects: MemoryEffects::Effect{}

Operands:

Results:

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

Returns a tensor that contains the addition of two tensor of encrypted integers.

Performs an addition following the broadcasting rules between two tensors of encrypted integers. The width of the encrypted integers must be equal.

Examples:

Traits: AlwaysSpeculatableImplTrait, TensorBinaryEint, TensorBroadcastingRules

Interfaces: BinaryEint, ConditionallySpeculatable, NoMemoryEffect (MemoryEffectOpInterface)

Effects: MemoryEffects::Effect{}

Operands:

Results:

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

Returns a tensor that contains the result of the lookup on a table.

For each encrypted index, performs a lookup table of clear integers.

The %lut argument must be a tensor with one dimension, where its dimension is 2^p where p is the width of the encrypted integers.

Examples:

Traits: AlwaysSpeculatableImplTrait

Interfaces: ConditionallySpeculatable, ConstantNoise, NoMemoryEffect (MemoryEffectOpInterface)

Effects: MemoryEffects::Effect{}

Operands:

Results:

FHELinalg.apply_mapped_lookup_table (::mlir::concretelang::FHELinalg::ApplyMappedLookupTableEintOp)

Returns a tensor that contains the result of the lookup on a table, using a different lookup table for each element, specified by a map.

Performs for each encrypted index a lookup table of clear integers. Multiple lookup tables are passed, and the application of lookup tables is performed following the broadcasting rules. The precise lookup is specified by a map.

Examples:

Others examples: // [0,1] [1, 0] = [3,2] // [3,0] lut [[1,3,5,7], [0,2,4,6]] with [0, 1] = [7,0] // [2,3] [1, 0] = [4,7]

// [0,1] [0, 0] = [1,3] // [3,0] lut [[1,3,5,7], [0,2,4,6]] with [1, 1] = [6,0] // [2,3] [1, 0] = [4,7]

// [0,1] [0] = [1,3] // [3,0] lut [[1,3,5,7], [0,2,4,6]] with [1] = [6,0] // [2,3] [0] = [5,7]

// [0,1] = [1,2] // [3,0] lut [[1,3,5,7], [0,2,4,6]] with [0, 1] = [7,0] // [2,3] = [5,6]

Traits: AlwaysSpeculatableImplTrait

Interfaces: ConditionallySpeculatable, ConstantNoise, NoMemoryEffect (MemoryEffectOpInterface)

Effects: MemoryEffects::Effect{}

Operands:

Results:

FHELinalg.apply_multi_lookup_table (::mlir::concretelang::FHELinalg::ApplyMultiLookupTableEintOp)

Returns a tensor that contains the result of the lookup on a table, using a different lookup table for each element.

Performs for each encrypted index a lookup table of clear integers. Multiple lookup tables are passed, and the application of lookup tables is performed following the broadcasting rules.

The %luts argument should be a tensor with M dimension, where the first M-1 dimensions are broadcastable with the N dimensions of the encrypted tensor, and where the last dimension dimension is equal to 2^p where p is the width of the encrypted integers.

Examples:

Traits: AlwaysSpeculatableImplTrait

Interfaces: ConditionallySpeculatable, ConstantNoise, NoMemoryEffect (MemoryEffectOpInterface)

Effects: MemoryEffects::Effect{}

Operands:

Results:

FHELinalg.broadcast (::mlir::concretelang::FHELinalg::BroadcastOp)

Broadcasts a tensor to a shape.

Broadcasting is used for expanding certain dimensions of a tensor or adding new dimensions to it at the beginning.

An example could be broadcasting a tensor with shape <1x2x1x4x1> to a tensor of shape <6x1x2x3x4x5>.

In this example:

• last dimension of the input (1) is expanded to (5)

• the dimension before that (4) is kept

• the dimension before that (1) is expanded to (3)

• the dimension before that (2) is kept

• the dimension before that (1) is kept

• a new dimension (6) is added to the beginning

See https://numpy.org/doc/stable/user/basics.broadcasting.html#general-broadcasting-rules for the semantics of broadcasting.

Examples:

Traits: AlwaysSpeculatableImplTrait

Interfaces: ConditionallySpeculatable, ConstantNoise, NoMemoryEffect (MemoryEffectOpInterface)

Effects: MemoryEffects::Effect{}

Operands:

Results:

FHELinalg.concat (::mlir::concretelang::FHELinalg::ConcatOp)

Concatenates a sequence of tensors along an existing axis.

Concatenates several tensors along a given axis.

Examples:

Traits: AlwaysSpeculatableImplTrait

Interfaces: ConditionallySpeculatable, NoMemoryEffect (MemoryEffectOpInterface)

Effects: MemoryEffects::Effect{}

Attributes:

Operands:

Results:

FHELinalg.conv2d (::mlir::concretelang::FHELinalg::Conv2dOp)

Returns the 2D convolution of a tensor in the form NCHW with weights in the form FCHW

Traits: AlwaysSpeculatableImplTrait

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

Effects: MemoryEffects::Effect{}

Attributes:

Operands:

Results:

FHELinalg.dot_eint_int (::mlir::concretelang::FHELinalg::Dot)

Returns the encrypted dot product between a vector of encrypted integers and a vector of clean integers.

Performs a dot product between a vector of encrypted integers and a vector of clear integers.

Examples:

Traits: AlwaysSpeculatableImplTrait

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

Effects: MemoryEffects::Effect{}

Operands:

Results:

FHELinalg.dot_eint_eint (::mlir::concretelang::FHELinalg::DotEint)

Returns the encrypted dot product between two vectors of encrypted integers.

Performs a dot product between two vectors of encrypted integers.

Examples:

Traits: AlwaysSpeculatableImplTrait

Interfaces: ConditionallySpeculatable, NoMemoryEffect (MemoryEffectOpInterface)

Effects: MemoryEffects::Effect{}

Operands:

Results:

FHELinalg.fancy_assign (::mlir::concretelang::FHELinalg::FancyAssignOp)

Assigns a tensor into another tensor at a tensor of indices.

Examples:

Notes:

• Assigning to the same output position results in undefined behavior.

Traits: AlwaysSpeculatableImplTrait

Interfaces: ConditionallySpeculatable, NoMemoryEffect (MemoryEffectOpInterface)

Effects: MemoryEffects::Effect{}

Operands:

Results:

FHELinalg.fancy_index (::mlir::concretelang::FHELinalg::FancyIndexOp)

Index into a tensor using a tensor of indices.

Examples:

Traits: AlwaysSpeculatableImplTrait

Interfaces: ConditionallySpeculatable, NoMemoryEffect (MemoryEffectOpInterface)

Effects: MemoryEffects::Effect{}

Operands:

Results:

FHELinalg.from_element (::mlir::concretelang::FHELinalg::FromElementOp)

Creates a tensor with a single element.

Creates a tensor with a single element.

Traits: AlwaysSpeculatableImplTrait

Interfaces: ConditionallySpeculatable, NoMemoryEffect (MemoryEffectOpInterface)

Effects: MemoryEffects::Effect{}

Operands:

Results:

FHELinalg.lsb (::mlir::concretelang::FHELinalg::LsbEintOp)

Extract the lowest significant bit at a given precision.

This operation extracts the lsb of a ciphertext tensor in a specific precision.

Extracting only 1 bit:

Traits: AlwaysSpeculatableImplTrait, TensorUnaryEint

Interfaces: ConditionallySpeculatable, ConstantNoise, NoMemoryEffect (MemoryEffectOpInterface), UnaryEint

Effects: MemoryEffects::Effect{}

Operands:

Results:

FHELinalg.matmul_eint_eint (::mlir::concretelang::FHELinalg::MatMulEintEintOp)

Returns a tensor that contains the result of the matrix multiplication of a matrix of encrypted integers and a second matrix of encrypted integers.

Performs a matrix multiplication of a matrix of encrypted integers and a second matrix of encrypted integers.

The behavior depends on the arguments in the following way:

Examples:

Traits: AlwaysSpeculatableImplTrait, TensorBinaryEint

Interfaces: ConditionallySpeculatable, NoMemoryEffect (MemoryEffectOpInterface)

Effects: MemoryEffects::Effect{}

Operands:

Results:

FHELinalg.matmul_eint_int (::mlir::concretelang::FHELinalg::MatMulEintIntOp)

Returns a tensor that contains the result of the matrix multiplication of a matrix of encrypted integers and a matrix of clear integers.

Performs a matrix multiplication of a matrix of encrypted integers and a matrix of clear integers. The width of the clear integers must be less than or equal to the width of encrypted integers.

The behavior depends on the arguments in the following way:

Examples:

Traits: AlwaysSpeculatableImplTrait, TensorBinaryEintInt

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

Effects: MemoryEffects::Effect{}

Operands:

Results:

FHELinalg.matmul_int_eint (::mlir::concretelang::FHELinalg::MatMulIntEintOp)

Returns a tensor that contains the result of the matrix multiplication of a matrix of clear integers and a matrix of encrypted integers.

Performs a matrix multiplication of a matrix of clear integers and a matrix of encrypted integers. The width of the clear integers must be less than or equal to the width of encrypted integers.

The behavior depends on the arguments in the following way:

Examples:

Traits: AlwaysSpeculatableImplTrait, TensorBinaryIntEint

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

Effects: MemoryEffects::Effect{}

Operands:

Results:

FHELinalg.maxpool2d (::mlir::concretelang::FHELinalg::Maxpool2dOp)

Returns the 2D maxpool of a tensor in the form NCHW

Interfaces: UnaryEint

Attributes:

Operands:

Results:

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

Returns a tensor that contains the multiplication of a tensor of encrypted integers and a tensor of clear integers.

Performs a multiplication following the broadcasting rules between a tensor of encrypted integers and a tensor of clear integers. The width of the clear integers must be less than or equal to the width of encrypted integers.

Examples:

Traits: AlwaysSpeculatableImplTrait, TensorBinaryEintInt, TensorBroadcastingRules

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

Effects: MemoryEffects::Effect{}

Operands:

Results:

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

Returns a tensor that contains the multiplication of two tensor of encrypted integers.

Performs an addition following the broadcasting rules between two tensors of encrypted integers. The width of the encrypted integers must be equal.

Examples:

Traits: AlwaysSpeculatableImplTrait, TensorBinaryEint, TensorBroadcastingRules

Interfaces: BinaryEint, ConditionallySpeculatable, NoMemoryEffect (MemoryEffectOpInterface)

Effects: MemoryEffects::Effect{}

Operands:

Results:

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

Returns a tensor that contains the negation of a tensor of encrypted integers.

Performs a negation to a tensor of encrypted integers.

Examples:

Traits: AlwaysSpeculatableImplTrait, TensorUnaryEint

Interfaces: ConditionallySpeculatable, NoMemoryEffect (MemoryEffectOpInterface), UnaryEint

Effects: MemoryEffects::Effect{}

Operands:

Results:

FHELinalg.reinterpret_precision (::mlir::concretelang::FHELinalg::ReinterpretPrecisionEintOp)

Reinterpret the ciphertext tensor with a different precision.

It's a reinterpretation cast which changes only the precision. On CRT represention, it does nothing. On Native representation, it moves the message/noise further forward, effectively changing the precision. Changing to - a bigger precision is safe, as the crypto-parameters are chosen such that only zeros will come from the noise part. This is equivalent to a shift left for the value - a smaller precision is only safe if you clear the lowest message bits first. If not, you can assume small errors with high probability and frequent bigger errors, which can be contained to small errors using margins. This is equivalent to a shift right for the value

Example:

Traits: AlwaysSpeculatableImplTrait, TensorUnaryEint

Interfaces: ConditionallySpeculatable, NoMemoryEffect (MemoryEffectOpInterface), UnaryEint

Effects: MemoryEffects::Effect{}

Operands:

Results:

FHELinalg.round (::mlir::concretelang::FHELinalg::RoundOp)

Rounds a tensor of ciphertexts into a smaller precision.

Traits: AlwaysSpeculatableImplTrait, TensorBinaryEintInt, TensorBroadcastingRules

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

Effects: MemoryEffects::Effect{}

Operands:

Results:

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

Returns a tensor that contains the subtraction of two tensor of encrypted integers.

Performs an subtraction following the broadcasting rules between two tensors of encrypted integers. The width of the encrypted integers must be equal.

Examples:

Traits: AlwaysSpeculatableImplTrait, TensorBinaryEint, TensorBroadcastingRules

Interfaces: BinaryEint, ConditionallySpeculatable, NoMemoryEffect (MemoryEffectOpInterface)

Effects: MemoryEffects::Effect{}

Operands:

Results:

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

Returns a tensor that contains the subtraction of a tensor of clear integers and a tensor of encrypted integers.

Performs a subtraction following the broadcasting rules between a tensor of clear integers and a tensor of encrypted integers. The width of the clear integers must be less than or equal to the width of encrypted integers.

Examples:

Traits: AlwaysSpeculatableImplTrait, TensorBinaryIntEint, TensorBroadcastingRules

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

Effects: MemoryEffects::Effect{}

Operands:

Results:

FHELinalg.sum (::mlir::concretelang::FHELinalg::SumOp)

Returns the sum of elements of a tensor of encrypted integers along specified axes.

Attributes:

• keep_dims: boolean = false whether to keep the rank of the tensor after the sum operation if true, reduced axes will have the size of 1

• axes: I64ArrayAttr = [] list of dimension to perform the sum along think of it as the dimensions to reduce (see examples below to get an intuition)

Examples:

Traits: AlwaysSpeculatableImplTrait, TensorUnaryEint

Interfaces: ConditionallySpeculatable, NoMemoryEffect (MemoryEffectOpInterface)

Effects: MemoryEffects::Effect{}

Attributes:

Operands:

Results:

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

Cast an unsigned integer tensor to a signed one

Cast an unsigned integer tensor to a signed one. The result must have the same width and the same shape as the input.

The behavior is undefined on overflow/underflow.

Examples:

Traits: AlwaysSpeculatableImplTrait

Interfaces: ConditionallySpeculatable, NoMemoryEffect (MemoryEffectOpInterface), UnaryEint

Effects: MemoryEffects::Effect{}

Operands:

Results:

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

Cast a signed integer tensor to an unsigned one

Cast a signed integer tensor to an unsigned one. The result must have the same width and the same shape as the input.

The behavior is undefined on overflow/underflow.

Examples:

Traits: AlwaysSpeculatableImplTrait

Interfaces: ConditionallySpeculatable, NoMemoryEffect (MemoryEffectOpInterface), UnaryEint

Effects: MemoryEffects::Effect{}

Operands:

Results:

FHELinalg.transpose (::mlir::concretelang::FHELinalg::TransposeOp)

Returns a tensor that contains the transposition of the input tensor.

Performs a transpose operation on an N-dimensional tensor.

Attributes:

• axes: I64ArrayAttr = [] list of dimension to perform the transposition contains a permutation of [0,1,..,N-1] where N is the number of axes think of it as a way to rearrange axes (see the example below)

Examples:

Traits: AlwaysSpeculatableImplTrait

Interfaces: ConditionallySpeculatable, NoMemoryEffect (MemoryEffectOpInterface), UnaryEint

Effects: MemoryEffects::Effect{}

Attributes:

Operands:

Results:

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

Effects: MemoryEffects::Effect{}

Operands:

Results:

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: AdditiveNoise, BinaryEint, ConditionallySpeculatable, NoMemoryEffect (MemoryEffectOpInterface)

Effects: MemoryEffects::Effect{}

Operands:

Results:

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:

Results:

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:

Results:

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:

Results:

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:

Results:

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:

Results:

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:

Results:

FHE.change_partition (::mlir::concretelang::FHE::ChangePartitionEintOp)

Change partition if necessary.

Changing the partition of a ciphertext. If necessary, it keyswitch the ciphertext to a different key having a different set of parameters than the original one.

Example:

  %from_src = "FHE.change_partition"(%eint) {src = #FHE.partition<name "tfhers", lwe_dim 761, glwe_dim 1, poly_size 2048, pbs_base_log 23, pbs_level 1>} : (!FHE.eint<16>) -> (!FHE.eint<16>)
  %to_dest = "FHE.change_partition"(%eint) {dest = #FHE.partition<name "tfhers", lwe_dim 761, glwe_dim 1, poly_size 2048, pbs_base_log 23, pbs_level 1>} : (!FHE.eint<16>) -> (!FHE.eint<16>)

Traits: AlwaysSpeculatableImplTrait

Interfaces: ConditionallySpeculatable, NoMemoryEffect (MemoryEffectOpInterface), UnaryEint

Effects: MemoryEffects::Effect{}

Attributes:

Operands:

Results:

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:

Results:

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:

Results:

FHE.lsb (::mlir::concretelang::FHE::LsbEintOp)

Extract the lowest significant bit at a given precision.

This operation extracts the lsb of a ciphertext in a specific precision.

Extracting the lsb with the smallest precision:

 // Checking if even or odd
 %even = "FHE.lsb"(%a): (!FHE.eint<4>) -> (!FHE.eint<1>)

Usually when you extract the lsb bit, you also need to extract the next one.
In that case you first need to clear the first lsb of the input to be able to reduce its precision and extract the next one.
To be able to clear the lsb just extracted, you can get it in the original precision.

Example:
```mlir
 // Extracting the first lsb with original precision
 %lsb_0 = "FHE.lsb"(%input): (!FHE.eint<4>) -> (!FHE.eint<4>)
 // Clearing the first lsb from original input
 %input_lsb0_cleared = "FHE.sub_eint"(%input, %lsb_0) : (!FHE.eint<4>, !FHE.eint<4>) -> (!FHE.eint<4>)
 // Reducing the precision of the input
 %input_3b = "FHE.reinterpret_precision(%input) : (!FHE.eint<4>) -> !FHE.eint<3>
 // Now, we can do it again with the second lsb
 %lsb_1 = "FHE.lsb"(%input_3b): (!FHE.eint<3>) -> (!FHE.eint<3>)
 ...
 // later if you need %b_lsb at same position as in the input
 %lsb_1_at_input_position = "FHE.reinterpret_precision(%b_lsb)" : (!FHE.eint<3>) -> !FHE.eint<4>
 // that way you can recombine the extracted bits
 %input_mod_4 = "FHE.add_eint"(%lsb_0, %lsb_1_at_input_position) : (!FHE.eint<4>, !FHE.eint<4>) -> (!FHE.eint<4>)

Traits: AlwaysSpeculatableImplTrait

Interfaces: ConditionallySpeculatable, ConstantNoise, NoMemoryEffect (MemoryEffectOpInterface), UnaryEint

Effects: MemoryEffects::Effect{}

Operands:

Results:

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:

Results:

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:

Results:

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:

Results:

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:

Results:

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: AdditiveNoise, ConditionallySpeculatable, NoMemoryEffect (MemoryEffectOpInterface), UnaryEint

Effects: MemoryEffects::Effect{}

Operands:

Results:

FHE.reinterpret_precision (::mlir::concretelang::FHE::ReinterpretPrecisionEintOp)

Reinterpret the ciphertext with a different precision.

Changing the precision of a ciphertext. It changes both the precision, the value, and in certain cases the correctness of the ciphertext.

Changing to - a bigger precision is always safe. This is equivalent to a shift left for the value. - a smaller precision is only safe if you clear the lowest bits that are discarded. If not, you can assume small errors on the next TLU. This is equivalent to a shift right for the value.

Example:

 // assuming %a is stored as 4bits but can be stored with only 2bits
 // we can reduce its storage precision
 %shifted_a = "FHE.mul_eint_int"(%a, %c_4): (!FHE.eint<4>) -> (!FHE.eint<4>)
 %a_small_precision = "FHE.reinterpret_precision"(%shifted_a, %lsb) : (!FHE.eint<4>) -> (!FHE.eint<2>)

Traits: AlwaysSpeculatableImplTrait

Interfaces: ConditionallySpeculatable, NoMemoryEffect (MemoryEffectOpInterface), UnaryEint

Effects: MemoryEffects::Effect{}

Operands:

Results:

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:

Results:

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

Effects: MemoryEffects::Effect{}

Operands:

Results:

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: AdditiveNoise, BinaryEint, ConditionallySpeculatable, NoMemoryEffect (MemoryEffectOpInterface)

Effects: MemoryEffects::Effect{}

Operands:

Results:

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

Effects: MemoryEffects::Effect{}

Operands:

Results:

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:

Results:

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:

Results:

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:

Results:

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, NoMemoryEffect (MemoryEffectOpInterface), ZeroNoise

Effects: MemoryEffects::Effect{}

Results:

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, NoMemoryEffect (MemoryEffectOpInterface), ZeroNoise

Effects: MemoryEffects::Effect{}

Results:

Attribute definition

PartitionAttr

An attribute representing a partition.

Syntax:

#FHE.partition<
  StringAttr,   # name
  uint64_t,   # lweDim
  uint64_t,   # glweDim
  uint64_t,   # polySize
  uint64_t,   # pbsBaseLog
  uint64_t   # pbsLevel
>

Parameters:

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:

EncryptedUnsignedIntegerType

An encrypted unsigned integer

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

Examples:

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

Parameters:

Runtime dialect A dialect for representation the abstraction needed for the runtime.

Operation definition

RT.await_future (::mlir::concretelang::RT::AwaitFutureOp)

Wait for a future and access its data.

The results of a dataflow task are always futures which could be further used as inputs to subsequent tasks. When the result of a task is needed in the outer execution context, the result future needs to be synchronized and its data accessed using RT.await_future.

Operands:

Results:

RT.build_return_ptr_placeholder (::mlir::concretelang::RT::BuildReturnPtrPlaceholderOp)

Results:

RT.clone_future (::mlir::concretelang::RT::CloneFutureOp)

Interfaces: AllocationOpInterface, MemoryEffectOpInterface

Operands:

Results:

RT.create_async_task (::mlir::concretelang::RT::CreateAsyncTaskOp)