PARITY CHALLENGE

Setting the Parameters

The config.json file provides a JSON definition of the scheme and bootstrapping parameters. We provide a list of the field that can be specified

Scheme Parameters

Mandatory

• LogN: base two logarithm of the ring degree, example: 16.
• LogQ: base two logarithm list of prime factors the ciphertext modulus, example: [60, 50, 50, 50].
• LogP: base two logarithm list of prime factors the auxiliary prime modulus, example: [61, 61].
• LogDefaultScale: base two logarithm of the default scaling factor: example 50.

Optional

• Xe: distribution of the error, for example {"Type": "DiscreteGaussian", "Sigma": 6.6, "Bound": 39.6}.
• Xs: distribution of the secret, for example {"Type": "Ternary", "H": 192} (Gaussian secret are also supported).
• RingType:
  • Standard for R[X]/(X^{N}+1): provides N/2 complex slots.
  • ConjugateInvariant for R[X+X^{-1}]/(X^{2N}+1): provides N real slots.

For additional information and other optional parameters see lattigo/schemes/ckks/params.go

Example

"Scheme":{
	"LogN":16,
	"LogQ": [60, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45],
	"LogP": [56, 55, 55, 55],
	"Xe": {"Type": "DiscreteGaussian", "Sigma": 3.2, "Bound": 19.0},
	"Xs": {"Type": "Ternary", "H": 192},
	"RingType": "ConjugateInvariant",
	"LogDefaultScale":45
}

Scheme Evaluation Keys

The user can ask the relinearization key and which Galois key to generate. The user can either specify the Galois keys by their acting rotation on an encoded plaintext or directly with the Galois element. Galois elements can be obtained from a rotation by calling .GaloisElement(k int) on the scheme parameters.

Example

"EvaluationKeys":{
	"Relinearization:": true,
	"Rotations": [1],
	"GaloisElements":[65535]
}

Bootstrapping Parameters

To enable bootstrapping, set Bootstrapping.Enable: true.

By default the bootstrapping works without having to set any optional field and provide the following performance:

• Depth 4 for CoeffsToSlots
• Depth 8 for EvalMod
• Depth 3 for SlotsToCoeffs for a total depth of 15 and a bit consumption of 821 A precision, for complex values with both real and imaginary parts uniformly distributed in -1, 1 of
• 27.25 bits for H=192
• 23.8 bits for H=32768, And a failure probability of 2^{-138.7} for 2^{15} slots.

There are up to 16 optional fields in the bootstrapping.ParametersLiteral, enabling fine customization of the bootstrapping. For additional information about these optional fields, see lattigo/he/hefloat/bootstrapping/paramters_literal.go.

Since the bootstrapping parameters are built as an extension of the scheme parameters, it is up to the user to ensure that the produced bootstrapping parameters are secure. See comments in bootstrapping.NewParametersFromLiteral, bootstrapping.EvaluationKeys.GenEvaluationKeys) and the examples in examples/single_party/applications/reals_bootstrapping.

Example

"Bootstrapping":{
	"Enable": true,
	"LogN": 16,
	"LogP": [61, 61, 61, 61],
	"Xs": {"Type": "Ternary", "H": 192},
	"Xe": {"Type": "DiscreteGaussian", "Sigma": 3.2, "Bound": 19.0},
	"LogSlots": 15,
	"CoeffsToSlotsFactorizationDepthAndLogScales": [[56], [56], [56], [56]],
	"SlotsToCoeffsFactorizationDepthAndLogScales": [[39], [39], [39]],
	"EvalModLogScale": 60,
	"EphemeralSecretWeight": 32,
	"IterationsParameters": {
		"BootstrappingPrecision": [27.5, 10.0],
		"ReservedPrimeBitSize": 20
	},
	"Mod1Type": 0,
	"LogMessageRatio": 8,
	"K": 16,
	"Mod1Degree": 30,
	"DoubleAngle": 3,
	"Mod1InvDegree": 0
}

Imputing Your Solution

All you have to do is put your solution in the function SolveTestcase, which is located in the file internal/solution/solution.go.

Testing Your Solution Locally

• $ make test-all to do an end-to-end test of your solution followed by a clean of the temporary files
• $ make setup to generate the keys and input ciphertext
• $ make solution to run the solution and verify it (assumes that the keys and input ciphertext have been generated)
• $ make clean to clean the temporary files

Packaging & Submitting Your Solution

Simply create a .zip containing the folder app and submit it on the website.