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fhe

package

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Versions in this module

v1

v1.3.6

Jun 6, 2026

v1.3.5

Jun 6, 2026

v1.3.4

Jun 6, 2026

v1.3.3

Jun 6, 2026

v1.3.2

Jun 6, 2026

v1.3.1

Jun 5, 2026

v1.3.0

Jun 5, 2026

v1.2.7

May 28, 2026

v1.2.6

May 22, 2026

v1.2.5

May 19, 2026

v1.2.4

May 19, 2026

v1.2.3

May 19, 2026

v1.2.2

May 16, 2026

Changes in this version

+ const DecryptStatusDenied

+ const DecryptStatusExpired

+ const DecryptStatusFailed

+ const DecryptStatusSuccess

+ const MaxBatchSize

+ const PayloadTypeFHEDecryptRequestV1

+ const PayloadTypeFHEDecryptResultV1

+ const PayloadTypeFHEKeyRotationV1

+ const PayloadTypeFHEReencryptRequestV1

+ const PayloadTypeFHETaskResultV1

+ const PayloadVersionV1

+ const PermitOpCompute

+ const PermitOpDecrypt

+ const PermitOpReencrypt

+ const PermitOpTransfer

+ const SelectorRequestDecryption

+ const SelectorRequestDecryptionCallback

+ const TaskStatusCompleted

+ const TaskStatusFailed

+ const TaskStatusTimeout

+ var ErrAlreadyFulfilled = errors.New("request already fulfilled")

+ var ErrAuthRequired = errors.New("authentication required")

+ var ErrBatchTooLarge = errors.New("batch size exceeds maximum")

+ var ErrCiphertextNotFound = errors.New("ciphertext not found in storage")

+ var ErrCommitteeFull = errors.New("committee is full")

+ var ErrDKGFailed = errors.New("DKG ceremony failed")

+ var ErrDKGInProgress = errors.New("DKG ceremony in progress")

+ var ErrDKGNotStarted = errors.New("DKG ceremony not started")

+ var ErrDecryptionFailed = errors.New("threshold decryption failed")

+ var ErrEpochAlreadyActive = errors.New("epoch already active")

+ var ErrEpochExpired = errors.New("epoch has expired")

+ var ErrEpochMismatch = errors.New("epoch mismatch")

+ var ErrEpochNotActive = errors.New("epoch not active")

+ var ErrEpochNotReady = errors.New("epoch not ready")

+ var ErrInsufficientShares = errors.New("insufficient decryption shares")

+ var ErrInsufficientWeight = errors.New("insufficient committee weight")

+ var ErrInvalidHandle = errors.New("invalid ciphertext handle")

+ var ErrInvalidPayload = errors.New("invalid payload format")

+ var ErrInvalidPayloadType = errors.New("invalid payload type")

+ var ErrInvalidPayloadVersion = errors.New("invalid payload version")

+ var ErrInvalidPermit = errors.New("invalid permit")

+ var ErrInvalidSelector = errors.New("invalid function selector")

+ var ErrInvalidThreshold = errors.New("invalid threshold")

+ var ErrMemberAlreadyExists = errors.New("committee member already exists")

+ var ErrMemberNotFound = errors.New("committee member not found")

+ var ErrMissingCommitment = errors.New("participant must submit commitment first")

+ var ErrNotInitialized = errors.New("FHE service not initialized")

+ var ErrNotParticipant = errors.New("node is not a DKG participant")

+ var ErrPayloadMalformed = errors.New("payload malformed")

+ var ErrPayloadTooShort = errors.New("payload too short")

+ var ErrPermitExpired = errors.New("permit expired")

+ var ErrPermitInvalid = errors.New("permit invalid")

+ var ErrPermitNotFound = errors.New("permit not found")

+ var ErrRequestExpired = errors.New("request has expired")

+ var ErrRequestInProgress = errors.New("request already in progress")

+ var ErrRequestNotFound = errors.New("decryption request not found")

+ var ErrSessionNotFound = errors.New("session not found")

+ var ErrTransitionInProgress = errors.New("epoch transition in progress")

+ var ErrUnauthorized = errors.New("caller not authorized")

+ func ParsePayload(data []byte) (uint8, interface{}, error)

+ type Authenticator interface

+ GetCallerAddress func(ctx context.Context) ([20]byte, error)

+ type CiphertextMeta struct

+ ChainID ids.ID

+ Epoch uint64

+ Handle [32]byte

+ Level int

+ Owner [20]byte

+ RegisteredAt int64

+ Size uint32

+ Type uint8

+ type CiphertextStorage interface

+ Delete func(handle common.Hash) error

+ Get func(handle common.Hash) ([]byte, error)

+ Put func(handle common.Hash, data []byte) error

+ type CommitteeMember struct

+ Index int

+ NodeID ids.NodeID

+ PublicKey []byte

+ Weight uint64

+ type CommitteeMemberInfo struct

+ Index int

+ NodeID string

+ PublicKey string

+ Weight uint64

+ type CreatePermitArgs struct

+ Attestation string

+ ChainID string

+ Expiry int64

+ Grantee string

+ Grantor string

+ Handle string

+ Operations uint32

+ type CreatePermitReply struct

+ CreatedAt int64

+ PermitID string

+ type DKGState struct

+ CeremonyID [32]byte

+ Commitments map[string][]byte

+ CompletedAt int64

+ Epoch uint64

+ Error string

+ Participants []ids.NodeID

+ PublicKey []byte

+ Shares map[string][]byte

+ StartedAt int64

+ Status DKGStatus

+ Threshold int

+ type DKGStatus uint8

+ const DKGAborted

+ const DKGCommitPhase

+ const DKGCompleted

+ const DKGFailed

+ const DKGPending

+ const DKGSharePhase

+ func (s DKGStatus) String() string

+ type DecryptRequest struct

+ Callback [20]byte

+ CallbackSelector [4]byte

+ CiphertextHandle [32]byte

+ CompletedAt int64

+ CreatedAt int64

+ Epoch uint64

+ Error string

+ Expiry int64

+ Nonce uint64

+ RequestID [32]byte

+ Requester [20]byte

+ ResultHandle [32]byte

+ SourceChain ids.ID

+ Status RequestStatus

+ type DecryptionRequest struct

+ CallbackAddress common.Address

+ CallbackSelector uint32

+ CiphertextHash common.Hash

+ DecryptionType uint8

+ Fulfilled bool

+ HasCallback bool

+ RequestID common.Hash

+ Requester common.Address

+ Result []byte

+ SourceChainID ids.ID

+ Timestamp time.Time

+ type DecryptionResult struct

+ Error error

+ Plaintext []byte

+ RequestID common.Hash

+ type DecryptionSession struct

+ AggregatedShare *multiparty.KeySwitchShare

+ Ciphertext *rlwe.Ciphertext

+ Complete bool

+ ID string

+ OwnPublicShare *multiparty.KeySwitchShare

+ OwnSecretShare *multiparty.AdditiveShareBigint

+ Participants map[ids.NodeID]bool

+ PublicShares []multiparty.KeySwitchShare

+ RequestID common.Hash

+ Result []byte

+ SecretShares []multiparty.AdditiveShareBigint

+ ShareCount int

+ type EpochInfo struct

+ Committee []CommitteeMember

+ EndTime int64

+ Epoch uint64

+ PublicKey []byte

+ StartTime int64

+ Status EpochStatus

+ Threshold int

+ type EpochKeyInfo struct

+ Committee int

+ Epoch uint64

+ IsActive bool

+ PublicKey []byte

+ Threshold int

+ type EpochStatus uint8

+ const EpochActive

+ const EpochEnded

+ const EpochPending

+ type FHEAccelerator struct

+ func GetFHEAccelerator() (*FHEAccelerator, error)

+ func NewFHEAccelerator(logger log.Logger) (*FHEAccelerator, error)

+ func NewFHEAcceleratorWithOptions(logger log.Logger, opts FHEOptions) (*FHEAccelerator, error)

+ func (g *FHEAccelerator) Backend() string

+ func (g *FHEAccelerator) BatchNTTForward(r *ring.Ring, polys []ring.Poly) error

+ func (g *FHEAccelerator) BatchNTTInverse(r *ring.Ring, polys []ring.Poly) error

+ func (g *FHEAccelerator) BatchPolyMul(r *ring.Ring, a, b, out []ring.Poly) error

+ func (g *FHEAccelerator) ClearCache()

+ func (g *FHEAccelerator) Close()

+ func (g *FHEAccelerator) IsEnabled() bool

+ func (g *FHEAccelerator) Stats() FHEStats

+ type FHEDecryptRequestV1 struct

+ Callback [20]byte

+ CallbackSelector [4]byte

+ CiphertextHandle [32]byte

+ Epoch uint64

+ Expiry int64

+ GasLimit uint32

+ Nonce uint64

+ PermitID [32]byte

+ RequestID [32]byte

+ Requester [20]byte

+ SourceChainID ids.ID

+ func ParseFHEDecryptRequestV1(data []byte) (*FHEDecryptRequestV1, error)

+ func (r *FHEDecryptRequestV1) Bytes() []byte

+ func (r *FHEDecryptRequestV1) Validate() error

+ type FHEDecryptResultV1 struct

+ CommitteeSignature [32]byte

+ Epoch uint64

+ Plaintext []byte

+ RequestID [32]byte

+ ResultHandle [32]byte

+ SourceChainID ids.ID

+ Status uint8

+ func ParseFHEDecryptResultV1(data []byte) (*FHEDecryptResultV1, error)

+ func (r *FHEDecryptResultV1) Bytes() []byte

+ type FHEDecryptionService struct

+ func NewFHEDecryptionService(logger log.Logger) *FHEDecryptionService

+ func (s *FHEDecryptionService) GetHandler(chainID ids.ID) (*WarpHandler, bool)

+ func (s *FHEDecryptionService) RegisterHandler(chainID ids.ID, handler *WarpHandler)

+ func (s *FHEDecryptionService) Start(ctx context.Context) error

+ func (s *FHEDecryptionService) Stop() error

+ type FHEKeyRotationV1 struct

+ CommitteeSize uint32

+ NewEpoch uint64

+ NewPublicKey []byte

+ NewThreshold uint32

+ OldEpoch uint64

+ func ParseFHEKeyRotationV1(data []byte) (*FHEKeyRotationV1, error)

+ func (r *FHEKeyRotationV1) Bytes() []byte

+ type FHEOptions struct

+ Backend string

+ Enabled bool

+ type FHEReencryptRequestV1 struct

+ CiphertextHandle [32]byte

+ Epoch uint64

+ PermitID [32]byte

+ Recipient [20]byte

+ RecipientPublicKey []byte

+ RequestID [32]byte

+ SourceChainID ids.ID

+ func ParseFHEReencryptRequestV1(data []byte) (*FHEReencryptRequestV1, error)

+ func (r *FHEReencryptRequestV1) Bytes() []byte

+ type FHEService struct

+ func NewFHEService(registry *Registry, integration *ThresholdFHEIntegration, logger log.Logger, ...) *FHEService

+ func (s *FHEService) CreatePermit(ctx context.Context, args *CreatePermitArgs, reply *CreatePermitReply) error

+ func (s *FHEService) GetCiphertextMeta(_ context.Context, args *GetCiphertextMetaArgs, reply *GetCiphertextMetaReply) error

+ func (s *FHEService) GetCommittee(_ context.Context, args *GetCommitteeArgs, reply *GetCommitteeReply) error

+ func (s *FHEService) GetDecryptBatchResult(ctx context.Context, args *GetDecryptBatchResultArgs, ...) error

+ func (s *FHEService) GetDecryptResult(_ context.Context, args *GetDecryptResultArgs, reply *GetDecryptResultReply) error

+ func (s *FHEService) GetPublicParams(_ context.Context, _ *GetPublicParamsArgs, reply *GetPublicParamsReply) error

+ func (s *FHEService) GetRequestReceipt(_ context.Context, args *GetRequestReceiptArgs, reply *GetRequestReceiptReply) error

+ func (s *FHEService) RegisterCiphertext(ctx context.Context, args *RegisterCiphertextArgs, ...) error

+ func (s *FHEService) RequestDecrypt(_ context.Context, args *RequestDecryptArgs, reply *RequestDecryptReply) error

+ func (s *FHEService) RequestDecryptBatch(ctx context.Context, args *RequestDecryptBatchArgs, ...) error

+ func (s *FHEService) VerifyPermit(_ context.Context, args *VerifyPermitArgs, reply *VerifyPermitReply) error

+ type FHEServiceOption func(*FHEService)

+ func WithAuthenticator(auth Authenticator) FHEServiceOption

+ type FHEStats struct

+ BatchCalls uint64

+ GPUFallbackCalls uint64

+ NTTForwardCalls uint64

+ NTTInverseCalls uint64

+ PolyMulCalls uint64

+ TotalGPUTimeNs uint64

+ type FHETaskResultV1 struct

+ Callback [20]byte

+ CallbackSelector [4]byte

+ Epoch uint64

+ ResultHandle [32]byte

+ Signature [32]byte

+ SourceChainID ids.ID

+ Status uint8

+ TaskID [32]byte

+ func ParseFHETaskResultV1(data []byte) (*FHETaskResultV1, error)

+ func (r *FHETaskResultV1) Bytes() []byte

+ type GetCiphertextMetaArgs struct

+ Handle string

+ type GetCiphertextMetaReply struct

+ ChainID string

+ Epoch uint64

+ Handle string

+ Level int

+ Owner string

+ RegisteredAt int64

+ Size uint32

+ Type uint8

+ type GetCommitteeArgs struct

+ Epoch *uint64

+ type GetCommitteeReply struct

+ Epoch uint64

+ Members []CommitteeMemberInfo

+ Threshold int

+ type GetDecryptBatchResultArgs struct

+ RequestIDs []string

+ type GetDecryptBatchResultReply struct

+ Results []GetDecryptResultReply

+ type GetDecryptResultArgs struct

+ RequestID string

+ type GetDecryptResultReply struct

+ CompletedAt int64

+ CreatedAt int64

+ Error string

+ Plaintext string

+ RequestID string

+ ResultHandle string

+ Status string

+ type GetPublicParamsArgs struct

+ type GetPublicParamsReply struct

+ ChainID string

+ Epoch uint64

+ LogN int

+ LogQP int

+ LogScale int

+ PublicKey string

+ Threshold int

+ type GetRequestReceiptArgs struct

+ RequestID string

+ type GetRequestReceiptReply struct

+ CreatedAt int64

+ Epoch uint64

+ ProcessedAt int64

+ RequestID string

+ SourceChain string

+ Status string

+ TxID string

+ WarpMessageID string

+ type InMemoryCiphertextStorage struct

+ func NewInMemoryCiphertextStorage() *InMemoryCiphertextStorage

+ func (s *InMemoryCiphertextStorage) Delete(handle common.Hash) error

+ func (s *InMemoryCiphertextStorage) Get(handle common.Hash) ([]byte, error)

+ func (s *InMemoryCiphertextStorage) Put(handle common.Hash, data []byte) error

+ type LifecycleConfig struct

+ DKGTimeout time.Duration

+ DefaultThreshold int

+ EpochDuration uint64

+ GracePeriod uint64

+ KeyRotationBlocks uint64

+ MaxCommitteeSize int

+ MinCommitteeSize int

+ func DefaultLifecycleConfig() *LifecycleConfig

+ type LifecycleManager struct

+ func NewLifecycleManager(registry *Registry, config *LifecycleConfig, logger log.Logger) *LifecycleManager

+ func (lm *LifecycleManager) AbortDKG(reason string) error

+ func (lm *LifecycleManager) ForceEpochTransition() error

+ func (lm *LifecycleManager) GetCommitteeWeight() (uint64, error)

+ func (lm *LifecycleManager) GetDKGState() *DKGState

+ func (lm *LifecycleManager) GetEpochKeyInfo(epoch uint64) (*EpochKeyInfo, error)

+ func (lm *LifecycleManager) GetStatus() (*LifecycleStatus, error)

+ func (lm *LifecycleManager) GetTransitionState() *TransitionState

+ func (lm *LifecycleManager) InitiateEpoch(committee []CommitteeMember, threshold int, publicKey []byte) error

+ func (lm *LifecycleManager) IsTransitioning() bool

+ func (lm *LifecycleManager) OnBlock(blockHeight uint64) error

+ func (lm *LifecycleManager) RegisterMember(nodeID ids.NodeID, publicKey []byte, stake uint64) error

+ func (lm *LifecycleManager) RemoveMember(nodeID ids.NodeID) error

+ func (lm *LifecycleManager) SetCallbacks(onEpochChange func(oldEpoch, newEpoch uint64), ...)

+ func (lm *LifecycleManager) SetDKGCallbacks(onDKGStart func(ceremonyID [32]byte, epoch uint64, participants []ids.NodeID), ...)

+ func (lm *LifecycleManager) SetSlashCallback(onSlash func(nodeID ids.NodeID, reason string))

+ func (lm *LifecycleManager) SlashMember(nodeID ids.NodeID, reason string) error

+ func (lm *LifecycleManager) Start() error

+ func (lm *LifecycleManager) StartDKG(epoch uint64, participants []ids.NodeID, threshold int) error

+ func (lm *LifecycleManager) Stop()

+ func (lm *LifecycleManager) SubmitDKGCommitment(nodeID ids.NodeID, commitment []byte) error

+ func (lm *LifecycleManager) SubmitDKGShare(nodeID ids.NodeID, share []byte) error

+ func (lm *LifecycleManager) ValidateThresholdMet(participantCount int) error

+ type LifecycleStatus struct

+ CommitteeSize int

+ CurrentBlock uint64

+ CurrentEpoch uint64

+ DKGStatus string

+ EpochProgress float64

+ IsTransitioning bool

+ Threshold int

+ TransitionStatus string

+ type MemberRegistration struct

+ ActivatedAt int64

+ NodeID ids.NodeID

+ PublicKey []byte

+ RegisteredAt int64

+ Stake uint64

+ Status MemberStatus

+ type MemberStatus uint8

+ const MemberActive

+ const MemberExiting

+ const MemberInactive

+ const MemberPending

+ const MemberSlashed

+ func (s MemberStatus) String() string

+ type Permit struct

+ Attestation []byte

+ ChainID ids.ID

+ CreatedAt int64

+ Expiry int64

+ Grantee [20]byte

+ Grantor [20]byte

+ Handle [32]byte

+ Operations uint32

+ PermitID [32]byte

+ type RegisterCiphertextArgs struct

+ ChainID string

+ Handle string

+ Level int

+ Owner string

+ Size uint32

+ Type uint8

+ type RegisterCiphertextReply struct

+ Epoch uint64

+ Handle string

+ RegisteredAt int64

+ type Registry struct

+ func NewRegistry(db database.Database) (*Registry, error)

+ func (r *Registry) AddCommitteeMember(member *CommitteeMember) error

+ func (r *Registry) Close() error

+ func (r *Registry) CreateDecryptRequest(req *DecryptRequest) error

+ func (r *Registry) CreatePermit(permit *Permit) error

+ func (r *Registry) DeleteCiphertext(handle [32]byte) error

+ func (r *Registry) DeleteSession(sessionID string) error

+ func (r *Registry) GetCiphertextMeta(handle [32]byte) (*CiphertextMeta, error)

+ func (r *Registry) GetCommittee() ([]CommitteeMember, error)

+ func (r *Registry) GetCommitteeMember(nodeID ids.NodeID) (*CommitteeMember, error)

+ func (r *Registry) GetCurrentEpoch() uint64

+ func (r *Registry) GetDecryptRequest(requestID [32]byte) (*DecryptRequest, error)

+ func (r *Registry) GetEpoch(epoch uint64) (*EpochInfo, error)

+ func (r *Registry) GetPermit(permitID [32]byte) (*Permit, error)

+ func (r *Registry) GetSession(sessionID string) (*SessionState, error)

+ func (r *Registry) RegisterCiphertext(meta *CiphertextMeta) error

+ func (r *Registry) RemoveCommitteeMember(nodeID ids.NodeID) error

+ func (r *Registry) RevokePermit(permitID [32]byte) error

+ func (r *Registry) SaveSession(session *SessionState) error

+ func (r *Registry) SetEpoch(epoch uint64, info *EpochInfo) error

+ func (r *Registry) UpdateDecryptRequest(requestID [32]byte, status RequestStatus, result [32]byte, errMsg string) error

+ func (r *Registry) VerifyPermit(permitID [32]byte, handle [32]byte, grantee [20]byte, operation uint32) error

+ type Relayer struct

+ func NewRelayer(logger log.Logger, decryptor *ThresholdDecryptor, storage CiphertextStorage, ...) *Relayer

+ func (r *Relayer) GetResult(requestID common.Hash) ([]byte, bool, error)

+ func (r *Relayer) Start(ctx context.Context) error

+ func (r *Relayer) Stop() error

+ func (r *Relayer) SubmitRequest(_ context.Context, req *DecryptionRequest) error

+ type RequestDecryptArgs struct

+ Callback string

+ CallbackSelector string

+ CiphertextHandle string

+ Expiry int64

+ GasLimit uint32

+ PermitID string

+ SourceChain string

+ type RequestDecryptBatchArgs struct

+ Requests []RequestDecryptArgs

+ type RequestDecryptBatchReply struct

+ Epoch uint64

+ RequestIDs []string

+ type RequestDecryptReply struct

+ Epoch uint64

+ RequestID string

+ Status string

+ type RequestStatus uint8

+ const RequestCompleted

+ const RequestExpired

+ const RequestFailed

+ const RequestPending

+ const RequestProcessing

+ func (s RequestStatus) String() string

+ type SessionState struct

+ CiphertextHandle [32]byte

+ CompletedAt int64

+ CreatedAt int64

+ Epoch uint64

+ Participants []ids.NodeID

+ Result []byte

+ SessionID string

+ SharesReceived int

+ Status SessionStatus

+ Threshold int

+ type SessionStatus uint8

+ const SessionActive

+ const SessionCompleted

+ const SessionExpired

+ const SessionFailed

+ type ThresholdConfig struct

+ CKKSParams ckks.Parameters

+ LogBound uint

+ Threshold int

+ TotalParties int

+ func DefaultThresholdConfig() ThresholdConfig

+ type ThresholdDecryptor struct

+ func NewThresholdDecryptor(logger log.Logger, params ckks.Parameters, ...) (*ThresholdDecryptor, error)

+ func (d *ThresholdDecryptor) AddShare(sessionID string, partyID int, shareBytes []byte) error

+ func (d *ThresholdDecryptor) Decrypt(ctx context.Context, sessionID string, ciphertextBytes []byte) ([]byte, error)

+ func (d *ThresholdDecryptor) SetSecretKey(sk *rlwe.SecretKey)

+ type ThresholdFHEIntegration struct

+ func NewThresholdFHEIntegration(logger log.Logger, config ThresholdConfig, partyID int) (*ThresholdFHEIntegration, error)

+ func (i *ThresholdFHEIntegration) CleanupSession(sessionID string)

+ func (i *ThresholdFHEIntegration) ContributeShare(sessionID string, nodeID ids.NodeID, publicShareBytes []byte) (bool, error)

+ func (i *ThresholdFHEIntegration) GenerateShare(sessionID string) (publicShareBytes []byte, err error)

+ func (i *ThresholdFHEIntegration) GetNetworkKey() *rlwe.PublicKey

+ func (i *ThresholdFHEIntegration) GetSessionResult(sessionID string) ([]byte, bool, error)

+ func (i *ThresholdFHEIntegration) InitiateDecryption(sessionID string, requestID common.Hash, ciphertextBytes []byte) error

+ func (i *ThresholdFHEIntegration) SetNetworkKey(pk *rlwe.PublicKey)

+ func (i *ThresholdFHEIntegration) SetSecretKey(sk *rlwe.SecretKey)

+ func (i *ThresholdFHEIntegration) Start(ctx context.Context) error

+ func (i *ThresholdFHEIntegration) Stop() error

+ type TransitionState struct

+ CompletedAt int64

+ Error string

+ FromEpoch uint64

+ MigratedCount int

+ PendingRequests int

+ StartedAt int64

+ Status TransitionStatus

+ ToEpoch uint64

+ type TransitionStatus uint8

+ const TransitionCompleted

+ const TransitionDKGPhase

+ const TransitionFailed

+ const TransitionFinalizingPhase

+ const TransitionMigrationPhase

+ const TransitionPending

+ func (s TransitionStatus) String() string

+ type VerifyPermitArgs struct

+ Grantee string

+ Handle string

+ Operation uint32

+ PermitID string

+ type VerifyPermitReply struct

+ Error string

+ Expiry int64

+ Valid bool

+ type WarpHandler struct

+ func NewWarpHandler(logger log.Logger, relayer *Relayer) *WarpHandler

+ func (h *WarpHandler) HandleMessage(ctx context.Context, msg *warp.Message) error

v1.2.1

May 5, 2026

v1.2.0

May 5, 2026

Other modules containing this package

github.com/luxfi/chains/thresholdvm