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February  2019, 13(1): 185-193. doi: 10.3934/amc.2019012

On the security of the WOTS-PRF signature scheme

Philip Lafrance 1, and  Alfred Menezes 2,

1. 

ISARA Corporation, Waterloo, Canada
2. 

Department of Combinatorics & Optimization, University of Waterloo, Canada

Received  July 2018 Published  December 2018

We identify a flaw in the security proof and a flaw in the concrete security analysis of the WOTS-PRF variant of the Winternitz one-time signature scheme, and discuss the implications to its concrete security.

Keywords: One-time signature schemes, pseudorandom functions, security proofs.
Mathematics Subject Classification: Primary: 94A60.
Citation: Philip Lafrance, Alfred Menezes. On the security of the WOTS-PRF signature scheme. Advances in Mathematics of Communications, 2019, 13 (1) : 185-193. doi: 10.3934/amc.2019012
References:
[1]

M. Bellare, New proofs for NMAC and HMAC: Security without collision resistance, in: Advances in Cryptology - CRYPTO 2006, LNCS, 4117 (2006), 602-619. doi: 10.1007/11818175_36. Google Scholar

[2]

D. Bernstein and T. Lange, Non-uniform cracks in the concrete: The power of free computation, in: Advances in Cryptology - ASIACRYPT 2013, LNCS, 8270 (2013), 321-340. doi: 10.1007/978-3-642-42045-0_17. Google Scholar

[3]

J. Buchmann, E. Dahmen, S. Ereth, A. Hülsing and M. Rückert, On the security of the Winternitz one-time signature scheme, in: Progress in Cryptology - AFRICACRYPT 2011, LNCS, 6737 (2011), 363-378. doi: 10.1007/978-3-642-21969-6_23. Google Scholar

[4]

J. Buchmann, E. Dahmen, S. Ereth, A. Hülsing and M. Rückert, On the security of the Winternitz one-time signature scheme, International Journal of Applied Cryptography, 3 (2013), 84-96. doi: 10.1504/IJACT.2013.053435. Google Scholar

[5]

J. Buchmann, E. Dahmen and A. H¨ulsing, XMSS - a practical forward secure signature scheme based on minimal security assumptions, in: Post-Quantum Cryptography - PQCrypto 2011, LNCS, 7071 (2011), 117-129. doi: 10.1007/978-3-642-25405-5_8. Google Scholar

[6]

C. Dods, N. Smart and M. Stam, Hash based digital signature schemes, in: Cryptography and Coding, LNCS, 3796 (2005), 96-115. doi: 10.1007/11586821_8. Google Scholar

[7]

E. Eaton, Leighton-Micali hash-based signatures in the quantum random-oracle model, in: Selected Areas in Cryptography - SAC 2017, LNCS 10719 (2018), 263-280. Google Scholar

[8]

S. Even, O. Goldreich and S. Micali, On-line/off-line digital signatures, Journal of Cryptology, 9 (1996), 35-67. doi: 10.1007/BF02254791. Google Scholar

[9]

O. Goldreich, S. Goldwasser and S. Micali, How to construct random functions, Journal of the ACM, 33 (1986), 792-807. doi: 10.1145/6490.6503. Google Scholar

[10]

J. Håstad, R. Impagliazzo, L. Levin and M. Luby, A pseudorandom generator from any oneway function, SIAM Journal on Computing, 28 (1999), 1364-1396. doi: 10.1137/S0097539793244708. Google Scholar

[11]

A. Hülsing, Practical Forward Secure Signatures Using Minimal Security Assumptions, Ph. D. thesis, Technical University of Darmstadt, 2013.Google Scholar

[12]

A. Hülsing, W-OTS+ - Shorter signatures for hash-based signature schemes, in: Progress in Cryptology - AFRICACRYPT 2013, LNCS 7918 (2013), 173-188.Google Scholar

[13]

A. Hülsing, C. Busold and J. Buchmann, Forward secure signatures on smart cards, in: Selected Areas in Cryptography - SAC 2012, LNCS 7707 (2013), 66-80.Google Scholar

[14]

A. Hülsing, D. Butin, S. Gazdag, J. Rijneveld and A. Mohaisen, XMSS: eXtended Merkle Signature Scheme, RFC 8391, May 31, 2018; available at https://datatracker.ietf.org/doc/rfc8391/.Google Scholar

[15]

A. Hülsing, L. Rausch and J. Buchmann, Optimal parameters for XMSSMT, in: Availability, Reliability, and Security in Information Systems and HCI - CD-ARES 2013, LNCS 8128 (2013), 194-208.Google Scholar

[16]

A. Hülsing, J. Rijneveld and F. Song, Mitigating multi-target attacks in hash-based signatures, in: Public-Key Cryptography - PKC 2016, LNCS 9614 (2016), 387-416. doi: 10.1007/978-3-662-49384-7_15. Google Scholar

[17]

J. Katz, Analysis of a proposed hash-based signature scheme, in: Security Standardisation Research - SSR 2016, LNCS 10074 (2016), 261-273.Google Scholar

[18]

N. Koblitz and A. Menezes, Another look at HMAC, Journal of Mathematical Cryptology, 7 (2013), 225-251. doi: 10.1515/jmc-2013-5004. Google Scholar

[19]

N. Koblitz and A. Menezes, Another look at non-uniformity, Groups Complexity Cryptology, 5 (2013), 117-139. doi: 10.1515/gcc-2013-0008. Google Scholar

[20]

L. Lamport, Constructing digital signatures from a one way function, Technical Report CSL-98, SRI International, 1979.Google Scholar

[21]

D. McGrew, M. Curcio and S. Fluhrer, Hash-based signatures, Internet Draft, April 5, 2018; available at https://datatracker.ietf.org/doc/draft-mcgrew-hash-sigs/.Google Scholar

[22]

R. Merkle, A digital signature based on a conventional encryption function, in: Advances in Cryptology - CRYPTO '87, LNCS 293 (1988), 369-378.Google Scholar

[23]

M. Raab and A. Steger, "Balls into bins" - = - a simple and tight analysis, in: Randomization and Approximation Techniques in Computer Science - RANDOM 1998, LNCS 1518 (1998), 159-170. doi: 10.1007/3-540-49543-6_13. Google Scholar

show all references

References:
[1]

M. Bellare, New proofs for NMAC and HMAC: Security without collision resistance, in: Advances in Cryptology - CRYPTO 2006, LNCS, 4117 (2006), 602-619. doi: 10.1007/11818175_36. Google Scholar

[2]

D. Bernstein and T. Lange, Non-uniform cracks in the concrete: The power of free computation, in: Advances in Cryptology - ASIACRYPT 2013, LNCS, 8270 (2013), 321-340. doi: 10.1007/978-3-642-42045-0_17. Google Scholar

[3]

J. Buchmann, E. Dahmen, S. Ereth, A. Hülsing and M. Rückert, On the security of the Winternitz one-time signature scheme, in: Progress in Cryptology - AFRICACRYPT 2011, LNCS, 6737 (2011), 363-378. doi: 10.1007/978-3-642-21969-6_23. Google Scholar

[4]

J. Buchmann, E. Dahmen, S. Ereth, A. Hülsing and M. Rückert, On the security of the Winternitz one-time signature scheme, International Journal of Applied Cryptography, 3 (2013), 84-96. doi: 10.1504/IJACT.2013.053435. Google Scholar

[5]

J. Buchmann, E. Dahmen and A. H¨ulsing, XMSS - a practical forward secure signature scheme based on minimal security assumptions, in: Post-Quantum Cryptography - PQCrypto 2011, LNCS, 7071 (2011), 117-129. doi: 10.1007/978-3-642-25405-5_8. Google Scholar

[6]

C. Dods, N. Smart and M. Stam, Hash based digital signature schemes, in: Cryptography and Coding, LNCS, 3796 (2005), 96-115. doi: 10.1007/11586821_8. Google Scholar

[7]

E. Eaton, Leighton-Micali hash-based signatures in the quantum random-oracle model, in: Selected Areas in Cryptography - SAC 2017, LNCS 10719 (2018), 263-280. Google Scholar

[8]

S. Even, O. Goldreich and S. Micali, On-line/off-line digital signatures, Journal of Cryptology, 9 (1996), 35-67. doi: 10.1007/BF02254791. Google Scholar

[9]

O. Goldreich, S. Goldwasser and S. Micali, How to construct random functions, Journal of the ACM, 33 (1986), 792-807. doi: 10.1145/6490.6503. Google Scholar

[10]

J. Håstad, R. Impagliazzo, L. Levin and M. Luby, A pseudorandom generator from any oneway function, SIAM Journal on Computing, 28 (1999), 1364-1396. doi: 10.1137/S0097539793244708. Google Scholar

[11]

A. Hülsing, Practical Forward Secure Signatures Using Minimal Security Assumptions, Ph. D. thesis, Technical University of Darmstadt, 2013.Google Scholar

[12]

A. Hülsing, W-OTS+ - Shorter signatures for hash-based signature schemes, in: Progress in Cryptology - AFRICACRYPT 2013, LNCS 7918 (2013), 173-188.Google Scholar

[13]

A. Hülsing, C. Busold and J. Buchmann, Forward secure signatures on smart cards, in: Selected Areas in Cryptography - SAC 2012, LNCS 7707 (2013), 66-80.Google Scholar

[14]

A. Hülsing, D. Butin, S. Gazdag, J. Rijneveld and A. Mohaisen, XMSS: eXtended Merkle Signature Scheme, RFC 8391, May 31, 2018; available at https://datatracker.ietf.org/doc/rfc8391/.Google Scholar

[15]

A. Hülsing, L. Rausch and J. Buchmann, Optimal parameters for XMSSMT, in: Availability, Reliability, and Security in Information Systems and HCI - CD-ARES 2013, LNCS 8128 (2013), 194-208.Google Scholar

[16]

A. Hülsing, J. Rijneveld and F. Song, Mitigating multi-target attacks in hash-based signatures, in: Public-Key Cryptography - PKC 2016, LNCS 9614 (2016), 387-416. doi: 10.1007/978-3-662-49384-7_15. Google Scholar

[17]

J. Katz, Analysis of a proposed hash-based signature scheme, in: Security Standardisation Research - SSR 2016, LNCS 10074 (2016), 261-273.Google Scholar

[18]

N. Koblitz and A. Menezes, Another look at HMAC, Journal of Mathematical Cryptology, 7 (2013), 225-251. doi: 10.1515/jmc-2013-5004. Google Scholar

[19]

N. Koblitz and A. Menezes, Another look at non-uniformity, Groups Complexity Cryptology, 5 (2013), 117-139. doi: 10.1515/gcc-2013-0008. Google Scholar

[20]

L. Lamport, Constructing digital signatures from a one way function, Technical Report CSL-98, SRI International, 1979.Google Scholar

[21]

D. McGrew, M. Curcio and S. Fluhrer, Hash-based signatures, Internet Draft, April 5, 2018; available at https://datatracker.ietf.org/doc/draft-mcgrew-hash-sigs/.Google Scholar

[22]

R. Merkle, A digital signature based on a conventional encryption function, in: Advances in Cryptology - CRYPTO '87, LNCS 293 (1988), 369-378.Google Scholar

[23]

M. Raab and A. Steger, "Balls into bins" - = - a simple and tight analysis, in: Randomization and Approximation Techniques in Computer Science - RANDOM 1998, LNCS 1518 (1998), 159-170. doi: 10.1007/3-540-49543-6_13. Google Scholar

Figure 1.  The incomplete $\alpha$'th Winternitz hash chain in ${\mathcal{A}}_{{\rm KOW}}$'s experiment
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Figure 2.  The tree of $w$-keychains to $pk_{\alpha}$
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