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default_params.go
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default_params.go
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package bootstrapping
import (
"github.com/tuneinsight/lattigo/v4/ckks"
"github.com/tuneinsight/lattigo/v4/ckks/advanced"
"github.com/tuneinsight/lattigo/v4/rlwe"
)
type defaultParametersLiteral struct {
SchemeParams ckks.ParametersLiteral
BootstrappingParams Parameters
}
// The parameters provided hereunder are the parameters used in the paper
// Bootstrapping for Approximate Homomorphic Encryption with Negligible
// Failure-Probability by Using Sparse-Secret Encapsulation,
// https://eprint.iacr.org/2022/024
// DefaultParametersSparse is a set of default bootstrapping parameters with H=192 as main secret and H=32 as ephemeral secret.
var DefaultParametersSparse = []defaultParametersLiteral{N16QP1546H192H32, N16QP1547H192H32, N16QP1553H192H32, N15QP768H192H32}
// DefaultParametersDense is a set of default bootstrapping parameters with H=N/2 as main secret and H=32 as ephemeral secret.
var DefaultParametersDense = []defaultParametersLiteral{N16QP1767H32768H32, N16QP1788H32768H32, N16QP1793H32768H32, N15QP880H16384H32}
var (
// N16QP1546H192H32 is a default bootstrapping parameters for a main secret with H=192 and an ephemeral secret with H=32.
// Residual Q : 420 bits.
// Precision : 26.6 bits for 2^{15} slots.
// Failure : 2^{-138.7} for 2^{15} slots.
N16QP1546H192H32 = defaultParametersLiteral{
ckks.ParametersLiteral{
LogN: 16,
Sigma: rlwe.DefaultSigma,
H: 192,
Q: []uint64{
0x10000000006e0001, // 60 Q0
0x10000140001, // 40
0xffffe80001, // 40
0xffffc40001, // 40
0x100003e0001, // 40
0xffffb20001, // 40
0x10000500001, // 40
0xffff940001, // 40
0xffff8a0001, // 40
0xffff820001, // 40
0x7fffe60001, // 39 StC
0x7fffe40001, // 39 StC
0x7fffe00001, // 39 StC
0xfffffffff840001, // 60 Sine (double angle)
0x1000000000860001, // 60 Sine (double angle)
0xfffffffff6a0001, // 60 Sine
0x1000000000980001, // 60 Sine
0xfffffffff5a0001, // 60 Sine
0x1000000000b00001, // 60 Sine
0x1000000000ce0001, // 60 Sine
0xfffffffff2a0001, // 60 Sine
0x100000000060001, // 56 CtS
0xfffffffff00001, // 56 CtS
0xffffffffd80001, // 56 CtS
0x1000000002a0001, // 56 CtS
},
P: []uint64{
0x1fffffffffe00001, // Pi 61
0x1fffffffffc80001, // Pi 61
0x1fffffffffb40001, // Pi 61
0x1fffffffff500001, // Pi 61
0x1fffffffff420001, // Pi 61
},
LogSlots: 15,
DefaultScale: 1 << 40,
},
Parameters{
EphemeralSecretWeight: 32,
SlotsToCoeffsParameters: advanced.EncodingMatrixLiteral{
LinearTransformType: advanced.SlotsToCoeffs,
RepackImag2Real: true,
LevelStart: 12,
BSGSRatio: 2.0,
BitReversed: false,
ScalingFactor: [][]float64{
{0x7fffe60001},
{0x7fffe40001},
{0x7fffe00001},
},
},
EvalModParameters: advanced.EvalModLiteral{
Q: 0x10000000006e0001,
LevelStart: 20,
SineType: advanced.Cos1,
MessageRatio: 256.0,
K: 16,
SineDeg: 30,
DoubleAngle: 3,
ArcSineDeg: 0,
ScalingFactor: 1 << 60,
},
CoeffsToSlotsParameters: advanced.EncodingMatrixLiteral{
LinearTransformType: advanced.CoeffsToSlots,
RepackImag2Real: true,
LevelStart: 24,
BSGSRatio: 2.0,
BitReversed: false,
ScalingFactor: [][]float64{
{0x100000000060001},
{0xfffffffff00001},
{0xffffffffd80001},
{0x1000000002a0001},
},
},
},
}
// N16QP1547H192H32 is a default bootstrapping parameters for a main secret with H=192 and an ephemeral secret with H=32.
// Residual Q : 285 bits.
// Precision : 32.1 bits for 2^{15} slots.
// Failure : 2^{-138.7} for 2^{15} slots.
N16QP1547H192H32 = defaultParametersLiteral{
ckks.ParametersLiteral{
LogN: 16,
Sigma: rlwe.DefaultSigma,
H: 192,
Q: []uint64{
0x10000000006e0001, // 60 Q0
0x2000000a0001, // 45
0x2000000e0001, // 45
0x1fffffc20001, // 45
0x200000440001, // 45
0x200000500001, // 45
0x3ffffe80001, // 42 StC
0x3ffffd20001, // 42 StC
0x3ffffca0001, // 42 StC
0xffffffffffc0001, // 60 ArcSine
0xfffffffff240001, // 60 ArcSine
0x1000000000f00001, // 60 ArcSine
0xfffffffff840001, // 60 Double angle
0x1000000000860001, // 60 Double angle
0xfffffffff6a0001, // 60 Sine
0x1000000000980001, // 60 Sine
0xfffffffff5a0001, // 60 Sine
0x1000000000b00001, // 60 Sine
0x1000000000ce0001, // 60 Sine
0xfffffffff2a0001, // 60 Sine
0x400000000360001, // 58 CtS
0x3ffffffffbe0001, // 58 CtS
0x400000000660001, // 58 CtS
0x4000000008a0001, // 58 CtS
},
P: []uint64{
0x1fffffffffe00001, // Pi 61
0x1fffffffffc80001, // Pi 61
0x1fffffffffb40001, // Pi 61
0x1fffffffff500001, // Pi 61
},
LogSlots: 15,
DefaultScale: 1 << 45,
},
Parameters{
EphemeralSecretWeight: 32,
SlotsToCoeffsParameters: advanced.EncodingMatrixLiteral{
LinearTransformType: advanced.SlotsToCoeffs,
RepackImag2Real: true,
LevelStart: 8,
BSGSRatio: 2.0,
BitReversed: false,
ScalingFactor: [][]float64{
{0x3ffffe80001},
{0x3ffffd20001},
{0x3ffffca0001},
},
},
EvalModParameters: advanced.EvalModLiteral{
Q: 0x10000000006e0001,
LevelStart: 19,
SineType: advanced.Cos1,
MessageRatio: 4.0,
K: 16,
SineDeg: 30,
DoubleAngle: 3,
ArcSineDeg: 7,
ScalingFactor: 1 << 60,
},
CoeffsToSlotsParameters: advanced.EncodingMatrixLiteral{
LinearTransformType: advanced.CoeffsToSlots,
RepackImag2Real: true,
LevelStart: 23,
BSGSRatio: 2.0,
BitReversed: false,
ScalingFactor: [][]float64{
{0x400000000360001},
{0x3ffffffffbe0001},
{0x400000000660001},
{0x4000000008a0001},
},
},
},
}
// N16QP1553H192H32 is a default bootstrapping parameters for a main secret with H=192 and an ephemeral secret with H=32.
// Residual Q : 505 bits.
// Precision : 19.1 bits for 2^{15} slots.
// Failure : 2^{-138.7} for 2^{15} slots.
N16QP1553H192H32 = defaultParametersLiteral{
ckks.ParametersLiteral{
LogN: 16,
Sigma: rlwe.DefaultSigma,
H: 192,
Q: []uint64{
0x80000000080001, // 55 Q0
0xffffffffffc0001, // 60
0x10000000006e0001, // 60
0xfffffffff840001, // 60
0x1000000000860001, // 60
0xfffffffff6a0001, // 60
0x1000000000980001, // 60
0xfffffffff5a0001, // 60
0x1000000000b00001, // 60 StC (30)
0x1000000000ce0001, // 60 StC (30+30)
0x80000000440001, // 55 Sine (double angle)
0x7fffffffba0001, // 55 Sine (double angle)
0x80000000500001, // 55 Sine
0x7fffffffaa0001, // 55 Sine
0x800000005e0001, // 55 Sine
0x7fffffff7e0001, // 55 Sine
0x7fffffff380001, // 55 Sine
0x80000000ca0001, // 55 Sine
0x200000000e0001, // 53 CtS
0x20000000140001, // 53 CtS
0x20000000280001, // 53 CtS
0x1fffffffd80001, // 53 CtS
},
P: []uint64{
0x1fffffffffe00001, // Pi 61
0x1fffffffffc80001, // Pi 61
0x1fffffffffb40001, // Pi 61
0x1fffffffff500001, // Pi 61
0x1fffffffff420001, // Pi 61
},
LogSlots: 15,
DefaultScale: 1 << 30,
},
Parameters{
EphemeralSecretWeight: 32,
SlotsToCoeffsParameters: advanced.EncodingMatrixLiteral{
LinearTransformType: advanced.SlotsToCoeffs,
RepackImag2Real: true,
LevelStart: 9,
BSGSRatio: 2.0,
BitReversed: false,
ScalingFactor: [][]float64{
{1073741824.0},
{1073741824.0062866, 1073741824.0062866},
},
},
EvalModParameters: advanced.EvalModLiteral{
Q: 0x80000000080001,
LevelStart: 17,
SineType: advanced.Cos1,
MessageRatio: 256.0,
K: 16,
SineDeg: 30,
DoubleAngle: 3,
ArcSineDeg: 0,
ScalingFactor: 1 << 55,
},
CoeffsToSlotsParameters: advanced.EncodingMatrixLiteral{
LinearTransformType: advanced.CoeffsToSlots,
RepackImag2Real: true,
LevelStart: 21,
BSGSRatio: 2.0,
BitReversed: false,
ScalingFactor: [][]float64{
{0x200000000e0001},
{0x20000000140001},
{0x20000000280001},
{0x1fffffffd80001},
},
},
},
}
// N15QP768H192H32 is a default bootstrapping parameters for a main secret with H=192 and an ephemeral secret with H=32.
// Residual Q : 110 bits.
// Precision : 15.4 bits for 2^{14} slots.
// Failure : 2^{-139.7} for 2^{14} slots.
N15QP768H192H32 = defaultParametersLiteral{
ckks.ParametersLiteral{
LogN: 15,
Sigma: rlwe.DefaultSigma,
H: 192,
Q: []uint64{
0x1fff90001, // 32 Q0
0x4000000420001, // 50
0x1fc0001, // 25
0xffffffffffc0001, // 60 StC (30+30)
0x4000000120001, // 50 Sine
0x40000001b0001, // 50 Sine
0x3ffffffdf0001, // 50 Sine
0x4000000270001, // 50 Sine
0x3ffffffd20001, // 50 Sine
0x3ffffffcd0001, // 50 Sine
0x4000000350001, // 50 Sine
0x3ffffffc70001, // 50 Sine
0x1fffffff50001, // 49 CtS
0x1ffffffea0001, // 49 CtS
},
P: []uint64{
0x7fffffffe0001, // 51
0x8000000110001, // 51
},
LogSlots: 14,
DefaultScale: 1 << 25,
},
Parameters{
EphemeralSecretWeight: 32,
SlotsToCoeffsParameters: advanced.EncodingMatrixLiteral{
LinearTransformType: advanced.SlotsToCoeffs,
RepackImag2Real: true,
LevelStart: 3,
BSGSRatio: 2.0,
BitReversed: false,
ScalingFactor: [][]float64{
{1073741823.9998779, 1073741823.9998779},
},
},
EvalModParameters: advanced.EvalModLiteral{
Q: 0x1fff90001,
LevelStart: 11,
SineType: advanced.Cos1,
MessageRatio: 256.0,
K: 16,
SineDeg: 30,
DoubleAngle: 3,
ArcSineDeg: 0,
ScalingFactor: 1 << 50,
},
CoeffsToSlotsParameters: advanced.EncodingMatrixLiteral{
LinearTransformType: advanced.CoeffsToSlots,
RepackImag2Real: true,
LevelStart: 13,
BSGSRatio: 2.0,
BitReversed: false,
ScalingFactor: [][]float64{
{0x1fffffff50001},
{0x1ffffffea0001},
},
},
},
}
// N16QP1767H32768H32 is a default bootstrapping parameters for a main secret with H=32768 and an ephemeral secret with H=32.
// Residual Q : 580 bits.
// Precision : 23.0 bits for 2^{15} slots.
// Failure : 2^{-138.7} for 2^{15} slots.
N16QP1767H32768H32 = defaultParametersLiteral{
ckks.ParametersLiteral{
LogN: 16,
Sigma: rlwe.DefaultSigma,
H: 32768,
Q: []uint64{
0x10000000006e0001, // 60 Q0
0x10000140001, // 40
0xffffe80001, // 40
0xffffc40001, // 40
0x100003e0001, // 40
0xffffb20001, // 40
0x10000500001, // 40
0xffff940001, // 40
0xffff8a0001, // 40
0xffff820001, // 40
0xffff780001, // 40
0x10000960001, // 40
0x10000a40001, // 40
0xffff580001, // 40
0x7fffe60001, // 39 StC
0x7fffe40001, // 39 StC
0x7fffe00001, // 39 StC
0xfffffffff840001, // 60 Sine (double angle)
0x1000000000860001, // 60 Sine (double angle)
0xfffffffff6a0001, // 60 Sine
0x1000000000980001, // 60 Sine
0xfffffffff5a0001, // 60 Sine
0x1000000000b00001, // 60 Sine
0x1000000000ce0001, // 60 Sine
0xfffffffff2a0001, // 60 Sine
0x100000000060001, // 56 CtS
0xfffffffff00001, // 56 CtS
0xffffffffd80001, // 56 CtS
0x1000000002a0001, // 56 CtS
},
P: []uint64{
0x1fffffffffe00001, // Pi 61
0x1fffffffffc80001, // Pi 61
0x1fffffffffb40001, // Pi 61
0x1fffffffff500001, // Pi 61
0x1fffffffff420001, // Pi 61
0x1fffffffff380001, // Pi 61
},
LogSlots: 15,
DefaultScale: 1 << 40,
},
Parameters{
EphemeralSecretWeight: 32,
SlotsToCoeffsParameters: advanced.EncodingMatrixLiteral{
LinearTransformType: advanced.SlotsToCoeffs,
RepackImag2Real: true,
LevelStart: 16,
BSGSRatio: 2.0,
BitReversed: false,
ScalingFactor: [][]float64{
{0x7fffe60001},
{0x7fffe40001},
{0x7fffe00001},
},
},
EvalModParameters: advanced.EvalModLiteral{
Q: 0x10000000006e0001,
LevelStart: 24,
SineType: advanced.Cos1,
MessageRatio: 256.0,
K: 16,
SineDeg: 30,
DoubleAngle: 3,
ArcSineDeg: 0,
ScalingFactor: 1 << 60,
},
CoeffsToSlotsParameters: advanced.EncodingMatrixLiteral{
LinearTransformType: advanced.CoeffsToSlots,
RepackImag2Real: true,
LevelStart: 28,
BSGSRatio: 2.0,
BitReversed: false,
ScalingFactor: [][]float64{
{0x100000000060001},
{0xfffffffff00001},
{0xffffffffd80001},
{0x1000000002a0001},
},
},
},
}
// N16QP1788H32768H32 is a default bootstrapping parameters for a main secret with H=32768 and an ephemeral secret with H=32.
// Residual Q : 465 bits.
// Precision : 29.0 bits for 2^{15} slots.
// Failure : 2^{-138.7} for 2^{15} slots.
N16QP1788H32768H32 = defaultParametersLiteral{
ckks.ParametersLiteral{
LogN: 16,
Sigma: rlwe.DefaultSigma,
H: 32768,
Q: []uint64{
0x10000000006e0001, // 60 Q0
0x2000000a0001, // 45
0x2000000e0001, // 45
0x1fffffc20001, // 45
0x200000440001, // 45
0x200000500001, // 45
0x200000620001, // 45
0x1fffff980001, // 45
0x2000006a0001, // 45
0x1fffff7e0001, // 45
0x3ffffe80001, // 42 StC
0x3ffffd20001, // 42 StC
0x3ffffca0001, // 42 StC
0xffffffffffc0001, // 60 ArcSine
0xfffffffff240001, // 60 ArcSine
0x1000000000f00001, // 60 ArcSine
0xfffffffff840001, // 60 Double angle
0x1000000000860001, // 60 Double angle
0xfffffffff6a0001, // 60 Sine
0x1000000000980001, // 60 Sine
0xfffffffff5a0001, // 60 Sine
0x1000000000b00001, // 60 Sine
0x1000000000ce0001, // 60 Sine
0xfffffffff2a0001, // 60 Sine
0x400000000360001, // 58 CtS
0x3ffffffffbe0001, // 58 CtS
0x400000000660001, // 58 CtS
0x4000000008a0001, // 58 CtS
},
P: []uint64{
0x1fffffffffe00001, // Pi 61
0x1fffffffffc80001, // Pi 61
0x1fffffffffb40001, // Pi 61
0x1fffffffff500001, // Pi 61
0x1fffffffff420001, // Pi 61
},
LogSlots: 15,
DefaultScale: 1 << 45,
},
Parameters{
EphemeralSecretWeight: 32,
SlotsToCoeffsParameters: advanced.EncodingMatrixLiteral{
LinearTransformType: advanced.SlotsToCoeffs,
RepackImag2Real: true,
LevelStart: 12,
BSGSRatio: 2.0,
BitReversed: false,
ScalingFactor: [][]float64{
{0x3ffffe80001},
{0x3ffffd20001},
{0x3ffffca0001},
},
},
EvalModParameters: advanced.EvalModLiteral{
Q: 0x10000000006e0001,
LevelStart: 23,
SineType: advanced.Cos1,
MessageRatio: 4.0,
K: 16,
SineDeg: 30,
DoubleAngle: 3,
ArcSineDeg: 7,
ScalingFactor: 1 << 60,
},
CoeffsToSlotsParameters: advanced.EncodingMatrixLiteral{
LinearTransformType: advanced.CoeffsToSlots,
RepackImag2Real: true,
LevelStart: 27,
BSGSRatio: 2.0,
BitReversed: false,
ScalingFactor: [][]float64{
{0x400000000360001},
{0x3ffffffffbe0001},
{0x400000000660001},
{0x4000000008a0001},
},
},
},
}
// N16QP1793H32768H32 is a default bootstrapping parameters for a main secret with H=32768 and an ephemeral secret with H=32.
// Residual Q : 745 bits.
// Precision : 17.8 bits for 2^{15} slots.
// Failure : 2^{-138.7} for 2^{15} slots.
N16QP1793H32768H32 = defaultParametersLiteral{
ckks.ParametersLiteral{
LogN: 16,
Sigma: rlwe.DefaultSigma,
H: 32768,
Q: []uint64{
0x80000000080001, // 55 Q0
0xffffffffffc0001, // 60
0x10000000006e0001, // 60
0xfffffffff840001, // 60
0x1000000000860001, // 60
0xfffffffff6a0001, // 60
0x1000000000980001, // 60
0xfffffffff5a0001, // 60
0xfffffffff2a0001, // 60
0xfffffffff240001, // 60
0x1000000000f00001, // 60
0xffffffffefe0001, // 60
0x1000000000b00001, // 60 StC (30)
0x1000000000ce0001, // 60 StC (30+30)
0x80000000440001, // 55 Sine (double angle)
0x7fffffffba0001, // 55 Sine (double angle)
0x80000000500001, // 55 Sine
0x7fffffffaa0001, // 55 Sine
0x800000005e0001, // 55 Sine
0x7fffffff7e0001, // 55 Sine
0x7fffffff380001, // 55 Sine
0x80000000ca0001, // 55 Sine
0x200000000e0001, // 53 CtS
0x20000000140001, // 53 CtS
0x20000000280001, // 53 CtS
0x1fffffffd80001, // 53 CtS
},
P: []uint64{
0x1fffffffffe00001, // Pi 61
0x1fffffffffc80001, // Pi 61
0x1fffffffffb40001, // Pi 61
0x1fffffffff500001, // Pi 61
0x1fffffffff420001, // Pi 61
},
LogSlots: 15,
DefaultScale: 1 << 30,
},
Parameters{
EphemeralSecretWeight: 32,
SlotsToCoeffsParameters: advanced.EncodingMatrixLiteral{
LinearTransformType: advanced.SlotsToCoeffs,
RepackImag2Real: true,
LevelStart: 13,
BSGSRatio: 2.0,
BitReversed: false,
ScalingFactor: [][]float64{
{1073741824.0},
{1073741824.0062866, 1073741824.0062866},
},
},
EvalModParameters: advanced.EvalModLiteral{
Q: 0x80000000080001,
LevelStart: 21,
SineType: advanced.Cos1,
MessageRatio: 256.0,
K: 16,
SineDeg: 30,
DoubleAngle: 3,
ArcSineDeg: 0,
ScalingFactor: 1 << 55,
},
CoeffsToSlotsParameters: advanced.EncodingMatrixLiteral{
LinearTransformType: advanced.CoeffsToSlots,
RepackImag2Real: true,
LevelStart: 25,
BSGSRatio: 2.0,
BitReversed: false,
ScalingFactor: [][]float64{
{0x200000000e0001},
{0x20000000140001},
{0x20000000280001},
{0x1fffffffd80001},
},
},
},
}
// N15QP880H16384H32 is a default bootstrapping parameters for a main secret with H=16384 and an ephemeral secret with H=32.
// Residual Q : 166 bits.
// Precision : 17.3 bits for 2^{14} slots.
// Failure : 2^{-139.7} for 2^{14} slots.
N15QP880H16384H32 = defaultParametersLiteral{
ckks.ParametersLiteral{
LogN: 15,
Sigma: rlwe.DefaultSigma,
H: 16384,
Q: []uint64{
0x10000140001, // 40 Q0
0x7ffe0001, // 31
0x7ff80001, // 31
0x80140001, // 31
0x7fea0001, // 31
0x1000000000ce0001, // 60 StC (30+30)
0x80000000080001, // 55 Sine (double angle)
0x80000000440001, // 55 Sine (double angle)
0x7fffffffba0001, // 55 Sine
0x80000000500001, // 55 Sine
0x7fffffffaa0001, // 55 Sine
0x800000005e0001, // 55 Sine
0x7fffffff7e0001, // 55 Sine
0x7fffffff380001, // 55 Sine
0x10000000060001, // 52 CtS
0xffffffff00001, // 52 CtS
},
P: []uint64{
0x100000000060001, // 56
0x1000000002a0001, // 56
},
LogSlots: 14,
DefaultScale: 1 << 31,
},
Parameters{
EphemeralSecretWeight: 32,
SlotsToCoeffsParameters: advanced.EncodingMatrixLiteral{
LinearTransformType: advanced.SlotsToCoeffs,
RepackImag2Real: true,
LevelStart: 5,
BSGSRatio: 2.0,
BitReversed: false,
ScalingFactor: [][]float64{
{1073741824.0062866, 1073741824.0062866},
},
},
EvalModParameters: advanced.EvalModLiteral{
Q: 0x10000140001,
LevelStart: 13,
SineType: advanced.Cos1,
MessageRatio: 256.0,
K: 16,
SineDeg: 30,
DoubleAngle: 3,
ArcSineDeg: 0,
ScalingFactor: 1 << 55,
},
CoeffsToSlotsParameters: advanced.EncodingMatrixLiteral{
LinearTransformType: advanced.CoeffsToSlots,
RepackImag2Real: true,
LevelStart: 15,
BSGSRatio: 2.0,
BitReversed: false,
ScalingFactor: [][]float64{
{0x10000000060001},
{0xffffffff00001},
},
},
},
}
)