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Introduction This document specifies the conventions for using the Hierarchical Signature System (HSS) / Leighton-Micali Signature (LMS) hash-based signature algorithm with the Cryptographic Message Syntax (CMS) signed-data content type. The LMS system provides a one-time digital signature that is a variant of the Merkle Tree Signature (MTS) scheme. The HSS is built on top of the LMS system to efficiently scale for a larger number of signatures. The HSS/LMS algorithm is one form of hash-based digital signature, and it is described in . The HSS/LMS signature algorithm can only be used for a fixed number of signing operations with a given private key, and the number of signing operations depends upon the size of the tree. The HSS/LMS signature algorithm uses small public keys, and it has low computational cost; however, the signatures are quite large. The HSS/LMS private key can be very small when the signer is willing to perform additional computation at signing time; alternatively, the private key can consume additional memory and provide a faster signing time. The HSS/LMS signatures are defined in . Currently, parameter sets are defined that use SHA-256 and SHAKE256 . ASN.1 CMS values are generated using ASN.1 , using the Basic Encoding Rules (BER) and the Distinguished Encoding Rules (DER) . Terminology The key words " MUST ", " MUST NOT ", " REQUIRED ", " SHALL ", " SHALL NOT ", " SHOULD ", " SHOULD NOT ", " RECOMMENDED ", " NOT RECOMMENDED ", " MAY ", and " OPTIONAL " in this document are to be interpreted as described in BCP 14 when, and only when, they appear in all capitals, as shown here. Motivation Advances in cryptanalysis and progress in the development of quantum computers pose a future threat to widely deployed digital signature algorithms. As a result, there is a need to prepare for a day when cryptosystems such as RSA and DSA that use discrete logarithms and factoring cannot be depended upon. If cryptographically relevant quantum computers (CRQCs) are ever built, they will be able to break many of the public key cryptosystems currently in use. A post-quantum cryptosystem is a system that is secure against quantum computers that have more than a trivial number of quantum bits (qubits). It is open to conjecture when it will be feasible to build such computers; however, RSA, DSA, Elliptic Curve Digital Signature Algorithm (ECDSA), and Edwards-curve Digital Signature Algorithm (EdDSA) are all vulnerable if CRQCs are ever developed. Since the HSS/LMS signature algorithm does not depend on the difficulty of discrete logarithms or factoring, but on a second-preimage-resistant cryptographic hash function, the HSS/LMS signature algorithm is considered to be post-quantum secure. One use of post-quantum-secure signatures is the protection of software updates, perhaps using the format described in , to enable deployment of software that implements new cryptosystems. Changes Since RFC 8708 At the time RFC 8708 was published, there were no plans to put an HSS/LMS public key in a certificate. The expectation was that the HSS/LMS public key would be distributed by some other means. Today, there are plans to put an HSS/LMS public key in a certificate . The KEY field of the pk-HSS-LMS-HashSig definition in the ASN.1 module does not come into play when using HSS/LMS signatures in the CMS; however, it needs to be consistent with the conventions for carrying an HSS/LMS public key in a certificate. The pk-HSS-LMS-HashSig definition is updated to reflect no ASN.1 wrapping for the public key. These changes resolve and . Additional HSS/LMS tree sizes have been defined. The list in was expanded to include the recently defined ones. Additional LM-OTS Signatures have been defined. The list in was expanded to include the recently defined ones. More detail has been provided in regarding allowed values in the X.509 certificate key usage extension for an HSS/LMS public key. HSS/LMS Hash-Based Signature Algorithm Overview The Merkle Tree Signature (MTS) scheme is a method for signing a large but fixed number of messages. An MTS system depends on a one-time signature method and a collision-resistant hash function. This specification makes use of the hash-based algorithm specified in , which is the Leighton and Micali adaptation of the original Lamport-Diffie-Winternitz-Merkle one-time signature system . As implied by the name, the hash-based signature algorithm depends on a collision-resistant hash function. The hash-based signature algorithm specified in uses only the SHA-256 one-way hash function , but it establishes an IANA registry to permit the registration of additional one-way hash functions in the future. Hierarchical Signature System (HSS) The MTS system specified in uses a hierarchy of trees. The N-time Hierarchical Signature System (HSS) allows subordinate trees to be generated when needed by the signer. Otherwise, generation of the entire tree might take weeks or longer. An HSS signature as specified in carries the number of signed public keys (Nspk), followed by that number of signed public keys, followed by the LMS signature as described in . The public key for the topmost LMS tree is the public key of the HSS system. The LMS private key in the parent tree signs the LMS public key in the child tree, and the LMS private key in the bottom-most tree signs the actual message. The signature over the public key and the signature over the actual message are LMS signatures as described in . The elements of the HSS signature value for a standalone tree (a top tree with no children) can be summarized as: u32str(0) || lms_signature /* signature of message */ where, u32str() and || are used as defined in . The elements of the HSS signature value for a tree with Nspk signed public keys can be summarized as: u32str(Nspk) || signed_public_key[0] || signed_public_key[1] || ... signed_public_key[Nspk-2] || signed_public_key[Nspk-1] || lms_signature /* signature of message */ where, as defined in , the signed_public_key structure contains the lms_signature over the public key, followed by the public key itself. Note that Nspk is the number of levels in the hierarchy of trees minus 1. Leighton-Micali Signature (LMS) Each tree in the system specified in uses the Leighton-Micali Signature (LMS) system. LMS systems have two parameters. The first parameter is the height of the tree, h, which is the number of levels in the tree minus one. The specification supports five values for this parameter: h=5, h=10, h=15, h=20, and h=25. There are 2 h leaves in the tree. The second parameter, m, is the number of bytes output by the hash function, and it is the amount of data associated with each node in the tree. The specification supports the SHA-256 hash function , with m=32. Additional LMS Signature parameter sets have been registered at . As specified in , the LMS public key consists of four elements: the lms_algorithm_type from the list above, the otstype to identify the Leighton-Micali One-Time Signature (LM-OTS) type as discussed in , the private key identifier (I) as described in , and the m-byte string associated with the root node of the tree (T[1]). The LMS public key can be summarized as: u32str(lms_algorithm_type) || u32str(otstype) || I || T[1] As specified in , an LMS signature consists of four elements: the number of the leaf (q) associated with the LM-OTS signature value, an LM-OTS signature value as described in , a typecode indicating the particular LMS algorithm, and an array of values that is associated with the path through the tree from the leaf associated with the LM-OTS signature value to the root. The array of values contains the siblings of the nodes on the path from the leaf to the root but does not contain the nodes on the path itself. The array for a tree with height h will have h values. The first value is the sibling of the leaf, the next value is the sibling of the parent of the leaf, and so on up the path to the root. The four elements of the LMS signature value can be summarized as: u32str(q) || ots_signature || u32str(type) || path[0] || path[1] || ... || path[h-1] Leighton-Micali One-Time Signature (LM-OTS) Algorithm Merkle Tree Signatures (MTS) depend on a one-time signature method, and specifies the use of the LM-OTS, which has five parameters:
n:
The length in bytes of the hash function output.
H:
A preimage-resistant hash function that accepts byte strings of any length and returns an n-byte string.
w:
The width in bits of the Winternitz coefficients. supports four values for this parameter: w=1, w=2, w=4, and w=8.
p:
The number of n-byte string elements that make up the LM-OTS signature value.
ls:
The number of bits that are left-shifted in the final step of the checksum function, which is defined in .
The values of p and ls are dependent on the choices of the parameters n and w, as described in . specifies four LM-OTS variants (as listed in Table 1 of ). Additional LM-OTS Signature parameter sets have been registered at . Signing involves the generation of C, an n-byte random value. The LM-OTS signature value can be summarized as the identifier of the LM-OTS variant, the random value, and a sequence of hash values (y[0] through y[p-1]) that correspond to the elements of the public key, as described in : u32str(otstype) || C || y[0] || ... || y[p-1] Algorithm Identifiers and Parameters The algorithm identifier for an HSS/LMS hash-based signature is: id-alg-hss-lms-hashsig OBJECT IDENTIFIER ::= { iso(1) member-body(2) us(840) rsadsi(113549) pkcs(1) pkcs-9(9) smime(16) alg(3) 17 } When this object identifier is used for an HSS/LMS signature, the AlgorithmIdentifier parameters field MUST be absent (that is, the parameters are not present, and the parameters are not set to NULL). In the CMS, the HSS/LMS signature value is a large OCTET STRING. The HSS/LMS signature generation is described in of this document. The signature format is designed for easy parsing. The HSS, LMS, and LM-OTS components of the signature value each include a counter and a typecode that indirectly provide all of the information that is needed to parse the value during signature validation. The signature value identifies the hash function used in the HSS/LMS tree. HSS/LMS Public Key Identifier The AlgorithmIdentifier for an HSS/LMS public key uses the id-alg-hss-lms-hashsig object identifier, and the parameters field MUST be absent. When this AlgorithmIdentifier appears in the SubjectPublicKeyInfo field of a certification authority (CA) X.509 certificate , the certificate key usage extension MUST contain at least one of the following values: digitalSignature, nonRepudiation, keyCertSign, and cRLSign. However, it MUST NOT contain other values. When this AlgorithmIdentifier appears in the SubjectPublicKeyInfo field of an end-entity X.509 certificate , the certificate key usage extension MUST contain at least one of the following: digitalSignature, nonRepudiation, or cRLSign. However, it MUST NOT contain other values. pk-HSS-LMS-HashSig PUBLIC-KEY ::= { IDENTIFIER id-alg-hss-lms-hashsig -- KEY no ASN.1 wrapping -- PARAMS ARE absent CERT-KEY-USAGE { digitalSignature, nonRepudiation, keyCertSign, cRLSign } } HSS-LMS-HashSig-PublicKey ::= OCTET STRING The id-alg-hss-lms-hashsig algorithm identifier is also referred to as id-alg-mts-hashsig. This synonym is based on the terminology used in an early draft version of the document that became . When the public key appears outside a certificate, it is an OCTET STRING. Like the signature format, it is designed for easy parsing. The value is the number of levels in the public key, L, followed by the LMS public key. The HSS/LMS public key value can be described as: u32str(L) || lms_public_key The public key for the topmost LMS tree is the public key of the HSS system. When L=1, the HSS system is a single tree. Signed-Data Conventions As specified in , the digital signature is produced from the message digest and the signer's private key. The signature is computed over different values depending on whether signed attributes are absent or present. When signed attributes are absent, the HSS/LMS signature is computed over the content. When signed attributes are present, a hash is computed over the content using the same hash function that is used in the HSS/LMS tree, then a message-digest attribute is constructed with the hash of the content, and then the HSS/LMS signature is computed over the DER-encoded set of signed attributes (which MUST include a content-type attribute and a message-digest attribute). In summary: IF (signed attributes are absent) THEN HSS_LMS_Sign(content) ELSE message-digest attribute = Hash(content); HSS_LMS_Sign(DER(SignedAttributes)) When using , the fields in the SignerInfo are used as follows: Security Considerations Implementations MUST protect the private keys. Compromise of the private keys will result in the ability to forge signatures. Along with the private key, the implementation MUST keep track of which leaf nodes in the tree have been used. Loss of integrity of this tracking data can cause a one-time key to be used more than once. As a result, when a private key and the tracking data are stored on non-volatile media or in a virtual machine environment, failed writes, virtual machine snapshotting or cloning, and other operational concerns must be considered to ensure confidentiality and integrity. When generating an LMS key pair, an implementation MUST generate each key pair independently of all other key pairs in the HSS tree. An implementation MUST ensure that an LM-OTS private key is used to generate a signature only one time and ensure that it cannot be used for any other purpose. The generation of private keys relies on random numbers. The use of inadequate pseudorandom number generators (PRNGs) to generate these values can result in little or no security. An attacker may find it much easier to reproduce the PRNG environment that produced the keys, searching the resulting small set of possibilities, rather than brute-force searching the whole key space. The generation of quality random numbers is difficult, and offers important guidance in this area. The generation of hash-based signatures also depends on random numbers. While the consequences of an inadequate PRNG to generate these values is much less severe than in the generation of private keys, the guidance in remains important. When computing signatures, the same hash function SHOULD be used to compute the message digest of the content and the signed attributes, if they are present. IANA Considerations In the "SMI Security for S/MIME Module Identifier (1.2.840.113549.1.9.16.0)" registry, IANA has changed the reference for value 64 to this document. In the "SMI Security for S/MIME Algorithms (1.2.840.113549.1.9.16.3)" registry, IANA has changed the reference for value 17 to this document.

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