diff --git a/pkg/rpc/client/native.go b/pkg/rpc/client/native.go
index 7839ab941..85a857ac3 100644
--- a/pkg/rpc/client/native.go
+++ b/pkg/rpc/client/native.go
@@ -5,6 +5,7 @@ package client
 import (
 	"errors"
 	"fmt"
+	"math/big"
 
 	"github.com/nspcc-dev/neo-go/pkg/core/native/nativenames"
 	"github.com/nspcc-dev/neo-go/pkg/core/native/noderoles"
@@ -55,11 +56,11 @@ func (c *Client) GetDesignatedByRole(role noderoles.Role, index uint32) (keys.Pu
 	result, err := c.InvokeFunction(rmHash, "getDesignatedByRole", []smartcontract.Parameter{
 		{
 			Type:  smartcontract.IntegerType,
-			Value: int64(role),
+			Value: big.NewInt(int64(role)),
 		},
 		{
 			Type:  smartcontract.IntegerType,
-			Value: int64(index),
+			Value: big.NewInt(int64(index)),
 		},
 	}, nil)
 	if err != nil {
@@ -84,7 +85,7 @@ func (c *Client) NNSResolve(nnsHash util.Uint160, name string, typ nns.RecordTyp
 		},
 		{
 			Type:  smartcontract.IntegerType,
-			Value: int64(typ),
+			Value: big.NewInt(int64(typ)),
 		},
 	}, nil)
 	if err != nil {
diff --git a/pkg/smartcontract/convertor.go b/pkg/smartcontract/convertor.go
deleted file mode 100644
index d4d9e45d7..000000000
--- a/pkg/smartcontract/convertor.go
+++ /dev/null
@@ -1,72 +0,0 @@
-package smartcontract
-
-import (
-	"fmt"
-	"math/big"
-
-	"github.com/nspcc-dev/neo-go/pkg/vm/stackitem"
-)
-
-// ParameterFromStackItem converts stackitem.Item to Parameter.
-func ParameterFromStackItem(i stackitem.Item, seen map[stackitem.Item]bool) Parameter {
-	switch t := i.(type) {
-	case stackitem.Null, *stackitem.Pointer:
-		return NewParameter(AnyType)
-	case *stackitem.BigInteger:
-		return Parameter{
-			Type:  IntegerType,
-			Value: i.Value().(*big.Int).Int64(),
-		}
-	case stackitem.Bool:
-		return Parameter{
-			Type:  BoolType,
-			Value: i.Value().(bool),
-		}
-	case *stackitem.ByteArray:
-		return Parameter{
-			Type:  ByteArrayType,
-			Value: i.Value().([]byte),
-		}
-	case *stackitem.Interop:
-		return Parameter{
-			Type:  InteropInterfaceType,
-			Value: nil,
-		}
-	case *stackitem.Buffer:
-		return Parameter{
-			Type:  ByteArrayType,
-			Value: i.Value().([]byte),
-		}
-	case *stackitem.Struct, *stackitem.Array:
-		var value []Parameter
-
-		if !seen[i] {
-			seen[i] = true
-			for _, stackItem := range i.Value().([]stackitem.Item) {
-				parameter := ParameterFromStackItem(stackItem, seen)
-				value = append(value, parameter)
-			}
-		}
-		return Parameter{
-			Type:  ArrayType,
-			Value: value,
-		}
-	case *stackitem.Map:
-		value := make([]ParameterPair, 0)
-		if !seen[i] {
-			seen[i] = true
-			for _, element := range i.Value().([]stackitem.MapElement) {
-				value = append(value, ParameterPair{
-					Key:   ParameterFromStackItem(element.Key, seen),
-					Value: ParameterFromStackItem(element.Value, seen),
-				})
-			}
-		}
-		return Parameter{
-			Type:  MapType,
-			Value: value,
-		}
-	default:
-		panic(fmt.Sprintf("unknown stack item type: %v", t))
-	}
-}
diff --git a/pkg/smartcontract/convertor_test.go b/pkg/smartcontract/convertor_test.go
deleted file mode 100644
index bd1585609..000000000
--- a/pkg/smartcontract/convertor_test.go
+++ /dev/null
@@ -1,79 +0,0 @@
-package smartcontract
-
-import (
-	"math/big"
-	"testing"
-
-	"github.com/nspcc-dev/neo-go/pkg/vm/stackitem"
-	"github.com/stretchr/testify/assert"
-)
-
-var toContractParameterTestCases = []struct {
-	input  stackitem.Item
-	result Parameter
-}{
-	{
-		input: stackitem.NewStruct([]stackitem.Item{
-			stackitem.NewBigInteger(big.NewInt(1)),
-			stackitem.NewBool(true),
-		}),
-		result: Parameter{Type: ArrayType, Value: []Parameter{
-			{Type: IntegerType, Value: int64(1)},
-			{Type: BoolType, Value: true},
-		}},
-	},
-	{
-		input:  stackitem.NewBool(false),
-		result: Parameter{Type: BoolType, Value: false},
-	},
-	{
-		input:  stackitem.NewByteArray([]byte{0x01, 0x02, 0x03}),
-		result: Parameter{Type: ByteArrayType, Value: []byte{0x01, 0x02, 0x03}},
-	},
-	{
-		input:  stackitem.NewBuffer([]byte{0x01, 0x02, 0x03}),
-		result: Parameter{Type: ByteArrayType, Value: []byte{0x01, 0x02, 0x03}},
-	},
-	{
-		input: stackitem.NewArray([]stackitem.Item{stackitem.NewBigInteger(big.NewInt(2)), stackitem.NewBool(true)}),
-		result: Parameter{Type: ArrayType, Value: []Parameter{
-			{Type: IntegerType, Value: int64(2)},
-			{Type: BoolType, Value: true},
-		}},
-	},
-	{
-		input:  stackitem.NewInterop(nil),
-		result: Parameter{Type: InteropInterfaceType, Value: nil},
-	},
-	{
-		input: stackitem.NewMapWithValue([]stackitem.MapElement{
-			{Key: stackitem.NewBigInteger(big.NewInt(1)), Value: stackitem.NewBool(true)},
-			{Key: stackitem.NewByteArray([]byte("qwerty")), Value: stackitem.NewBigInteger(big.NewInt(3))},
-			{Key: stackitem.NewBool(true), Value: stackitem.NewBool(false)},
-		}),
-		result: Parameter{
-			Type: MapType,
-			Value: []ParameterPair{
-				{
-					Key:   Parameter{Type: IntegerType, Value: int64(1)},
-					Value: Parameter{Type: BoolType, Value: true},
-				}, {
-					Key:   Parameter{Type: ByteArrayType, Value: []byte("qwerty")},
-					Value: Parameter{Type: IntegerType, Value: int64(3)},
-				}, {
-
-					Key:   Parameter{Type: BoolType, Value: true},
-					Value: Parameter{Type: BoolType, Value: false},
-				},
-			},
-		},
-	},
-}
-
-func TestToContractParameter(t *testing.T) {
-	for _, tc := range toContractParameterTestCases {
-		seen := make(map[stackitem.Item]bool)
-		res := ParameterFromStackItem(tc.input, seen)
-		assert.Equal(t, res, tc.result)
-	}
-}
diff --git a/pkg/smartcontract/param_type.go b/pkg/smartcontract/param_type.go
index 2ea611a95..1f432536b 100644
--- a/pkg/smartcontract/param_type.go
+++ b/pkg/smartcontract/param_type.go
@@ -5,13 +5,14 @@ import (
 	"encoding/json"
 	"errors"
 	"fmt"
-	"strconv"
+	"math/big"
 	"strings"
 
 	"github.com/nspcc-dev/neo-go/pkg/crypto/keys"
 	"github.com/nspcc-dev/neo-go/pkg/encoding/address"
 	"github.com/nspcc-dev/neo-go/pkg/io"
 	"github.com/nspcc-dev/neo-go/pkg/util"
+	"github.com/nspcc-dev/neo-go/pkg/vm/stackitem"
 )
 
 // ParamType represents the Type of the smart contract parameter.
@@ -208,7 +209,11 @@ func adjustValToType(typ ParamType, val string) (interface{}, error) {
 			return nil, errors.New("invalid boolean value")
 		}
 	case IntegerType:
-		return strconv.ParseInt(val, 10, 64)
+		bi, ok := new(big.Int).SetString(val, 10)
+		if !ok || stackitem.CheckIntegerSize(bi) != nil {
+			return nil, errors.New("invalid integer value")
+		}
+		return bi, nil
 	case Hash160Type:
 		u, err := address.StringToUint160(val)
 		if err == nil {
@@ -250,8 +255,8 @@ func adjustValToType(typ ParamType, val string) (interface{}, error) {
 func inferParamType(val string) ParamType {
 	var err error
 
-	_, err = strconv.Atoi(val)
-	if err == nil {
+	bi, ok := new(big.Int).SetString(val, 10)
+	if ok && stackitem.CheckIntegerSize(bi) == nil {
 		return IntegerType
 	}
 
diff --git a/pkg/smartcontract/param_type_test.go b/pkg/smartcontract/param_type_test.go
index 1d3c54819..0620e52e1 100644
--- a/pkg/smartcontract/param_type_test.go
+++ b/pkg/smartcontract/param_type_test.go
@@ -2,9 +2,11 @@ package smartcontract
 
 import (
 	"encoding/hex"
+	"math/big"
 	"testing"
 
 	"github.com/nspcc-dev/neo-go/pkg/util"
+	"github.com/nspcc-dev/neo-go/pkg/vm/stackitem"
 	"github.com/stretchr/testify/assert"
 	"github.com/stretchr/testify/require"
 )
@@ -76,6 +78,7 @@ func TestParseParamType(t *testing.T) {
 }
 
 func TestInferParamType(t *testing.T) {
+	bi := new(big.Int).Lsh(big.NewInt(1), stackitem.MaxBigIntegerSizeBits-2)
 	var inouts = []struct {
 		in  string
 		out ParamType
@@ -88,6 +91,15 @@ func TestInferParamType(t *testing.T) {
 	}, {
 		in:  "0",
 		out: IntegerType,
+	}, {
+		in:  "8765432187654321111",
+		out: IntegerType,
+	}, {
+		in:  bi.String(),
+		out: IntegerType,
+	}, {
+		in:  bi.String() + "0", // big for Integer but is still a valid hex
+		out: ByteArrayType,
 	}, {
 		in:  "2e10",
 		out: ByteArrayType,
@@ -150,6 +162,8 @@ func TestInferParamType(t *testing.T) {
 }
 
 func TestAdjustValToType(t *testing.T) {
+	bi := big.NewInt(1).Lsh(big.NewInt(1), stackitem.MaxBigIntegerSizeBits-2)
+
 	var inouts = []struct {
 		typ ParamType
 		val string
@@ -190,15 +204,23 @@ func TestAdjustValToType(t *testing.T) {
 	}, {
 		typ: IntegerType,
 		val: "0",
-		out: int64(0),
+		out: big.NewInt(0),
 	}, {
 		typ: IntegerType,
 		val: "42",
-		out: int64(42),
+		out: big.NewInt(42),
 	}, {
 		typ: IntegerType,
 		val: "-42",
-		out: int64(-42),
+		out: big.NewInt(-42),
+	}, {
+		typ: IntegerType,
+		val: bi.String(),
+		out: bi,
+	}, {
+		typ: IntegerType,
+		val: bi.String() + "0",
+		err: true,
 	}, {
 		typ: IntegerType,
 		val: "q",
diff --git a/pkg/smartcontract/parameter.go b/pkg/smartcontract/parameter.go
index 91f773fed..55683fa1a 100644
--- a/pkg/smartcontract/parameter.go
+++ b/pkg/smartcontract/parameter.go
@@ -8,16 +8,16 @@ import (
 	"encoding/json"
 	"errors"
 	"fmt"
-	"math"
+	"math/big"
 	"math/bits"
 	"os"
-	"strconv"
 	"strings"
 	"unicode/utf8"
 
 	"github.com/nspcc-dev/neo-go/pkg/crypto/keys"
-	"github.com/nspcc-dev/neo-go/pkg/io"
+	"github.com/nspcc-dev/neo-go/pkg/encoding/bigint"
 	"github.com/nspcc-dev/neo-go/pkg/util"
+	"github.com/nspcc-dev/neo-go/pkg/vm/stackitem"
 )
 
 // Parameter represents a smart contract parameter.
@@ -65,13 +65,12 @@ func (p Parameter) MarshalJSON() ([]byte, error) {
 	case BoolType, StringType, Hash160Type, Hash256Type:
 		resultRawValue, resultErr = json.Marshal(p.Value)
 	case IntegerType:
-		val, ok := p.Value.(int64)
+		val, ok := p.Value.(*big.Int)
 		if !ok {
 			resultErr = errors.New("invalid integer value")
 			break
 		}
-		valStr := strconv.FormatInt(val, 10)
-		resultRawValue = json.RawMessage(`"` + valStr + `"`)
+		resultRawValue = json.RawMessage(`"` + val.String() + `"`)
 	case PublicKeyType, ByteArrayType, SignatureType:
 		if p.Type == PublicKeyType {
 			resultRawValue, resultErr = json.Marshal(hex.EncodeToString(p.Value.([]byte)))
@@ -145,17 +144,22 @@ func (p *Parameter) UnmarshalJSON(data []byte) (err error) {
 		p.Value = s
 	case IntegerType:
 		if err = json.Unmarshal(r.Value, &i); err == nil {
-			p.Value = i
+			p.Value = big.NewInt(i)
 			return
 		}
 		// sometimes integer comes as string
-		if err = json.Unmarshal(r.Value, &s); err != nil {
-			return
+		if jErr := json.Unmarshal(r.Value, &s); jErr != nil {
+			return jErr
 		}
-		if i, err = strconv.ParseInt(s, 10, 64); err != nil {
-			return
+		bi, ok := new(big.Int).SetString(s, 10)
+		if !ok {
+			// In this case previous err should mean string contains non-digit characters.
+			return err
+		}
+		err = stackitem.CheckIntegerSize(bi)
+		if err == nil {
+			p.Value = bi
 		}
-		p.Value = i
 	case ArrayType:
 		// https://github.com/neo-project/neo/blob/3d59ecca5a8deb057bdad94b3028a6d5e25ac088/neo/Network/RPC/RpcServer.cs#L67
 		var rs []Parameter
@@ -190,87 +194,6 @@ func (p *Parameter) UnmarshalJSON(data []byte) (err error) {
 	return
 }
 
-// EncodeBinary implements io.Serializable interface.
-func (p *Parameter) EncodeBinary(w *io.BinWriter) {
-	w.WriteB(byte(p.Type))
-	switch p.Type {
-	case BoolType:
-		w.WriteBool(p.Value.(bool))
-	case ByteArrayType, PublicKeyType, SignatureType:
-		if p.Value == nil {
-			w.WriteVarUint(math.MaxUint64)
-		} else {
-			w.WriteVarBytes(p.Value.([]byte))
-		}
-	case StringType:
-		w.WriteString(p.Value.(string))
-	case IntegerType:
-		w.WriteU64LE(uint64(p.Value.(int64)))
-	case ArrayType:
-		w.WriteArray(p.Value.([]Parameter))
-	case MapType:
-		w.WriteArray(p.Value.([]ParameterPair))
-	case Hash160Type:
-		w.WriteBytes(p.Value.(util.Uint160).BytesBE())
-	case Hash256Type:
-		w.WriteBytes(p.Value.(util.Uint256).BytesBE())
-	case InteropInterfaceType, AnyType:
-	default:
-		w.Err = fmt.Errorf("unknown type: %x", p.Type)
-	}
-}
-
-// DecodeBinary implements io.Serializable interface.
-func (p *Parameter) DecodeBinary(r *io.BinReader) {
-	p.Type = ParamType(r.ReadB())
-	switch p.Type {
-	case BoolType:
-		p.Value = r.ReadBool()
-	case ByteArrayType, PublicKeyType, SignatureType:
-		ln := r.ReadVarUint()
-		if ln != math.MaxUint64 {
-			b := make([]byte, ln)
-			r.ReadBytes(b)
-			p.Value = b
-		}
-	case StringType:
-		p.Value = r.ReadString()
-	case IntegerType:
-		p.Value = int64(r.ReadU64LE())
-	case ArrayType:
-		ps := []Parameter{}
-		r.ReadArray(&ps)
-		p.Value = ps
-	case MapType:
-		ps := []ParameterPair{}
-		r.ReadArray(&ps)
-		p.Value = ps
-	case Hash160Type:
-		var u util.Uint160
-		r.ReadBytes(u[:])
-		p.Value = u
-	case Hash256Type:
-		var u util.Uint256
-		r.ReadBytes(u[:])
-		p.Value = u
-	case InteropInterfaceType, AnyType:
-	default:
-		r.Err = fmt.Errorf("unknown type: %x", p.Type)
-	}
-}
-
-// EncodeBinary implements io.Serializable interface.
-func (p *ParameterPair) EncodeBinary(w *io.BinWriter) {
-	p.Key.EncodeBinary(w)
-	p.Value.EncodeBinary(w)
-}
-
-// DecodeBinary implements io.Serializable interface.
-func (p *ParameterPair) DecodeBinary(r *io.BinReader) {
-	p.Key.DecodeBinary(r)
-	p.Value.DecodeBinary(r)
-}
-
 // Params is an array of Parameter (TODO: drop it?).
 type Params []Parameter
 
@@ -318,6 +241,9 @@ func (p Parameter) TryParse(dest interface{}) error {
 				return err
 			}
 			return nil
+		case **big.Int:
+			*dest = bigint.FromBytes(data)
+			return nil
 		case *int64, *int32, *int16, *int8, *int, *uint64, *uint32, *uint16, *uint8, *uint:
 			var size int
 			switch dest.(type) {
diff --git a/pkg/smartcontract/parameter_test.go b/pkg/smartcontract/parameter_test.go
index 82aba2317..e52cc67a1 100644
--- a/pkg/smartcontract/parameter_test.go
+++ b/pkg/smartcontract/parameter_test.go
@@ -5,10 +5,11 @@ import (
 	"encoding/hex"
 	"encoding/json"
 	"math"
+	"math/big"
 	"reflect"
+	"strings"
 	"testing"
 
-	"github.com/nspcc-dev/neo-go/internal/testserdes"
 	"github.com/nspcc-dev/neo-go/pkg/crypto/keys"
 	"github.com/nspcc-dev/neo-go/pkg/io"
 	"github.com/nspcc-dev/neo-go/pkg/util"
@@ -22,9 +23,13 @@ var marshalJSONTestCases = []struct {
 	result string
 }{
 	{
-		input:  Parameter{Type: IntegerType, Value: int64(12345)},
+		input:  Parameter{Type: IntegerType, Value: big.NewInt(12345)},
 		result: `{"type":"Integer","value":12345}`,
 	},
+	{
+		input:  Parameter{Type: IntegerType, Value: new(big.Int).Lsh(big.NewInt(1), 254)},
+		result: `{"type":"Integer","value":"` + new(big.Int).Lsh(big.NewInt(1), 254).String() + `"}`,
+	},
 	{
 		input:  Parameter{Type: StringType, Value: "Some string"},
 		result: `{"type":"String","value":"Some string"}`,
@@ -57,7 +62,7 @@ var marshalJSONTestCases = []struct {
 			Type: ArrayType,
 			Value: []Parameter{
 				{Type: StringType, Value: "str 1"},
-				{Type: IntegerType, Value: int64(2)},
+				{Type: IntegerType, Value: big.NewInt(2)},
 			},
 		},
 		result: `{"type":"Array","value":[{"type":"String","value":"str 1"},{"type":"Integer","value":2}]}`,
@@ -84,7 +89,7 @@ var marshalJSONTestCases = []struct {
 			Value: []ParameterPair{
 				{
 					Key:   Parameter{Type: StringType, Value: "key1"},
-					Value: Parameter{Type: IntegerType, Value: int64(1)},
+					Value: Parameter{Type: IntegerType, Value: big.NewInt(1)},
 				},
 				{
 					Key:   Parameter{Type: StringType, Value: "key2"},
@@ -102,7 +107,7 @@ var marshalJSONTestCases = []struct {
 					Key: Parameter{Type: StringType, Value: "key1"},
 					Value: Parameter{Type: ArrayType, Value: []Parameter{
 						{Type: StringType, Value: "str 1"},
-						{Type: IntegerType, Value: int64(2)},
+						{Type: IntegerType, Value: big.NewInt(2)},
 					}},
 				},
 			},
@@ -185,11 +190,11 @@ var unmarshalJSONTestCases = []struct {
 	},
 	{
 		input:  `{"type":"Integer","value":12345}`,
-		result: Parameter{Type: IntegerType, Value: int64(12345)},
+		result: Parameter{Type: IntegerType, Value: big.NewInt(12345)},
 	},
 	{
 		input:  `{"type":"Integer","value":"12345"}`,
-		result: Parameter{Type: IntegerType, Value: int64(12345)},
+		result: Parameter{Type: IntegerType, Value: big.NewInt(12345)},
 	},
 	{
 		input:  `{"type":"ByteString","value":"` + hexToBase64("010203") + `"}`,
@@ -215,7 +220,7 @@ var unmarshalJSONTestCases = []struct {
 			Type: ArrayType,
 			Value: []Parameter{
 				{Type: StringType, Value: "str 1"},
-				{Type: IntegerType, Value: int64(2)},
+				{Type: IntegerType, Value: big.NewInt(2)},
 			},
 		},
 	},
@@ -248,7 +253,7 @@ var unmarshalJSONTestCases = []struct {
 			Value: []ParameterPair{
 				{
 					Key:   Parameter{Type: StringType, Value: "key1"},
-					Value: Parameter{Type: IntegerType, Value: int64(1)},
+					Value: Parameter{Type: IntegerType, Value: big.NewInt(1)},
 				},
 				{
 					Key:   Parameter{Type: StringType, Value: "key2"},
@@ -266,7 +271,7 @@ var unmarshalJSONTestCases = []struct {
 					Key: Parameter{Type: StringType, Value: "key1"},
 					Value: Parameter{Type: ArrayType, Value: []Parameter{
 						{Type: StringType, Value: "str 1"},
-						{Type: IntegerType, Value: int64(2)},
+						{Type: IntegerType, Value: big.NewInt(2)},
 					}},
 				},
 			},
@@ -310,6 +315,8 @@ var unmarshalJSONErrorCases = []string{
 	`{"type": "String","value":1}`,         // incorrect Value
 	`{"type": "Integer","value": "nn"}`,    // incorrect Integer value
 	`{"type": "Integer","value": []}`,      // incorrect Integer value
+	`{"type": "Integer","value":"` +
+		strings.Repeat("9", 100) + `"}`, // too big Integer
 	`{"type": "Array","value": 123}`,       // incorrect Array value
 	`{"type": "Hash160","value": "0bcd"}`,  // incorrect Uint160 value
 	`{"type": "Hash256","value": "0bcd"}`,  // incorrect Uint256 value
@@ -330,7 +337,7 @@ func TestParam_UnmarshalJSON(t *testing.T) {
 	}
 
 	for _, input := range unmarshalJSONErrorCases {
-		assert.Error(t, json.Unmarshal([]byte(input), &s))
+		assert.Error(t, json.Unmarshal([]byte(input), &s), input)
 	}
 }
 
@@ -370,6 +377,10 @@ var tryParseTestCases = []struct {
 		input:    []byte{0x63, 0x78, 0x29, 0xcd, 0x0b},
 		expected: int64(50686687331),
 	},
+	{
+		input:    []byte{0x63, 0x78, 0x29, 0xcd, 0x0b},
+		expected: big.NewInt(50686687331),
+	},
 	{
 		input:    []byte("this is a test string"),
 		expected: "this is a test string",
@@ -450,13 +461,13 @@ func TestNewParameterFromString(t *testing.T) {
 		out: Parameter{StringType, "qwerty"},
 	}, {
 		in:  "42",
-		out: Parameter{IntegerType, int64(42)},
+		out: Parameter{IntegerType, big.NewInt(42)},
 	}, {
 		in:  "Hello, 世界",
 		out: Parameter{StringType, "Hello, 世界"},
 	}, {
 		in:  `\4\2`,
-		out: Parameter{IntegerType, int64(42)},
+		out: Parameter{IntegerType, big.NewInt(42)},
 	}, {
 		in:  `\\4\2`,
 		out: Parameter{StringType, `\42`},
@@ -465,7 +476,7 @@ func TestNewParameterFromString(t *testing.T) {
 		out: Parameter{StringType, `\42`},
 	}, {
 		in:  "int:42",
-		out: Parameter{IntegerType, int64(42)},
+		out: Parameter{IntegerType, big.NewInt(42)},
 	}, {
 		in:  "true",
 		out: Parameter{BoolType, true},
@@ -514,20 +525,6 @@ func TestNewParameterFromString(t *testing.T) {
 	}
 }
 
-func TestEncodeDecodeBinary(t *testing.T) {
-	for _, tc := range marshalJSONTestCases {
-		testserdes.EncodeDecodeBinary(t, &tc.input, new(Parameter))
-	}
-
-	t.Run("unknown", func(t *testing.T) {
-		p := Parameter{Type: UnknownType}
-		_, err := testserdes.EncodeBinary(&p)
-		require.Error(t, err)
-
-		require.Error(t, testserdes.DecodeBinary([]byte{0xAA}, &p))
-	})
-}
-
 func hexToBase64(s string) string {
 	b, _ := hex.DecodeString(s)
 	return base64.StdEncoding.EncodeToString(b)
@@ -544,8 +541,8 @@ func TestExpandParameterToEmitable(t *testing.T) {
 			Expected: true,
 		},
 		{
-			In:       Parameter{Type: IntegerType, Value: int64(123)},
-			Expected: int64(123),
+			In:       Parameter{Type: IntegerType, Value: big.NewInt(123)},
+			Expected: big.NewInt(123),
 		},
 		{
 			In:       Parameter{Type: ByteArrayType, Value: []byte{1, 2, 3}},
@@ -575,7 +572,7 @@ func TestExpandParameterToEmitable(t *testing.T) {
 			In: Parameter{Type: ArrayType, Value: []Parameter{
 				{
 					Type:  IntegerType,
-					Value: int64(123),
+					Value: big.NewInt(123),
 				},
 				{
 					Type:  ByteArrayType,
@@ -591,7 +588,7 @@ func TestExpandParameterToEmitable(t *testing.T) {
 					},
 				},
 			}},
-			Expected: []interface{}{int64(123), []byte{1, 2, 3}, []interface{}{true}},
+			Expected: []interface{}{big.NewInt(123), []byte{1, 2, 3}, []interface{}{true}},
 		},
 	}
 	bw := io.NewBufBinWriter()