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Hash-based Signatures: State and Backup Management

Document Type Active Internet-Draft (individual)
Authors Thom Wiggers , Kaveh Bashiri , Stefan Kölbl , Jim Goodman , Stavros Kousidis
Last updated 2024-02-19
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Network Working Group                                         T. Wiggers
Internet-Draft                                                  PQShield
Intended status: Informational                                K. Bashiri
Expires: 22 August 2024                                              BSI
                                                                S. Kölbl
                                                              J. Goodman
                                                   Crypto4A Technologies
                                                             S. Kousidis
                                                        19 February 2024

           Hash-based Signatures: State and Backup Management


   Stateful Hash-Based Signature Schemes (S-HBS) such as LMS, HSS, XMSS
   and XMSS^MT combine Merkle trees with One-Time Signatures (OTS) to
   provide signatures that are resistant against attacks using large-
   scale quantum computers.  Unlike conventional stateless digital
   signature schemes, S-HBS have a state to keep track of which OTS keys
   have been used, as double-signing with the same OTS key allows

   This document provides guidance and documents security considerations
   for the operational and technical aspects of deploying systems that
   rely on S-HBS.  Management of the state of the S-HBS, including any
   handling of redundant key material, is a sensitive topic, and we
   discuss some approaches to handle the associated challenges.  We also
   describe the challenges that need to be resolved before certain
   approaches should be considered.

Discussion Venues

   This note is to be removed before publishing as an RFC.

   Source for this draft and an issue tracker can be found at

Status of This Memo

   This Internet-Draft is submitted in full conformance with the
   provisions of BCP 78 and BCP 79.

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Table of Contents

   1.  Introduction  . . . . . . . . . . . . . . . . . . . . . . . .   3
   2.  Conventions and Definitions . . . . . . . . . . . . . . . . .   4
     2.1.  Specific terminology in the context of S-HBS  . . . . . .   4
       2.1.1.  State management  . . . . . . . . . . . . . . . . . .   4
       2.1.2.  Backup management . . . . . . . . . . . . . . . . . .   5
       2.1.3.  Key export, key import and key transfer . . . . . . .   5
   3.  Operational Considerations  . . . . . . . . . . . . . . . . .   6
   4.  Requirements for secure state management  . . . . . . . . . .   8
   5.  Potential Solutions . . . . . . . . . . . . . . . . . . . . .   9
     5.1.  Multiple Public Keys (SP-800-208) . . . . . . . . . . . .   9
     5.2.  Distributed Multi-trees (SP-800-208)  . . . . . . . . . .  10
     5.3.  Sectorization . . . . . . . . . . . . . . . . . . . . . .  10
     5.4.  Key/State Transfer  . . . . . . . . . . . . . . . . . . .  11
     5.5.  Key Rotation  . . . . . . . . . . . . . . . . . . . . . .  12
     5.6.  Variable-length Signature Chains  . . . . . . . . . . . .  12
     5.7.  Pre-assigning States  . . . . . . . . . . . . . . . . . .  13
     5.8.  Time-based State Management . . . . . . . . . . . . . . .  13
   6.  Backup management beyond NIST SP-800-208  . . . . . . . . . .  15
   7.  Security Considerations . . . . . . . . . . . . . . . . . . .  17
   8.  IANA Considerations . . . . . . . . . . . . . . . . . . . . .  17

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   9.  References  . . . . . . . . . . . . . . . . . . . . . . . . .  17
     9.1.  Normative References  . . . . . . . . . . . . . . . . . .  17
     9.2.  Informative References  . . . . . . . . . . . . . . . . .  18
   Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . .  19
   Contributors  . . . . . . . . . . . . . . . . . . . . . . . . . .  19
   Authors' Addresses  . . . . . . . . . . . . . . . . . . . . . . .  20

1.  Introduction

   Stateful Hash-Based Signature Schemes (S-HBS) such as LMS, HSS, XMSS
   and XMSS^MT combine Merkle trees with One-Time Signatures (OTS) in
   order to provide digital signature schemes that remain secure even
   when large-scale quantum computers become available.  Their theoretic
   security is well understood and depends only on the security of the
   underlying hash function.  As such, they can serve as an important
   building block for quantum-resistant information and communication
   technology.  S-HBS are specified in [RFC8391], [RFC8554], and NIST

   The private key of an S-HBS is a finite collection of OTS keys and an
   associated data structure which keeps track of which OTS keys have
   been used.  This data structure is typically a simple counter and
   often called an index; we refer to it as the *state* of the private
   key.  Each S-HBS private key can be used to sign a finite number of
   messages, and the state must be updated with each generated

   One must not reuse any OTS key that is part of an S-HBS private key.
   If an attacker is able to obtain signatures for two different
   messages created using the same OTS key, it is computationally
   feasible for that attacker to create forgeries [BH16].  As noted in
   [MCGREW] and [ETSI-TR-103-692], extreme care should be taken in order
   to avoid the risk that an OTS key will be reused accidentally.

   The statefulness of S-HBS leads to significant challenges in

   *  Implementers must ensure that each creation of a signature updates
      the state correctly.

   *  If the S-HBS private key is distributed to multiple signers at the
      same time, implementers must ensure that they never use the same
      OTS key.  This may require synchronization between all signers.

   *  If key backups are required, implementers must ensure that any
      backup mechanism can not lead to re-using a previously used OTS

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   These issues lead to new requirements that most developers will not
   be familiar with and that require careful handling in practice.  Due
   to these challenges, most applications should use stateless
   alternatives like SLH-DSA [FIPS205] instead.  However, if
   performance, signature or key sizes of stateless alternatives are
   prohibitive, and the specific use case allows a very tight control of
   the signing environment, using S-HBS may be an appropriate solution.
   It seems likely that in many scenarios, this will only be possible
   when using purpose-designed hardware, such as hardware-security

   The purpose of this document is to present, recall, and discuss
   various strategies for a correct state and backup management for

2.  Conventions and Definitions

   The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
   "OPTIONAL" in this document are to be interpreted as described in
   BCP 14 [RFC2119] [RFC8174] when, and only when, they appear in all
   capitals, as shown here.

2.1.  Specific terminology in the context of S-HBS

   In this subsection we specify certain notions which are important in
   the context of S-HBS.

2.1.1.  State management

   In this document _state management_ refers to the handling and
   implementation of the state of the private key.

   This includes mechanisms, which aim:

   *  to securely update the state after each signature,

   *  to set up S-HBS with a split state and/or private key, so that
      signatures can be generated from either part without risk of state

   *  to enable effective but secure handling of private key and state
      backup material,

   *  to guarantee the availability of both the private key and its
      state across the lifetime of the key.

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   Note that in particular implementations of S-HBS, or in alternative
   signature mechanisms such as, e.g., puncturable schemes [BSW16], the
   state and private key might be inseparable.  However, even in these
   scenarios, this document's guidance should still apply.

2.1.2.  Backup management

   In order to mitigate failure of, e.g., devices storing key material
   and to facilitate other types of disaster recovery, backups of
   private keys and their associated states SHOULD be considered as part
   of a security architecture.

   In this document, _backup management_ refers to all mechanisms
   surrounding the goal to guarantee the availability of the private key
   and state, but with special care to avoid state reuse by rolling back
   to a state in which already-used OTS keys are still available.

   These mechanisms include procedures and protocols, which aim:

   *  to securely store this private key and state material outside the
      in-use signing device,

   *  to import an externally stored private key and state to a newly
      initiated signing device,

   *  allow practicing with backup recovery and to ensure backups are

   Backup management can be viewed as a more specific type of state
   management; we make this distinction to clarify the aims of our

2.1.3.  Key export, key import and key transfer

   As part of state and backup management, we will discuss mechanisms to
   export, import or transfer private key and state material.  In order
   to avoid misunderstandings we now specify these notions more

   key export  mechanism of exporting secret data, which yields
      (partial) private key and state material, from the signing device
      to external storage.  This external storage may be given in
      digital or non-digital form.

   key import  mechanism of importing secret data, which loads (partial)
      private key and state material, from external storage to the
      signing device.

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   key transfer  direct and cryptographically protected migration of
      private key and state material from one signing device to another
      signing device.

   Systems and architectures relying on key transfer are generally
   expected to require fewer operational and manually-executed steps and
   checks to avoid state reuse.

   Note that, at times, secure variants of the aforementioned primitives
   may be required (e.g., securely importing/exporting the key).  In
   these situations cryptographic mechanisms SHOULD be utilized to
   provide assurances related to the confidentiality (e.g., utilizing
   symmetric/asymmetric encryption mechanisms) and/or integrity/
   authenticity (e.g., utilizing digital signatures, hash functions, and
   keyed message authentication codes) of the associated operations.

3.  Operational Considerations

   An important aspect of the evaluation of various hash-based signature
   state and backup management options is to consider the operational
   costs associated with the option(s) being evaluated.  In the past, a
   traditional trust infrastructure solution could utilize
   straightforward archival procedures to make copies of the keys, which
   could then be distributed geographically to ensure their availability
   and deliver a sufficiently resilient solution, all the while
   enforcing whatever security protocols and procedures were required.
   Unfortunately, stateful hash-based signatures introduce an additional
   constraint in that they need to ensure the state is never re-used.
   Hence, archival procedures used for traditional trust infrastructures
   MUST be amended/redesigned to be used as viable options.

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   One of the most problematic aspects of providing a long-lived
   resilient solution is simply managing the physical media on which the
   keys/state are stored externally (i.e., outside of the signing
   device) throughout the course of their lifetime.  Physical media/
   devices degrade over time, and the more complex the media/device, the
   more likely it is to fail at some point in time (e.g., data stored on
   a CD vs. data stored on a USB drive vs. data stored in a Hardware
   Security Module).  Combine that fact with the long lifetimes
   associated with stateful hash-based signature keys (e.g., 10-20+
   years) and the difficulties associated with transferring keys between
   devices, and one finds them self with a perplexing set of challenges
   that needs to be accounted for in any state selection process of a
   proper state and backup management solution.  Compounding these
   complexities is the fact any resilient state management system SHOULD
   also provide some means to verify the integrity of these long lived
   backups to ensure they will be valid when they are required, and to
   ensure the operators know how to execute the necessary recovery

   Similarly, many of the prescribed state management options require a
   high degree of human involvement which means one SHOULD consider the
   costs associated with training the human element to ensure processes
   and procedures are adhered to and failures caught early and corrected
   before a catastrophic loss of security can occur (e.g., accidentally
   instantiating multiple instances of a stateful hash-based signature
   key/state).  Note that training is not a fixed one-time cost either
   as long lifetimes will necessitate succession planning amongst the
   human element, and training of each successive generation of
   participants.  Mechanisms also SHOULD be put in place to mitigate the
   ever-present insider threat via mechanisms such as M-of-N controls,
   ensuring least-privileges amongst participants, and enforcing a
   segregation of duties to ensure multiple parties are required to
   collude to undermine a solution's security.  Note that the
   segregation of duties MUST persist across successive generations to
   ensure participants do not acquire multiple roles over time, thereby
   undermining the intended segregation.

   Lastly, costs associated with any external dependencies required by a
   particular solution (e.g., access to a public ledger or transparency
   log, providing accurate time references and synchronization
   mechanisms, access to attestation facilities, etc.)  MUST be
   accounted for as well, particularly if a system is operating in an
   offline mode that makes delivering these additional capabilities all
   the more complicated and expensive.

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4.  Requirements for secure state management

   A system deploying S-HBS SHOULD fulfill certain requirements to allow
   securely handling the state.  The system MUST ensure that no two
   signing operations can ever be issued from the same state.  In
   addition, the generation of a signature and update of the state
   SHOULD appear to be an _atomic transaction_. This means that the
   system MUST NOT release a signature without irrevocably and correctly
   updating the state.

   These requirements impose significant restrictions on the underlying
   technical approach and a careful implementation of how the state will
   be updated or synchronized.  The abstraction layers of modern systems
   can make it particularly difficult to guarantee that no two versions
   of the same state are present.  The main concerns here are

   *  how the actual storage for the state is implemented,

   *  how it is modified,

   *  how an accidental/intentional failure/glitch might affect the
      state security, and

   *  cloning.

   A system may have a version of the private key stored in non-volatile
   memory (e.g. a disk) and will load it into volatile memory (e.g.
   RAM) while processing.  Here, an implementer MUST ensure that these
   are always perfectly synchronized [MCGREW].  This can be particularly
   challenging if there are additional abstraction layers present in the
   system, like additional caches which may affect reading/writing the
   state and its potential existence in multiple locations.

   Cloning is another concern, as it can easily lead to re-using the
   same state.  This can happen for instance if a process which issues a
   signing operation is forked, and no proper synchronization is
   enforced in the implementation to guarantee correct state update.
   Virtual machine (VM) cloning is another potential security risk here,
   as both backing up a VM into non-volatile memory or live cloning of a
   VM can easily lead to a state re-use [MCGREW].  With users shifting
   workloads to cloud service providers, the issue of VM cloning may
   become more prevalent.

   Using dedicated cryptographic hardware is RECOMMENDED to enforce
   these requirements, ensure correct behavior and handle the complexity
   of state management.  In particular, this enables implementing
   rollback resistant counters which can be difficult to achieve in a
   software-only fashion.

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   On the verifier side, no state management is required.  However, the
   verifier needs to trust the signer to not have re-used the state.  A
   verifier MAY want to check that no state re-use happened in the past
   by a signer, before accepting a signature.

   In practice, this can be done if the verifier has access to all
   signatures issued by the signer.  As the signatures contain the index
   of the OTS key used, detecting if an index was used more than once
   becomes trivial.  In practice, such a (public) data structure which
   contains all signatures MAY already be present in some use cases
   (e.g. certificate transparency [RFC9162]) or could be built.  It is
   worth noting that while trusting the signer to not re-use the state
   is a strong assumption, other signature schemes like ECDSA introduce
   similar assumptions for the verifier, by requiring the signer to
   never re-use the nonce.

5.  Potential Solutions

   A variety of potential solutions have been proposed both within the
   [SP-800-208] specification, as well as from external sources.  This
   section describes a number of approaches and their potential

5.1.  Multiple Public Keys (SP-800-208)

   The [SP-800-208] proposes generating multiple S-HBS keypairs and
   configuring devices and clients to accept signatures created by any
   of these keys.

   This negatively impacts one of the advantages of using S-HBS by
   increasing the public key footprint within the client, which can be
   problematic if it has limited public key storage capacity.
   [SP-800-208] addresses this concern by suggesting using a mechanism
   such as that proposed in [RFC8649] to update the stored public key by
   having the current key endorse the next key that is to be installed.
   Unfortunately, for many constrained devices the public key is
   embedded in immutable ROM or fuses due to security reasons, so it
   cannot be updated in this manner.

   The proposal of using multiple S-HBS keypairs for a single instance
   also generates questions as to how to establish that approach in
   existing public key infrastructures.  For example, issueing multiple
   certificates adds the storage needs of the certificate material to
   the public key footprint.  In order to alternatively issue multiple
   public keys encoded inside a single certificate one would need a
   standardized format if interoperability is a concern.

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5.2.  Distributed Multi-trees (SP-800-208)

   The [SP-800-208] also proposes creating multiple S-HBS keys across
   multiple cryptographic modules using a distributed multi-tree
   approach that is a variant of the standard hyper-tree based S-HBS
   schemes HSS and XMSS^MT.  In this approach trees are instantiated on
   a root device (HSM_root), as well as one or more subordinate devices
   (HSM_(sub[i])), and the root tree is used to sign the root nodes of
   the subordinate trees to synthesize a multi-level S-HBS key.  The
   root device is only ever used to sign subordinate device root nodes,
   while the subordinate device(s) is(are) used to sign messages.  This
   is relatively straightforward to do using HSS, and [SP-800-208]
   describes the necessary algorithmic modifications when using XMSS^MT.

   One drawback of this approach is the increased signature size as an
   additional OTS needs to be generated, effectively doubling the
   overall signature size.  Another concern is the single point of
   failure nature of relying on the root tree module to sign all of the
   subordinate trees; if the root tree device fails then no new
   subordinate trees can be signed.  [SP-800-208] suggested that as many
   subordinate trees as possible be generated during the initial root
   key generation and subordinate-signing procedure.  Unfortunately,
   this can incur a large capital expenditure to procure all of the
   necessary devices, many of which may not be used for a long period of
   time, if at all.  The subordinate tree root node signing process MUST
   also be carefully managed to ensure top level trees are only ever
   used to sign the root nodes of trusted/approved subordinate trees to
   ensure that no malicious signing request is accepted, which would
   effectively give a rogue entity the ability to generate valid
   signatures, thereby undermining the security of the entire system.

   The [SP-800-208] also suggests combining distributed multi-trees with
   multiple root public keys as a means to mitigate some of the concerns
   regarding having a single point of failure in the root tree.
   However, even if a system operator does everything right, use cases
   with exceptionally long lifetimes of 10-20+ years (e.g., automotive
   and aerospace/satellite applications) will require system operators
   to rely on devices well beyond their expected lifetimes of 5-10
   years, which may constitute an unacceptable business risk.

5.3.  Sectorization

   Distributed multi-trees attempt to partition a S-HBS signing space
   amongst multiple cryptographic modules by breaking up the signing
   space along the boundaries of the subordinate trees generated during
   the multi-tree key generation process.  An alternative approach would
   be to use only a single tree, and partition its signature space along
   some power-of-2 less than the total number of leaves in the tree

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   (e.g., 2^s for a tree of height h > s), creating N = 2^(h-s)
   partitions or sectors, which are instantiated as N height-s Merkle
   trees whose root nodes are considered interior nodes of the overall
   height-h Merkle tree.  Hence, there is no additional OTS required to
   sign their root nodes; their values are used as-is in the underlying
   S-HBS scheme's tree ascent mechanism, yielding a common public key
   (i.e., root node) for all sectors.  Care MUST be taken to ensure that
   each sector uses the same root tree identifier (i.e., the "I" value
   for HSS/LMS and "root" value for XMSS/XMSS^MT).

   Each of the N sectors can be generated with a unique seed value to
   cryptographically isolate the sectors from each other, though this
   REQUIRES that the path information for each sector's root node (i.e.,
   all off-path nodes between the sector root node and the top level
   node value) be stored with each sector's private key at key
   generation time since a sector will not know the seed information
   required to compute any of the other sectors' root nodes during the
   tree ascent phase of a signature generation operation.  During
   signature generation the signer appends the stored path information
   to the path information it computes to ascend from the leaf OTS to
   the sector's root node (which it can compute given that it knows its
   own seed value).

   Hence, sectorized key generation results in a single public key value
   and 2^(h-s) private key values, each capable of generating 2^s
   signatures, after which the sectorized key is exhausted.

   In addition to avoiding an increased signature size; when unique
   seeds are utilized sectorization breaks a given S-HBS key/state into
   multiple independent fragments that can be managed as independent
   objects.  As a result, system operators MAY distribute sectors to
   multiple cryptographic devices, allowing for performance scaling, and
   resiliency/availability, while only requiring them to manage the
   uniqueness of each sector instead of having to co-ordinate state
   usage between devices since in this scenario a sector cannot generate
   signatures from another sector's signature space.

5.4.  Key/State Transfer

   S-HBS key/state transfer between cryptographic modules entails having
   a means to migrate one instance of a S-HBS key/state on a source
   device to a separate destination device, while ensuring that any copy
   of the key/state is deleted from the source device.

   This capability may help alleviate the aforementioned concern
   regarding operating devices beyond their expected lifetimes by
   allowing operators to migrate S-HBS key/state to a newer device when
   the original device begins to approach its end-of-life.  However, it

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   still leaves the operator vulnerable to having the source device fail
   before the key/state can be transferred, effectively causing the loss
   of the key/state.  Hence, it will not be of much help addressing the
   single point of failure issue identified for root trees, but may be
   useful for managing subordinate trees.

   A more elaborate variant of key transfer, going beyond what
   [SP-800-208] allows, can be found described in Section 6 where key
   transfer is accomplished using a two-step export and import process
   with hash-based transfer validation to yield a more robust transfer

5.5.  Key Rotation

   Key rotation, such as that defined in [RFC8649], would generate new
   S-HBS keys on an as-needed basis, and provide a means to transition
   the system on to using this new S-HBS key, while generating the next
   key in the chain in preparation of a future rotation/update.
   However, this just shifts the problem to the PKI and certificate

   Key rotation is not foolproof since in most use cases it will require
   redundancy to ensure there is at least one S-HBS signing key
   available to attest to newly generated keys.  In addition, for many
   applications the device keys cannot be updated due to engineering
   constraints or security reasons.

5.6.  Variable-length Signature Chains

   A variant of the key rotation approach is to simply have an available
   signing tree endorse a new subordinate tree when it is about to
   become exhausted (e.g., use its final OTS to sign the root node of a
   new subordinate tree, creating a {n+1}-layer multi-tree from a {n}-
   layer multi-tree).  This process can in theory be repeated as many
   times as necessary.  However, this entails having a multi-tree scheme
   with a variable number of levels, and hence, variable length

   In addition to departing quite significantly from the current S-HBS
   specifications and [SP-800-208], this approach has a number of
   significant challenges on both the engineering and operational
   fronts.  Firstly, the variable length nature of the signature can
   lead to variable length verification of signatures, which may cause
   significant issues for use cases with strict time constraints (e.g.,
   secure booting of a semiconductor device).  From an operational
   perspective, the ability of a subordinate tree to sign either
   messages or new subordinate trees leads to severe security
   implications as the rigor around authorizing those two types of

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   operations will vary dramatically, leading to either a much more
   onerous message signing operation, or a much more risky subordinate
   tree signing operation.  This may put the system operator in an
   untenable situation where no users are satisfied with the resulting
   solution, and hence, SHOULD NOT be considered as a viable solution.

5.7.  Pre-assigning States

   In some applications, individual one-time signatures (or states) can
   be pre-assigned to the to-be-signed objects.  This may for example be
   possible if the signed objects are monotonically increasingly
   numbered.  One example of such a use case may be software signing.
   This solution basically externalizes the state management to the to-
   be signed messages.

   Expanding on the given example, for software that is released with
   strictly increasing, simple single-position version numbers (i.e.,
   versions 1, 2, 3...), this can be trivially implemented.  As versions
   have a one-to-one correspondence to an S-HBS signing state, operators
   MUST ensure that versions can only be minted a single time.  This MAY
   require skipping version numbers if a release process failed, to
   avoid double-signing.

   This scheme can be adapted to more complicated release schemes: for
   example, minor update-releases 1.0 to 1.99 can be accommodated by
   assigning signatures 1-100 for these version numbers, while release
   2.0-2.99 would get signatures 101-200.  The assignments MUST be fixed
   as the scheme is set up, and operators SHOULD take into account that
   they are strictly limiting the number of update releases.  In the
   described solution to state management, one MUST move up a major
   release number after 99 minor releases, even if this would break,
   e.g., semantic versioning conventions.

   A variant of pre-assigning signatures is doing this on the basis of
   time, which we describe in the next section.

5.8.  Time-based State Management

   As a variant of pre-assigning one-time signatures based on external
   counters, it is in theory possible to base the selection of one-time
   signature indexes on the current date and time.  For example, if a
   given S-HBS instance offers 1024 total signatures, they could be
   broken up into 8 groups of 128 OTS instances each, with the first 128
   allowed to be used in the first time window, the second 128 in the
   second time window, and so on, until the signature space is
   effectively exhausted after 8 time windows.  Note that a time-based
   approach to state management will "waste" any OTS keys that are
   unused in past time windows.  One MUST NOT attempt to use these keys

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   after the time window has gone by.

   Any time-based approach has a very strict reliance on accurate time-
   keeping and synchronization of clocks.  In particular, we identify
   that at least the following engineering-related challenges need to be

   *  Signing devices MUST have accurate timekeeping (which is a very
      challenging engineering problem [XKCD1883], [XKCD2867],

   *  Time on signing devices MUST NOT be allowed to ever move
      backwards, as this can cause double-signing.

   *  Within time windows, signers MUST track the number of signatures
      produced to ensure it does not exceed the number allowed within
      the window.

   *  Signing devices MUST still operate consistently with the
      requirements of state keeping for S-HBS: the signature index
      within a time window SHOULD still appear to be updated atomically,
      and signatures MUST NOT be released before state changes have been

   *  A system SHOULD be robust against exhaustion of the number of
      signatures available in a time window, as in this case it is
      REQUIRED to wait until the next time window starts before new
      messages can be signed.

   *  Time on signing devices SHOULD NOT be allowed to be moved forward
      maliciously or accidentally, which would allow for a simple
      denial-of-service attack by skipping over portions of the
      signature space.

   *  If a signing device needs to be replaced, the replacement device
      MUST be set up with its time in sync with or ahead of the device
      it is to replace.  This implies the current time on signing
      devices SHOULD be continuously recorded.

   *  Rate limiting MAY need to be considered, as exhausting the
      available signatures in a given time window may otherwise be easy.

   *  It MAY be necessary for signers to keep a separate clock for time-
      based state management, and one for not necessarily monotonically
      increasing "wall-time", e.g., if signed artifacts are expected to
      be time-stamped with real-world time.

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   If these concerns can not be sufficiently addressed, time-based state
   management as described in this paragraph SHOULD NOT be used.  Note
   that this list of concerns is not exhaustive, and other, unmentioned,
   concerns may also be relevant to the security of a time-based

   Time-based systems can be backed up by simply recording the private
   keys and the configuration of the time windows.  In case of loss of a
   signing device, a time-based state management system can be recovered
   by using this information to bring online a new device in the next
   time window.  This approach MAY also be used as a recovery mechanism
   in the case of (suspected) state consistency problems during a time
   window.  However, the operator MUST NOT allow new signatures to be
   produced before the new time window starts, unless they know the
   exact state at which the previous device became unavailable and are
   able to set up the new device accordingly.  Waiting until the start
   of the next time window avoids double signing, as the OTS keys
   assigned to future time windows are guaranteed to have not yet been
   used.  However, this might incur significant downtime of the signing
   systems.  Downtime MAY be avoided by forcibly moving the signing
   device to the next time window by incrementing its clock; however,
   this induced clock drift will then need to be accounted for in the
   future.  If clock drift is to be avoided, this approach SHOULD
   account for availability considerations.

6.  Backup management beyond NIST SP-800-208

   In this section, an alternative backup mechanism for S-HBS is
   presented in a generic form, which makes the strategy applicable for
   both multi-tree instances XMSS^MT and HSS.  However, following the
   same arguments as in Section 5.3, with minor modifications, the
   presented strategy is also applicable for single-tree instances such
   as XMSS and LMS.

   The strategy presented in this section builds upon the multi-tree
   variant approach from [SP-800-208], and aims to mitigate its
   limitations described in Section 5.2.  Thus, it is assumed that
   already a top-level Merkle tree (for signing the root-nodes of sub-
   trees) and several bottom-level Merkle trees (for signing messages)
   are initiated.  These bottom-level trees MAY be implemented on
   different hardware modules in order to obtain redundancy and improve
   availability.  Let R be the number of these already initiated bottom-
   level trees.  Let h_0 be the height of the top-level-tree.  It is
   assumed that R + 1 is strictly smaller than 2^(h_0), the number of
   leaves of the top-level tree.

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   In this new strategy, after the completed key generation procedure
   from the multi-tree variant approach from [SP-800-208], further
   bottom-level trees are generated, one by one, in one of the hardware
   modules.  These new bottom-level trees are each generated from a
   different seed, which is chosen uniformly at random.  For the sake of
   clarity, let us introduce some notation:

   *  S denotes the number of these newly generated bottom-level trees.
      Note that at most 2^(h_0) - R new bottom-level trees can be
      generated, i.e. S is lower or equal to 2^(h_0) - R.  In the
      following we suppose that S is _strictly smaller_ than 2^(h_0) -

   *  I_new denotes the set of indices that belong to these newly
      generated bottom-level trees, i.e. I_new = {R, R+1, ..., R+S-1}.

   For each new bottom-level tree, after it has been generated, the
   following steps MUST be performed:

   *  sign the corresponding root node with an unused OTS key from the
      top-level tree,

   *  securely _key export_ (as decribed in Section 2.1.3) the seed,
      which was used to generate the bottom-level tree,

   *  export the signature of the root node, the corresponding OTS key
      index and finally the hash of the seed, using appropriate domain
      separation (i.e. ensuring there is no domain overlap with the
      hashes in the S-HBS scheme, and the hash of the seed includes the
      public key and leaf index to mitigate multi-target attacks),

   *  irreversibly delete the seed and the bottom-level tree from the
      hardware module.

   The newly generated bottom-level trees (i.e. those bottom-level
   trees, whose indices belong to I_new) are only used in order to
   guarantee availability in the _worst-case scenario_, where at the
   same time both

   *  none of the R bottom-level Merkle trees (which were generated
      according to the multi-tree variant approach from [SP-800-208])
      are available for signing messages and

   *  the top-level Merkle tree (which is used for signing the root-
      nodes of sub-trees) is also not available any more.

   This scenario may, for example, happen if all hardware modules are
   broken at the same time.

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   As soon as this worst-case scenario occurs, the newly generated
   bottom-level trees (i.e. those bottom-level trees, whose indices
   belong to I_new) need to be initiated in order to ensure
   availability.  In order to do this the following steps MUST be

   *  initiate a new hardware module

   *  securely _key import_ (as decribed in Section 2.1.3) the first
      unused seed into this hardware module

   *  generate the bottom-level tree corresponding to the seed

   *  irreversibly delete the seed from the backup medium

   *  perform a correctness check by letting the hardware module output
      the hash of the seed

   Now this bottom-level tree can be used to sign messages.  As soon as
   no more OTS on the bottom-level tree are available or as soon as the
   hardware module is broken, the above steps with a new seed from the
   backup medium can be repeated.

   Note that the resulting signatures generated from these backed up
   seeds do not require any special processing on the verifier side.
   The signature stored alongside the backed up seed, and the signature
   generated from the bottom-level trees created from the backed up seed
   can be combined to match the format of a signature over the complete

7.  Security Considerations

   Further security considerations, which are not already covered in
   this document, are given in [SP-800-208], [MCGREW], [FIPS205],
   [RFC8391] and [RFC8554].

8.  IANA Considerations

   This document has no IANA actions.

9.  References

9.1.  Normative References

   [RFC2119]  Bradner, S., "Key words for use in RFCs to Indicate
              Requirement Levels", BCP 14, RFC 2119,
              DOI 10.17487/RFC2119, March 1997,

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   [RFC8174]  Leiba, B., "Ambiguity of Uppercase vs Lowercase in RFC
              2119 Key Words", BCP 14, RFC 8174, DOI 10.17487/RFC8174,
              May 2017, <>.

9.2.  Informative References

   [BH16]     Bruinderink, L. and A. Hülsing, "Oops, I did it again –
              Security of One-Time Signatures under Two-Message
              Attacks.", 2016, <>.

   [BSW16]    Bellare, M., Stepanovss, I., and B. Waters, "New Negative
              Results on Differing-Inputs Obfuscation", n.d.,

              European Telecommunications Standards Institute (ETSI),
              "State management for stateful authentication mechanisms",
              November 2021, <

   [FIPS205]  National Institute of Standards and Technology, "FIPS 205
              (draft): Stateless Hash-Based Digital Signature Standard",
              Federal Information Processing Standards , 24 August 2023,

   [HBSX509]  Bashiri, K., Fluhrer, S., Gazdag, S., Van Geest, D., and
              S. Kousidis, "Internet X.509 Public Key Infrastructure:
              Algorithm Identifiers for Hash-based Signatures", n.d.,

   [MCGREW]   McGrew, D., Kampanakis, P., Fluhrer, S., Gazdag, S.,
              Butin, D., and J. Buchmann, "State Management for Hash-
              Based Signatures", 2 November 2016,

   [RFC8391]  Huelsing, A., Butin, D., Gazdag, S., Rijneveld, J., and A.
              Mohaisen, "XMSS: eXtended Merkle Signature Scheme",
              RFC 8391, DOI 10.17487/RFC8391, May 2018,

   [RFC8411]  Schaad, J. and R. Andrews, "IANA Registration for the
              Cryptographic Algorithm Object Identifier Range",
              RFC 8411, DOI 10.17487/RFC8411, August 2018,

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   [RFC8554]  McGrew, D., Curcio, M., and S. Fluhrer, "Leighton-Micali
              Hash-Based Signatures", RFC 8554, DOI 10.17487/RFC8554,
              April 2019, <>.

   [RFC8649]  Housley, R., "Hash Of Root Key Certificate Extension",
              RFC 8649, DOI 10.17487/RFC8649, August 2019,

   [RFC9162]  Laurie, B., Messeri, E., and R. Stradling, "Certificate
              Transparency Version 2.0", RFC 9162, DOI 10.17487/RFC9162,
              December 2021, <>.

              Cooper, D., Apon, D., Dang, Q., Davidson, M., Dworkin, M.,
              and C. Miller, "Recommendation for Stateful Hash-Based
              Signature Schemes", NIST Special Publication 800-208 ,
              October 2020, <>.

              Visée, T., "Falsehoods programmers believe about time",
              n.d., <

   [XKCD1883] Munroe, R., "xkcd: Timezones", n.d.,

   [XKCD2867] Munroe, R., "xkcd: DateTime", n.d.,


   This document was inspired by discussions at the 2nd Oxford Post-
   Quantum Cryptography Summit 2023.

   We gratefully acknowledge Melissa Azouaoui for her input to this

   The abstract and the introduction are based on the introduction in
   [HBSX509].  Thanks go to the authors of this document.  "Copying
   always makes things easier and less error-prone" - [RFC8411].


   *  Jeff Andersen (Google)

   *  Bruno Couillard (Crypto4A Technologies)

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Authors' Addresses

   Thom Wiggers

   Kaveh Bashiri

   Stefan Kölbl

   Jim Goodman
   Crypto4A Technologies

   Stavros Kousidis

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