feat: add Poseidon implementation over bn254

frontend/api.go

@@ -109,6 +109,8 @@ type API interface {
 	// it is more efficient to use the bounded methdods in package
 	// [github.com/consensys/gnark/std/math/bits].
 	Cmp(i1, i2 Variable) Variable
+	// Optimized version of Cmp for the case where i1 and i2 are variables less than 2^maxBits
+	CmpNOp(i1, i2 Variable, maxBits int, omitRangeCheck ...bool) Variable
 
 	// ---------------------------------------------------------------------------------------------
 	// Assertions
@@ -130,6 +132,8 @@ type API interface {
 	// it is more efficient to use the bounded methdods in package
 	// [github.com/consensys/gnark/std/math/bits].
 	AssertIsLessOrEqual(v Variable, bound Variable)
+	// Optimized version of AssertIsLessOrEqual for the case where v and bound are variables less than 2^maxBits
+	AssertIsLessOrEqualNOp(v, bound Variable, maxBits int, omitRangeCheck ...bool)
 
 	// Println behaves like fmt.Println but accepts cd.Variable as parameter
 	// whose value will be resolved at runtime when computed by the solver

frontend/cs/r1cs/api.go

@@ -19,6 +19,7 @@ package r1cs
 import (
 	"errors"
 	"fmt"
+	"math/big"
 	"path/filepath"
 	"reflect"
 	"runtime"
@@ -599,6 +600,33 @@ func (builder *builder) Cmp(i1, i2 frontend.Variable) frontend.Variable {
 	return res
 }
 
+func (builder *builder) CmpNOp(i1, i2 frontend.Variable, maxBits int, omitRangeCheck ...bool) frontend.Variable {
+
+	nbBits := builder.cs.FieldBitLen()
+	if maxBits > nbBits {
+		panic("CmpNOp: maxBits > nbBits")
+	}
+	omitRangeCheckFlag := false
+	if len(omitRangeCheck) > 0 {
+		omitRangeCheckFlag = omitRangeCheck[0]
+	}
+	if !omitRangeCheckFlag {
+		bits.ToBinary(builder, i1, bits.WithNbDigits(maxBits))
+		bits.ToBinary(builder, i2, bits.WithNbDigits(maxBits))
+	}
+
+	c := new(big.Int).Exp(big.NewInt(2), big.NewInt(int64(maxBits)), nil)
+	isEqual := builder.IsZero(builder.Sub(i1, i2))
+	// res = i1 + 2^maxBits - i2
+	// if i1 < i2, res <= 2^maxBits - 1, then the max bit of res is 0
+	// if i1 > i2, 2^maxBits < res < 2^(maxBits + 1), then the max bit of res is 1
+	res := builder.Add(i1, c)
+	res = builder.Sub(res, i2)
+	resBits := bits.ToBinary(builder, res, bits.WithNbDigits(maxBits+1))
+	ret := builder.Select(isEqual, 0, builder.Select(resBits[maxBits], 1, -1))
+	return ret
+}
+
 // Println enables circuit debugging and behaves almost like fmt.Println()
 //
 // the print will be done once the R1CS.Solve() method is executed

frontend/cs/r1cs/api_assertions.go

@@ -247,3 +247,93 @@ func (builder *builder) MustBeLessOrEqCst(aBits []frontend.Variable, bound *big.
 		builder.cs.AttachDebugInfo(debug, added)
 	}
 }
+
+func (builder *builder) AssertIsLessOrEqualNOp(_v frontend.Variable, bound frontend.Variable, maxBits int, omitRangeCheck ...bool) {
+	cv, vConst := builder.constantValue(_v)
+	cb, bConst := builder.constantValue(bound)
+
+	// both inputs are constants
+	if vConst && bConst {
+		bv, bb := builder.cs.ToBigInt(cv), builder.cs.ToBigInt(cb)
+		if bv.Cmp(bb) == 1 {
+			panic(fmt.Sprintf("AssertIsLessOrEqual: %s > %s", bv.String(), bb.String()))
+		}
+	}
+	omitRangeCheckFlag := false
+	if len(omitRangeCheck) > 0 {
+		omitRangeCheckFlag = omitRangeCheck[0]
+	}
+
+	// bound is constant
+	if bConst {
+		builder.MustBeLessOrEqCstNOp(_v, builder.cs.ToBigInt(cb), _v, maxBits, omitRangeCheckFlag)
+		return
+	}
+	builder.mustBeLessOrEqVarNOp(_v, bound, maxBits, omitRangeCheckFlag)
+}
+
+func (builder *builder) mustBeLessOrEqVarNOp(v, bound frontend.Variable, maxBits int, omitRangeCheck bool) {
+	c := new(big.Int).Exp(big.NewInt(2), big.NewInt(int64(maxBits)), nil)
+	if !omitRangeCheck {
+		// make sure v and bound are less than 2^maxBits
+		bits.ToBinary(builder, v, bits.WithNbDigits(maxBits))
+		bits.ToBinary(builder, bound, bits.WithNbDigits(maxBits))
+	}
+
+	// res := v + 2^maxBits - (bound + 1)
+	// if v <= bound, res <= 2^maxBits - 1, then the max bit of res is 0
+	// if v > bound, 2^maxBits <= res < 2^(maxBits + 1), then the max bit of res is 1
+	res := builder.Add(v, c)
+	res = builder.Sub(res, bound)
+	res = builder.Sub(res, 1)
+	resBits := bits.ToBinary(builder, res, bits.WithNbDigits(maxBits+1))
+	builder.AssertIsEqual(resBits[maxBits], 0)
+}
+
+func (builder *builder) MustBeLessOrEqCstNOp(a frontend.Variable, bound *big.Int, aForDebug frontend.Variable, maxBits int, omitRangeCheck bool) {
+	nbBits := builder.cs.FieldBitLen()
+	if maxBits > nbBits {
+		panic("maxBits is larger than field bit length")
+	}
+
+	aBits := bits.ToBinary(builder, a, bits.WithNbDigits(maxBits), bits.WithUnconstrainedOutputs())
+	// ensure the bound is positive, it's bit-len doesn't matter
+	if bound.Sign() == -1 {
+		panic("AssertIsLessOrEqual: bound must be positive")
+	}
+	if bound.BitLen() > maxBits {
+		panic("AssertIsLessOrEqual: bound is too large, constraint will always be satisfied, please check the bound is correct")
+	}
+
+	// t trailing bits in the bound
+	t := 0
+	for i := 0; i < maxBits; i++ {
+		if bound.Bit(i) == 0 {
+			break
+		}
+		t++
+	}
+
+	p := make([]frontend.Variable, maxBits+1)
+	// p[i] == 1 → a[j] == c[j] for all j ⩾ i
+	p[maxBits] = builder.cstOne()
+
+	for i := maxBits - 1; i >= t; i-- {
+		if bound.Bit(i) == 0 {
+			p[i] = p[i+1]
+		} else {
+			p[i] = builder.Mul(p[i+1], aBits[i])
+		}
+	}
+
+	for i := maxBits - 1; i >= 0; i-- {
+		if bound.Bit(i) == 0 {
+			// (1 - p(i+1) - ai) * ai == 0
+			l := builder.Sub(1, p[i+1])
+			l = builder.Sub(l, aBits[i])
+			builder.cs.AddR1C(builder.newR1C(l, aBits[i], builder.cstZero()), builder.genericGate)
+		} else {
+			builder.AssertIsBoolean(aBits[i])
+		}
+	}
+}

frontend/cs/scs/api.go

@@ -736,3 +736,7 @@ func (*builder) FrontendType() frontendtype.Type {
 func (builder *builder) SetGkrInfo(info constraint.GkrInfo) error {
 	return builder.cs.AddGkr(info)
 }
+
+func (builder *builder) CmpNOp(i1, i2 frontend.Variable, maxBits int, omitRangeCheck ...bool) frontend.Variable {
+	panic("not implemented")
+}

frontend/cs/scs/api_assertions.go

@@ -296,3 +296,7 @@ func (builder *builder) MustBeLessOrEqCst(aBits []frontend.Variable, bound *big.
 	}
 
 }
+
+func (builder *builder) AssertIsLessOrEqualNOp(_v frontend.Variable, bound frontend.Variable, maxBits int, omitRangeCheck ...bool) {
+	panic("not implemented")
+}

std/hash/poseidon/constants/constants.go

@@ -0,0 +1,45 @@
+package constants
+
+import (
+	"math/big"
+)
+
+// Number of full rounds
+const RF = 8
+
+// Generated by https://extgit.iaik.tugraz.at/krypto/hadeshash/-/blob/master/code/calc_round_numbers.py
+// And rounded up to nearest integer that divides by t in [2, 13]
+var RP = []int{56, 57, 56, 60, 60, 63, 64, 63, 60, 66, 60, 65}
+
+// Round constants
+var RC [][]*big.Int
+
+// Maximum distance separable matrix
+var MDS [][][]*big.Int
+
+func init() {
+	// Parameters are generated by a reference script https://extgit.iaik.tugraz.at/krypto/hadeshash/-/blob/master/code/generate_parameters_grain.sage
+	// Used like so: sage generate_parameters_grain.sage 1 0 254 2 8 57 0x30644e72e131a029b85045b68181585d2833e84879b9709143e1f593f0000001
+	constantsSTR := [][]string{constantsT2, constantsT3, constantsT4, constantsT5, constantsT6, constantsT7, constantsT8, constantsT9, constantsT10, constantsT11, constantsT12, constantsT13}
+	mdsSTR := [][][]string{mdsT2, mdsT3, mdsT4, mdsT5, mdsT6, mdsT7, mdsT8, mdsT9, mdsT10, mdsT11, mdsT12, mdsT13}
+	size := len(RP)
+	RC = make([][]*big.Int, size)
+	MDS = make([][][]*big.Int, size)
+
+	for i := 0; i < size; i++ {
+		// initialize round constants field elements
+		RC[i] = make([]*big.Int, len(constantsSTR[i]))
+		for j := 0; j < len(RC[i]); j++ {
+			RC[i][j], _ = new(big.Int).SetString(constantsSTR[i][j], 16)
+		}
+		// initialize MDS matrix field elements
+		MDS[i] = make([][]*big.Int, len(mdsSTR[i]))
+		for j := 0; j < len(MDS[i]); j++ {
+			MDS[i][j] = make([]*big.Int, len(mdsSTR[i][j]))
+			for k := 0; k < len(MDS[i][j]); k++ {
+				MDS[i][j][k], _ = new(big.Int).SetString(mdsSTR[i][j][k], 16)
+			}
+		}
+
+	}
+}

std/hash/poseidon/constants/t2.go

@@ -0,0 +1,76 @@
+package constants
+
+// Parameters are generated by a reference script https://extgit.iaik.tugraz.at/krypto/hadeshash/-/blob/master/code/generate_parameters_grain.sage
+// Used like so: sage generate_parameters_grain.sage 1 0 254 2 8 56 0x30644e72e131a029b85045b68181585d2833e84879b9709143e1f593f0000001
+
+var constantsT2 = []string{
+	"09c46e9ec68e9bd4fe1faaba294cba38a71aa177534cdd1b6c7dc0dbd0abd7a7", "0c0356530896eec42a97ed937f3135cfc5142b3ae405b8343c1d83ffa604cb81",
+	"1e28a1d935698ad1142e51182bb54cf4a00ea5aabd6268bd317ea977cc154a30", "27af2d831a9d2748080965db30e298e40e5757c3e008db964cf9e2b12b91251f",
+	"1e6f11ce60fc8f513a6a3cfe16ae175a41291462f214cd0879aaf43545b74e03", "2a67384d3bbd5e438541819cb681f0be04462ed14c3613d8f719206268d142d3",
+	"0b66fdf356093a611609f8e12fbfecf0b985e381f025188936408f5d5c9f45d0", "012ee3ec1e78d470830c61093c2ade370b26c83cc5cebeeddaa6852dbdb09e21",
+	"0252ba5f6760bfbdfd88f67f8175e3fd6cd1c431b099b6bb2d108e7b445bb1b9", "179474cceca5ff676c6bec3cef54296354391a8935ff71d6ef5aeaad7ca932f1",
+	"2c24261379a51bfa9228ff4a503fd4ed9c1f974a264969b37e1a2589bbed2b91", "1cc1d7b62692e63eac2f288bd0695b43c2f63f5001fc0fc553e66c0551801b05",
+	"255059301aada98bb2ed55f852979e9600784dbf17fbacd05d9eff5fd9c91b56", "28437be3ac1cb2e479e1f5c0eccd32b3aea24234970a8193b11c29ce7e59efd9",
+	"28216a442f2e1f711ca4fa6b53766eb118548da8fb4f78d4338762c37f5f2043", "2c1f47cd17fa5adf1f39f4e7056dd03feee1efce03094581131f2377323482c9",
+	"07abad02b7a5ebc48632bcc9356ceb7dd9dafca276638a63646b8566a621afc9", "0230264601ffdf29275b33ffaab51dfe9429f90880a69cd137da0c4d15f96c3c",
+	"1bc973054e51d905a0f168656497ca40a864414557ee289e717e5d66899aa0a9", "2e1c22f964435008206c3157e86341edd249aff5c2d8421f2a6b22288f0a67fc",
+	"1224f38df67c5378121c1d5f461bbc509e8ea1598e46c9f7a70452bc2bba86b8", "02e4e69d8ba59e519280b4bd9ed0068fd7bfe8cd9dfeda1969d2989186cde20e",
+	"1f1eccc34aaba0137f5df81fc04ff3ee4f19ee364e653f076d47e9735d98018e", "1672ad3d709a353974266c3039a9a7311424448032cd1819eacb8a4d4284f582",
+	"283e3fdc2c6e420c56f44af5192b4ae9cda6961f284d24991d2ed602df8c8fc7", "1c2a3d120c550ecfd0db0957170fa013683751f8fdff59d6614fbd69ff394bcc",
+	"216f84877aac6172f7897a7323456efe143a9a43773ea6f296cb6b8177653fbd", "2c0d272becf2a75764ba7e8e3e28d12bceaa47ea61ca59a411a1f51552f94788",
+	"16e34299865c0e28484ee7a74c454e9f170a5480abe0508fcb4a6c3d89546f43", "175ceba599e96f5b375a232a6fb9cc71772047765802290f48cd939755488fc5",
+	"0c7594440dc48c16fead9e1758b028066aa410bfbc354f54d8c5ffbb44a1ee32", "1a3c29bc39f21bb5c466db7d7eb6fd8f760e20013ccf912c92479882d919fd8d",
+	"0ccfdd906f3426e5c0986ea049b253400855d349074f5a6695c8eeabcd22e68f", "14f6bc81d9f186f62bdb475ce6c9411866a7a8a3fd065b3ce0e699b67dd9e796",
+	"0962b82789fb3d129702ca70b2f6c5aacc099810c9c495c888edeb7386b97052", "1a880af7074d18b3bf20c79de25127bc13284ab01ef02575afef0c8f6a31a86d",
+	"10cba18419a6a332cd5e77f0211c154b20af2924fc20ff3f4c3012bb7ae9311b", "057e62a9a8f89b3ebdc76ba63a9eaca8fa27b7319cae3406756a2849f302f10d",
+	"287c971de91dc0abd44adf5384b4988cb961303bbf65cff5afa0413b44280cee", "21df3388af1687bbb3bca9da0cca908f1e562bc46d4aba4e6f7f7960e306891d",
+	"1be5c887d25bce703e25cc974d0934cd789df8f70b498fd83eff8b560e1682b3", "268da36f76e568fb68117175cea2cd0dd2cb5d42fda5acea48d59c2706a0d5c1",
+	"0e17ab091f6eae50c609beaf5510ececc5d8bb74135ebd05bd06460cc26a5ed6", "04d727e728ffa0a67aee535ab074a43091ef62d8cf83d270040f5caa1f62af40",
+	"0ddbd7bf9c29341581b549762bc022ed33702ac10f1bfd862b15417d7e39ca6e", "2790eb3351621752768162e82989c6c234f5b0d1d3af9b588a29c49c8789654b",
+	"1e457c601a63b73e4471950193d8a570395f3d9ab8b2fd0984b764206142f9e9", "21ae64301dca9625638d6ab2bbe7135ffa90ecd0c43ff91fc4c686fc46e091b0",
+	"0379f63c8ce3468d4da293166f494928854be9e3432e09555858534eed8d350b", "002d56420359d0266a744a080809e054ca0e4921a46686ac8c9f58a324c35049",
+	"123158e5965b5d9b1d68b3cd32e10bbeda8d62459e21f4090fc2c5af963515a6", "0be29fc40847a941661d14bbf6cbe0420fbb2b6f52836d4e60c80eb49cad9ec1",
+	"1ac96991dec2bb0557716142015a453c36db9d859cad5f9a233802f24fdf4c1a", "1596443f763dbcc25f4964fc61d23b3e5e12c9fa97f18a9251ca3355bcb0627e",
+	"12e0bcd3654bdfa76b2861d4ec3aeae0f1857d9f17e715aed6d049eae3ba3212", "0fc92b4f1bbea82b9ea73d4af9af2a50ceabac7f37154b1904e6c76c7cf964ba",
+	"1f9c0b1610446442d6f2e592a8013f40b14f7c7722236f4f9c7e965233872762", "0ebd74244ae72675f8cde06157a782f4050d914da38b4c058d159f643dbbf4d3",
+	"2cb7f0ed39e16e9f69a9fafd4ab951c03b0671e97346ee397a839839dccfc6d1", "1a9d6e2ecff022cc5605443ee41bab20ce761d0514ce526690c72bca7352d9bf",
+	"2a115439607f335a5ea83c3bc44a9331d0c13326a9a7ba3087da182d648ec72f", "23f9b6529b5d040d15b8fa7aee3e3410e738b56305cd44f29535c115c5a4c060",
+	"05872c16db0f72a2249ac6ba484bb9c3a3ce97c16d58b68b260eb939f0e6e8a7", "1300bdee08bb7824ca20fb80118075f40219b6151d55b5c52b624a7cdeddf6a7",
+	"19b9b63d2f108e17e63817863a8f6c288d7ad29916d98cb1072e4e7b7d52b376", "015bee1357e3c015b5bda237668522f613d1c88726b5ec4224a20128481b4f7f",
+	"2953736e94bb6b9f1b9707a4f1615e4efe1e1ce4bab218cbea92c785b128ffd1", "0b069353ba091618862f806180c0385f851b98d372b45f544ce7266ed6608dfc",
+	"304f74d461ccc13115e4e0bcfb93817e55aeb7eb9306b64e4f588ac97d81f429", "15bbf146ce9bca09e8a33f5e77dfe4f5aad2a164a4617a4cb8ee5415cde913fc",
+	"0ab4dfe0c2742cde44901031487964ed9b8f4b850405c10ca9ff23859572c8c6", "0e32db320a044e3197f45f7649a19675ef5eedfea546dea9251de39f9639779a",
+	"0a1756aa1f378ca4b27635a78b6888e66797733a82774896a3078efa516da016", "044c4a33b10f693447fd17177f952ef895e61d328f85efa94254d6a2a25d93ef",
+	"2ed3611b725b8a70be655b537f66f700fe0879d79a496891d37b07b5466c4b8b", "1f9ba4e8bab7ce42c8ecc3d722aa2e0eadfdeb9cfdd347b5d8339ea7120858aa",
+	"1b233043052e8c288f7ee907a84e518aa38e82ac4502066db74056f865c5d3da", "2431e1cc164bb8d074031ab72bd55b4c902053bfc0f14db0ca2f97b020875954",
+	"082f934c91f5aac330cd6953a0a7db45a13e322097583319a791f273965801fd", "2b9a0a223e7538b0a34be074315542a3c77245e2ae7cbe999ad6bb930c48997c",
+	"0e1cd91edd2cfa2cceb85483b887a9be8164163e75a8a00eb0b589cc70214e7d", "2e1eac0f2bfdfd63c951f61477e3698999774f19854d00f588d324601cebe2f9",
+	"0cbfa95f37fb74060c76158e769d6d157345784d8efdb33c23d748115b500b83", "08f05b3be923ed44d65ad49d8a61e9a676d991e3a77513d9980c232dfa4a4f84",
+	"22719e2a070bcd0852bf8e21984d0443e7284925dc0758a325a2dd510c047ef6", "041f596a9ee1cb2bc060f7fcc3a1ab4c7bdbf036119982c0f41f62b2f26830c0",
+	"233fd35de1be520a87628eb06f6b1d4c021be1c2d0dc464a19fcdd0986b10f89", "0524b46d1aa87a5e4325e0a423ebc810d31e078aa1b4707eefcb453c61c9c267",
+	"2c34f424c81e5716ce47fcac894b85824227bb954b0f3199cc4486237c515211", "0b5f2a4b63387819207effc2b5541fb72dd2025b5457cc97f33010327de4915e",
+	"22207856082ccc54c5b72fe439d2cfd6c17435d2f57af6ceaefac41fe05c659f", "24d57a8bf5da63fe4e24159b7f8950b5cdfb210194caf79f27854048ce2c8171",
+	"0afab181fdd5e0583b371d75bd693f98374ad7097bb01a8573919bb23b79396e", "2dba9b108f208772998a52efac7cbd5676c0057194c16c0bf16290d62b1128ee",
+	"26349b66edb8b16f56f881c788f53f83cbb83de0bd592b255aff13e6bce420b3", "25af7ce0e5e10357685e95f92339753ad81a56d28ecc193b235288a3e6f137db",
+	"25b4ce7bd2294390c094d6a55edd68b970eed7aae88b2bff1f7c0187fe35011f", "22c543f10f6c89ec387e53f1908a88e5de9cef28ebdf30b18cb9d54c1e02b631",
+	"0236f93e7789c4724fc7908a9f191e1e425e906a919d7a34df668e74882f87a9", "29350b401166ca010e7d27e37d05da99652bdae114eb01659cb497af980c4b52",
+	"0eed787d65820d3f6bd31bbab547f75a65edb75d844ebb89ee1260916652363f", "07cc1170f13b46f2036a753f520b3291fdcd0e99bd94297d1906f656f4de6fad",
+	"22b939233b1d7205f49bcf613a3d30b1908786d7f9f5d10c2059435689e8acea", "01451762a0aab81c8aad1dc8bc33e870740f083a5aa85438add650ace60ae5a6",
+	"23506bb5d8727d4461fabf1025d46d1fe32eaa61dec7da57e704fec0892fce89", "2e484c44e838aea0bac06ae3f71bdd092a3709531e1efea97f8bd68907355522",
+	"0f4bc7d07ebafd64379e78c50bd2e42baf4a594545cedc2545418da26835b54c", "1f4d3c8f6583e9e5fa76637862faaee851582388725df460e620996d50d8e74e",
+	"093514e0c70711f82660d07be0e4a988fae02abc7b681d9153eb9bcb48fe7389", "1adab0c8e2b3bad346699a2b5f3bc03643ee83ece47228f24a58e0a347e153d8",
+	"1672b1726057d99dd14709ebb474641a378c1b94b8072bac1a22dbef9e80dad2", "1dfd53d4576af2e38f44f53fdcab468cc5d8e2fae0acc4ee30d47b239b479c14",
+	"0c6888a10b75b0f3a70a36263a37e17fe6d77d640f6fc3debc7f207753205c60", "1addb933a65be77092b34a7e77d12fe8611a61e00ee6848b85091ecca9d1e508",
+	"00d7540dcd268a845c10ae18d1de933cf638ff5425f0afff7935628e299d1791", "140c0e42687e9ead01b2827a5664ca9c26fedde4acd99db1d316939d20b82c0e",
+	"2f0c3a115d4317d191ba89b8d13d1806c20a0f9b24f8c5edc091e2ae56565984", "0c4ee778ff7c14553006ed220cf9c81008a0cff670b22b82d8c538a1dc958c61",
+	"1704f2766d46f82c3693f00440ccc3609424ed26c0acc66227c3d7485de74c69", "2f2d19cc3ea5d78ea7a02c1b51d244abf0769c9f8544e40239b66fe9009c3cfa",
+	"1ae03853b75fcaba5053f112e2a8e8dcdd7ee6cb9cfed9c7d6c766a806fc6629", "0971aabf795241df51d131d0fa61aa5f3556921b2d6f014e4e41a86ddaf056d5",
+	"1408c316e6014e1a91d4cf6b6e0de73eda624f8380df1c875f5c29f7bfe2f646", "1667f3fe2edbe850248abe42b543093b6c89f1f773ef285341691f39822ef5bd",
+	"13bf7c5d0d2c4376a48b0a03557cdf915b81718409e5c133424c69576500fe37", "07620a6dfb0b6cec3016adf3d3533c24024b95347856b79719bc0ba743a62c2c",
+	"1574c7ef0c43545f36a8ca08bdbdd8b075d2959e2f322b731675de3e1982b4d0", "269e4b5b7a2eb21afd567970a717ceec5bd4184571c254fdc06e03a7ff8378f0",
+}
+
+var mdsT2 = [][]string{
+	{"066f6f85d6f68a85ec10345351a23a3aaf07f38af8c952a7bceca70bd2af7ad5", "2b9d4b4110c9ae997782e1509b1d0fdb20a7c02bbd8bea7305462b9f8125b1e8"},
+	{"0cc57cdbb08507d62bf67a4493cc262fb6c09d557013fff1f573f431221f8ff9", "1274e649a32ed355a31a6ed69724e1adade857e86eb5c3a121bcd147943203c8"},
+}