Hash-based cryptography is the generic term for constructions of cryptanalytic primitives based on the security of hashish functions. It is of interest as a type of post-quantum cryptanalysis. then far, hash-based cryptanalysis is used to construct digital signatures schemes such as the Merkle signature system, zero cognition and computationally integrity proof, such as the zk-STARK [ 1 ] proof system and range proof over issue credentials via the HashWires [ 2 ] protocol. Hash-based key signature schemes combine a erstwhile signature scheme with a Merkle tree structure. Since a erstwhile signature system cardinal can lone sign a single message securely, it is practical to combine many such keys within a unmarried, larger structure. A Merkle tree structure is used to this conclusion. In this hierarchical datum structure, a hash function and concatenation are used repeatedly to compute tree nodes. Lamport signatures are an exemplar of a erstwhile signature system that can be combined with a Merkle tree social organization. In 2019, the US National Institute of Standards and Technology announced its intention to promulgate standards for stateful hash-based cryptography based on the offer Merkle Signature Scheme ( XMSS ) and Leighton-Micali Signatures ( LMS ), which are applicable in different circumstances. [ 3 ]

history [edit ]

Leslie Lamport invented hash-based signatures in 1979. The XMSS ( eXtended Merkle Signature Scheme ) [ 4 ] and SPHINCS [ 5 ] [ 6 ] hash-based signature schemes were introduced in 2011 and 2015, respectively. XMSS was developed by a team of researchers under the steering of Johannes Buchmann and is based both on Merkle ‘s germinal system and on the 2007 Generalized Merkle Signature Scheme ( GMSS ). [ 7 ] A multi-tree discrepancy of XMSS, XMSS MT, was described in 2013. [ 8 ]

erstwhile signature schemes [edit ]

Hash-based signature schemes use erstwhile key signature schemes as their build obstruct. A given erstwhile sign key can alone be used to sign a single message securely. indeed, signatures reveal depart of the sign winder. The security of ( hash-based ) erstwhile touch schemes relies entirely on the security of an underlie hash function. normally used erstwhile touch schemes include the Lamport-Diffie outline, the Winternitz scheme [ 9 ] and its improvements, such as the W-OTS+ outline. [ 10 ] Unlike the seminal Lamport-Diffie schema, the Winternitz schema and variants can sign many bits at once. The act of bits to be signed at once is determined by a respect : the Winternitz parameter. The universe of this parameter provides a tradeoff between size and accelerate. bombastic values of the Winternitz parameter give short signatures and keys, at the price of slower sign and collateral. In rehearse, a typical value for this parameter is 16. In the character of homeless hash-based signatures, few-time signature schemes are used. such schemes allow security to decrease gradually in case a few-time keystone is used more than once. HORST is an exemplar of a few-time touch scheme .

Combining many erstwhile key pairs into a hash-based key signature scheme [edit ]

The central mind of hash-based key signature schemes is to combine a larger total of erstwhile key pairs into a single structure to obtain a virtual way of signing more than once ( yet a limited number of times ). This is done using a Merkle tree structure, with possible variations. One public and one secret key are constructed from the numerous populace and secret keys of the underlying erstwhile scheme. The ball-shaped populace key is the single node at the very top of the Merkle tree. Its value is an output of the selected hash serve, so a typical public key size is 32 bytes. The robustness of this ball-shaped public samara is related to the validity of a given erstwhile public key using a sequence of tree nodes. This sequence is called the authentication path. It is stored as separate of the signature, and allows a voucher to reconstruct the node path between those two populace keys. The global private cardinal is broadly handled using a pseudo-random number generator. It is then sufficient to store a seeded player value. erstwhile privy keys are derived successively from the sow rate using the generator. With this approach, the global individual key is besides very little, e.g. typically 32 bytes. The problem of tree traversal is critical to signing performance. Increasingly efficient approaches have been introduced, dramatically speeding up signing time. Some hash-based signature schemes use multiple layers of tree, offering faster signing at the price of larger signatures. In such schemes, alone the lowest layer of trees is used to sign messages, while all early trees sign rout values of lower trees.

The Naor-Yung work [ 11 ] shows the model by which to transfer a limited time signature of the Merkle type syndicate into an unlimited ( regular ) touch scheme .

Properties of hash-based signature schemes [edit ]

Hash-based signature schemes trust on security assumptions about the implicit in hash function, but any hash function fulfilling these assumptions can be used. As a consequence, each adequate hashish function yields a different corresponding hash-based key signature system. evening if a given hash function becomes insecure, it is sufficient to replace it by a different, secure one to obtain a guarantee instantiation of the hash-based signature schema under consideration. Some hash-based signature schemes ( such as XMSS with pseudorandom key genesis ) are forward guarantee, meaning that previous signatures remain valid if a privy key is compromised. The minimality of security assumptions is another characteristic of hash-based signature schemes. generally, these schemes only require a plug ( for example in the sense of second preimage immunity ) cryptographic hash routine to guarantee the overall security system of the schema. This kind of assumption is necessary for any digital touch outline ; however, other signature schemes require extra security assumptions, which is not the case here. Because of their reliance on an underlie erstwhile signature schema, hash-based signature schemes can only sign a fixed numeral of messages securely. In the case of the Merkle and XMSS schemes, a maximal of 2 h { \displaystyle 2^ { heat content } } {\displaystyle 2^{h}} messages can be signed securely, with planck’s constant { \displaystyle h } h the sum Merkle tree acme .

Examples of hash-based signature schemes [edit ]

Since Merkle ‘s initial scheme, numerous hash-based touch schemes with operation improvements have been introduced. recent ones include the XMSS, the Leighton-Micali ( LMS ), the SPHINCS and the BPQS schemes. Most hash-based signature schemes are stateful, meaning that signing requires updating the unavowed key, unlike ceremonious digital signature schemes. For stateful hash-based touch schemes, signing requires keeping state of the used erstwhile keys and making certain they are never reused. The XMSS, LMS and BPQS [ 12 ] schemes are stateful, while the SPHINCS outline is homeless. SPHINCS signatures are larger than XMSS, LMS signatures, while BPQS has been designed specifically for blockchain systems. additionally to the WOTS+ erstwhile signature scheme, [ 10 ] SPHINCS besides uses a few-time ( hash-based ) touch scheme called HORST. HORST is an improvement of an older few-time key signature scheme, HORS ( Hash to Obtain Random Subset ). [ 13 ] The stateful hash-based schemes XMSS and XMSS MT are specified in RFC 8391 ( XMSS : eXtended Merkle Signature Scheme ). [ 14 ] Leighton-Micali Hash-Based Signatures are specified in RFC 8554. [ 15 ] Practical improvements have been proposed in the literature that alleviate the concerns introduced by stateful schemes. [ 16 ] Hash functions appropriate for these schemes include SHA-2, SHA-3 and BLAKE .

Implementations [edit ]

Unlike early democratic blockchain networks and cryptocurrencies that use already NIST standardized Elliptic Curve Digital Signature Algorithms ( ECDSA ), [ 17 ] The Quantum Resistant Ledger ( QRL ) is the first loose source network to implement widen Merkle Signature Scheme. [ 18 ] In contrast to traditional ECDSA signatures, this stateful touch dodge is demonstrably insubordinate to a sufficiently mighty quantum calculator running Shor ‘s algorithm. [ 19 ] [ 20 ]

The XMSS, GMSS and SPHINCS schemes are available in the Java Bouncy Castle cryptanalytic APIs. [ 21 ] SPHINCS is implemented in the SUPERCOP benchmarking toolkit. [ 22 ] Optimised [ 23 ] and unoptimised [ 24 ] reference point implementations of the XMSS RFC exist. The LMS scheme has been implemented in Python [ 25 ] and in C [ 26 ] following its Internet-Draft .

References [edit ]

  • T. Lange. “Hash-Based Signatures”. Encyclopedia of Cryptography and Security, Springer US, 2011. [2]
  • F. T. Leighton, S. Micali. “Large provably fast and secure digital signature schemes based one secure hash functions”. US Patent 5,432,852, [3] 1995.
  • G. Becker. “Merkle Signature Schemes, Merkle Trees and Their Cryptanalysis”, seminar ‘Post Quantum Cryptology’ at the Ruhr-University Bochum, Germany, 2008. [4]
  • E. Dahmen, M. Dring, E. Klintsevich, J. Buchmann, L.C. Coronado Garcia. “CMSS — An Improved Merkle Signature Scheme”. Progress in Cryptology – Indocrypt 2006. [5]
  • R. Merkle. “Secrecy, authentication and public key systems / A certified digital signature”. Ph.D. dissertation, Dept. of Electrical Engineering, Stanford University, 1979. [6]
  • S. Micali, M. Jakobsson, T. Leighton, M. Szydlo. “Fractal Merkle Tree Representation and Traversal”. RSA-CT 03. [7]
  • P. Kampanakis, S. Fluhrer. “LMS vs XMSS: A comparison of the Stateful Hash-Based Signature Proposed Standards”. Cryptology ePrint Archive, Report 2017/349. [8]
  • D. Naor, A. Shenhav, A. Wool. “One-Time Signatures Revisited: Practical Fast Signatures Using Fractal Merkle Tree Traversal”. IEEE 24th Convention of Electrical and Electronics Engineers in Israel, 2006. [9]
  • [10] A commented list of literature about hash-based signature schemes.
  • [11] Another list of references (uncommented).
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