Vigil Security, LLC

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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). In addition, the algorithm identifier and public key syntax are provided. The HSS/LMS algorithm is one form of hash-based digital signature; it is described in RFC 8554.

Status of This Memo This is an Internet Standards Track document. This document is a product of the Internet Engineering Task Force (IETF). It represents the consensus of the IETF community. It has received public review and has been approved for publication by the Internet Engineering Steering Group (IESG). Further information on Internet Standards is available in Section 2 of RFC 7841. Information about the current status of this document, any errata, and how to provide feedback on it may be obtained at .

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Table of Contents

• .  Introduction
  • .  ASN.1
  • .  Terminology
  • .  Motivation
• .  HSS/LMS Hash-Based Signature Algorithm Overview
  • .  Hierarchical Signature System (HSS)
  • .  Leighton-Micali Signature (LMS)
  • .  Leighton-Micali One-Time Signature (LM-OTS) Algorithm
• .  Algorithm Identifiers and Parameters
• .  HSS/LMS Public Key Identifier
• .  Signed-Data Conventions
• .  Security Considerations
• .  IANA Considerations
• .  References
  • .  Normative References
  • .  Informative References
• .  ASN.1 Module
• Acknowledgements
• Author's Address

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 Merkle Tree Signatures (MTS). The HSS is built on top of the LMS system to efficiently scale for a larger numbers 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 currently defined to exclusively use SHA-256 .

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 Recent advances in cryptanalysis and progress in the development of quantum computers pose a 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 depend on discrete logarithms and factoring cannot be depended upon. If large-scale quantum computers are ever built, these computers 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 large-scale quantum computers are ever developed. Since the HSS/LMS signature algorithm does not depend on the difficulty of discrete logarithms or factoring, 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.

HSS/LMS Hash-Based Signature Algorithm Overview Merkle Tree Signatures (MTS) are 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. Note that 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 only the SHA-256 hash function , with m=32. As a result, the specification supports five tree sizes; they are identified as:

• LMS_SHA256_M32_H5
• LMS_SHA256_M32_H10
• LMS_SHA256_M32_H15
• LMS_SHA256_M32_H20
• LMS_SHA256_M32_H25

The specification establishes an IANA registry to permit the registration of additional hash functions and additional tree sizes in the future. 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. supports only SHA-256 , with n=32.

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 . The specification supports four LM-OTS variants:

• LMOTS_SHA256_N32_W1
• LMOTS_SHA256_N32_W2
• LMOTS_SHA256_N32_W4
• LMOTS_SHA256_N32_W8

The specification establishes an IANA registry to permit the registration of additional variants in the future. 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) pkcs9(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). The signature value is a large OCTET STRING, as 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. uses only the SHA-256 hash function , but it establishes an IANA registry to permit the registration of additional hash functions in the future.

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 an X.509 certificate , the certificate key usage extension MAY contain digitalSignature, nonRepudiation, keyCertSign, and cRLSign; however, it MUST NOT contain other values. pk-HSS-LMS-HashSig PUBLIC-KEY ::= { IDENTIFIER id-alg-hss-lms-hashsig KEY HSS-LMS-HashSig-PublicKey PARAMS ARE absent CERT-KEY-USAGE { digitalSignature, nonRepudiation, keyCertSign, cRLSign } } HSS-LMS-HashSig-PublicKey ::= OCTET STRING Note that 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 . The public key value 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 Note that 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:

• digestAlgorithm MUST contain the one-way hash function used in the HSS/LMS tree. In , SHA-256 is the only supported hash function, but other hash functions might be registered in the future. For convenience, the AlgorithmIdentifier for SHA-256 from is repeated here:

mda-sha256 DIGEST-ALGORITHM ::= { IDENTIFIER id-sha256 PARAMS TYPE NULL ARE preferredAbsent } id-sha256 OBJECT IDENTIFIER ::= { joint-iso-itu-t(2) country(16) us(840) organization(1) gov(101) csor(3) nistAlgorithms(4) hashalgs(2) 1 }

• signatureAlgorithm MUST contain id-alg-hss-lms-hashsig, and the algorithm parameters field MUST be absent.
• signature contains the single HSS signature value resulting from the signing operation as specified in .

Security Considerations Implementations MUST protect the private keys. Compromise of the private keys may 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 pseudorandom number generator (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 updated the reference for value 64 to point to this document. In the "SMI Security for S/MIME Algorithms (1.2.840.113549.1.9.16.3)" registry, IANA has updated the description for value 17 to "id-alg-hss-lms-hashsig" and updated the reference to point to this document. IANA has also added the following note to the "SMI Security for S/⁠MIME Algorithms (1.2.840.113549.1.9.16.3)" registry:

• Value 17, "id-alg-hss-lms-hashsig", is also referred to as "id-alg-mts-hashsig".

References Normative References ITU-T ITU-T This document describes the Cryptographic Message Syntax (CMS). This syntax is used to digitally sign, digest, authenticate, or encrypt arbitrary message content. [STANDARDS-TRACK] This note describes a digital-signature system based on cryptographic hash functions, following the seminal work in this area of Lamport, Diffie, Winternitz, and Merkle, as adapted by Leighton and Micali in 1995. It specifies a one-time signature scheme and a general signature scheme. These systems provide asymmetric authentication without using large integer mathematics and can achieve a high security level. They are suitable for compact implementations, are relatively simple to implement, and are naturally resistant to side-channel attacks. Unlike many other signature systems, hash-based signatures would still be secure even if it proves feasible for an attacker to build a quantum computer. This document is a product of the Crypto Forum Research Group (CFRG) in the IRTF. This has been reviewed by many researchers, both in the research group and outside of it. The Acknowledgements section lists many of them. In many standards track documents several words are used to signify the requirements in the specification. These words are often capitalized. This document defines these words as they should be interpreted in IETF documents. This document specifies an Internet Best Current Practices for the Internet Community, and requests discussion and suggestions for improvements. This memo profiles the X.509 v3 certificate and X.509 v2 certificate revocation list (CRL) for use in the Internet. An overview of this approach and model is provided as an introduction. The X.509 v3 certificate format is described in detail, with additional information regarding the format and semantics of Internet name forms. Standard certificate extensions are described and two Internet-specific extensions are defined. A set of required certificate extensions is specified. The X.509 v2 CRL format is described in detail along with standard and Internet-specific extensions. An algorithm for X.509 certification path validation is described. An ASN.1 module and examples are provided in the appendices. [STANDARDS-TRACK] RFC 2119 specifies common key words that may be used in protocol specifications. This document aims to reduce the ambiguity by clarifying that only UPPERCASE usage of the key words have the defined special meanings. National Institute of Standards and Technology (NIST) Informative References The Cryptographic Message Syntax (CMS) format, and many associated formats, are expressed using ASN.1. The current ASN.1 modules conform to the 1988 version of ASN.1. This document updates those ASN.1 modules to conform to the 2002 version of ASN.1. There are no bits-on-the-wire changes to any of the formats; this is simply a change to the syntax. This document is not an Internet Standards Track specification; it is published for informational purposes. The Cryptographic Message Syntax (CMS) format, and many associated formats, are expressed using ASN.1. The current ASN.1 modules conform to the 1988 version of ASN.1. This document updates some auxiliary ASN.1 modules to conform to the 2008 version of ASN.1; the 1988 ASN.1 modules remain the normative version. There are no bits- on-the-wire changes to any of the formats; this is simply a change to the syntax. This document is not an Internet Standards Track specification; it is published for informational purposes. This document describes the use of the Cryptographic Message Syntax (CMS) to protect firmware packages, which provide object code for one or more hardware module components. CMS is specified in RFC 3852. A digital signature is used to protect the firmware package from undetected modification and to provide data origin authentication. Encryption is optionally used to protect the firmware package from disclosure, and compression is optionally used to reduce the size of the protected firmware package. A firmware package loading receipt can optionally be generated to acknowledge the successful loading of a firmware package. Similarly, a firmware package load error report can optionally be generated to convey the failure to load a firmware package. [STANDARDS-TRACK] IANA Advances in Cryptology -- CRYPTO '87 Proceedings Lecture Notes in Computer Science Vol. 293 Advances in Cryptology -- CRYPTO '89 Proceedings Lecture Notes in Computer Science Vol. 435 Advances in Cryptology -- CRYPTO '89 Proceedings Lecture Notes in Computer Science Vol. 435 National Academies of Sciences, Engineering, and Medicine The National Academies Press The Public Key Infrastructure using X.509 (PKIX) certificate format, and many associated formats, are expressed using ASN.1. The current ASN.1 modules conform to the 1988 version of ASN.1. This document updates those ASN.1 modules to conform to the 2002 version of ASN.1. There are no bits-on-the-wire changes to any of the formats; this is simply a change to the syntax. This document is not an Internet Standards Track specification; it is published for informational purposes. Security systems are built on strong cryptographic algorithms that foil pattern analysis attempts. However, the security of these systems is dependent on generating secret quantities for passwords, cryptographic keys, and similar quantities. The use of pseudo-random processes to generate secret quantities can result in pseudo-security. A sophisticated attacker may find it easier to reproduce the environment that produced the secret quantities and to search the resulting small set of possibilities than to locate the quantities in the whole of the potential number space. Choosing random quantities to foil a resourceful and motivated adversary is surprisingly difficult. This document points out many pitfalls in using poor entropy sources or traditional pseudo-random number generation techniques for generating such quantities. It recommends the use of truly random hardware techniques and shows that the existing hardware on many systems can be used for this purpose. It provides suggestions to ameliorate the problem when a hardware solution is not available, and it gives examples of how large such quantities need to be for some applications. This document specifies an Internet Best Current Practices for the Internet Community, and requests discussion and suggestions for improvements.

ASN.1 Module <CODE STARTS> MTS-HashSig-2013 { iso(1) member-body(2) us(840) rsadsi(113549) pkcs(1) pkcs9(9) id-smime(16) id-mod(0) id-mod-mts-hashsig-2013(64) } DEFINITIONS IMPLICIT TAGS ::= BEGIN EXPORTS ALL; IMPORTS PUBLIC-KEY, SIGNATURE-ALGORITHM, SMIME-CAPS FROM AlgorithmInformation-2009 -- RFC 5911 [CMSASN1] { iso(1) identified-organization(3) dod(6) internet(1) security(5) mechanisms(5) pkix(7) id-mod(0) id-mod-algorithmInformation-02(58) } ; -- -- Object Identifiers -- id-alg-hss-lms-hashsig OBJECT IDENTIFIER ::= { iso(1) member-body(2) us(840) rsadsi(113549) pkcs(1) pkcs9(9) smime(16) alg(3) 17 } id-alg-mts-hashsig OBJECT IDENTIFIER ::= id-alg-hss-lms-hashsig -- -- Signature Algorithm and Public Key -- sa-HSS-LMS-HashSig SIGNATURE-ALGORITHM ::= { IDENTIFIER id-alg-hss-lms-hashsig PARAMS ARE absent PUBLIC-KEYS { pk-HSS-LMS-HashSig } SMIME-CAPS { IDENTIFIED BY id-alg-hss-lms-hashsig } } pk-HSS-LMS-HashSig PUBLIC-KEY ::= { IDENTIFIER id-alg-hss-lms-hashsig KEY HSS-LMS-HashSig-PublicKey PARAMS ARE absent CERT-KEY-USAGE { digitalSignature, nonRepudiation, keyCertSign, cRLSign } } HSS-LMS-HashSig-PublicKey ::= OCTET STRING -- -- Expand the signature algorithm set used by CMS [CMSASN1U] -- SignatureAlgorithmSet SIGNATURE-ALGORITHM ::= { sa-HSS-LMS-HashSig, ... } -- -- Expand the S/MIME capabilities set used by CMS [CMSASN1] -- SMimeCaps SMIME-CAPS ::= { sa-HSS-LMS-HashSig.&smimeCaps, ... } END <CODE ENDS>

Acknowledgements Many thanks to , , , , , , , , , , , and for their careful review and comments.

Author's Address Vigil Security, LLC

516 Dranesville Road Herndon VA 20170 United States of America housley@vigilsec.com