Research and Development of Digital Signatures
DOI:
https://doi.org/10.54097/2g9b0j24Keywords:
Digital Signature Technology, Privacy-Enhancing Mechanisms, Standardization ProcessAbstract
Since Diffie and Hellman's pioneering work on asymmetric cryptography in 1976, digital signature technology has evolved through three phases—theoretical foundation, standardization, and diversified innovation—emerging as a cornerstone of trust in digital societies. Theoretically, foundational frameworks were established by RSA, DSA, and Schnorr algorithms. Standardization efforts, including NIST DSS, ISO/IEC series, and national systems (e.g., China's SM2/SM9, Russia's GOST), fostered a multipolar ecosystem. Extended-attribution technologies (blind, group, and ring signatures) addressed privacy and scenario-specific demands. Current challenges, such as quantum computing threats and privacy-regulation trade-offs, drive advancements in post-quantum cryptography (lattice-based signatures, hash-based XMSS) and privacy-enhancing mechanisms (verifiably encrypted signatures, homomorphic signatures), guided by ISO/IEC redactable standards and NIST's post-quantum initiative. Moving forward, digital signatures will deepen capabilities in provable security, quantum resistance, and adaptive policy control, underpinning trust architectures for emerging ecosystems like Web3 and the metaverse.
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[1] Goldwasser S., Micali S., Rivest R. L. “A Paradoxical Solution to the Signature Problem.” In Proc. CRYPTO’84, Berlin, Heidelberg, 1985, pp. 467–477.
[2] An J.H., Dodis Y., Rabin T. On the Security of Joint Signature and Encryption. Advances in Cryptology — EUROCRYPT 2002. Amsterdam, 2002-04-28, p. 83-107.
[3] 3. Diffie W., Hellman M. “New Directions in Cryptography.” IEEE Trans. Inf. Theory, vol. 22, no. 6, pp. 644–654, 1976.
[4] Rivest R., Shamir A., Adleman L. “A Method for Obtaining Digital Signatures and Public-Key Cryptosystems.” Commun. ACM, vol. 21, no. 2, pp. 120–126, 1978.
[5] 5. Rabin M. “Digitalized Signatures and Public Key Functions as Intractable as Factorization.” MIT Lab. Comput. Sci. Tech. Rep, 1979, pp. 1–22.
[6] Merkle R. Secrecy, Authentication and Public Key Systems / A Certified Digital Signature (Ph.D. dissertation, Stanford University, America 1979). p. 1-150.
[7] Lamport L. “Constructing Digital Signatures from a One-Way Function.” Tech. Rep. CSL-98, SRI International, Palo Alto, CA, USA, 1979.
[8] Buchmann J., Dahmen E., Hülsing A. XMSS - A Practical Forward Secure Signature Scheme Based on Minimal Security Assumptions. Post Quantum Cryptography. Darmstadt, 2011-11-29, p. 117-129.
[9] ElGamal T. A Public Key Cryptosystem and a Signature Scheme Based on Discrete Logarithms. Advances in Cryptology. CRYPTO 1984. Berlin, Heidelberg, 1985, p. 10-18.
[10] Shamir A. Identity-Based Cryptosystems and Signature Schemes. Advances in Cryptology. CRYPTO 1984. Berlin, Heidelberg, 1985, p. 47-53.
[11] Fiat A., Shamir A. How To Prove Yourself: Practical Solutions to Identification and Signature Problems. Advances in Cryptology — CRYPTO’ 86. Santa Barbara, 1986-08-11, p. 186-194.
[12] Schnorr C.P. Efficient Identification and Signatures for Smart Cards. Advances in Cryptology — EUROCRYPT ’89. Houthalen, 1989-04-10, p. 239-252.
[13] Bernstein D.J., Duif N., Lange T., Schwabe P., Yang B.-Y. High-Speed High-Security Signatures. Journal of Cryptographic Engineering. 2012, Vol. 2 (No. 2), p. 77-89.
[14] 14. Lotus Domino Wiki. “Supported Key Sizes in Notes/Domino.” [Online]. Available: https://www-10.lotus.com/ldd/dominowiki.nsf/dx/supported-key-sizes-in-notesdomino [Accessed: Sep. 15, 2023].
[15] FIPS PUB 186: Digital Signature Standard (DSS). NIST, America 1994.
[16] Brown D.R.L. The Exact Security of ECDSA. Technical Report CORR 2000-54. University of Waterloo, 2000.
[17] Stallings W., Zimmermann P. PGP Message Exchange Formats. RFC 1991. Internet Engineering Task Force, 1996-08-01.
[18] Girault M. Self-Certified Public Keys. Advances in Cryptology — EUROCRYPT ’91. Brighton, 1991-04-08, p. 490-497.
[19] Poupard G., Stern J. Security Analysis of A Practical "On The Fly" Authentication and Signature Generation. Advances in Cryptology — EUROCRYPT'98. Helsinki, 1998-05-31, p. 422-436.
[20] Kaliski B. PKCS #1: RSA Encryption 1.5. RFC 2313. Internet Engineering Task Force, 1998-03-01.
[21] Information on: https://tools.ietf.org/html/draft-hickman-netscape-ssl-00
[22] Bellare M., Rogaway P. The Exact Security of Digital Signatures-How to Sign with RSA and Rabin. Advances in Cryptology — EUROCRYPT ’96. Zaragoza, 1996-05-12, p. 399-416.
[23] Pointcheval D., Stern J. Security Proofs for Signature Schemes. Advances in Cryptology — EUROCRYPT ’96. Zaragoza, 1996-05-12, p. 387-398.
[24] Kocher P.C. Timing Attacks on Implementations of Diffie-Hellman, RSA, DSS, and Other Systems. Advances in Cryptology — CRYPTO ’96. Santa Barbara, 1996-08-18, p. 104-113.
[25] Gennaro R., Halevi S., Rabin T. Secure Hash and-Sign Signatures Without the Random Oracle. Advances in Cryptology — EUROCRYPT ’99. Prague, 1999-05-02, p. 123-139.
[26] Cramer S., Shoup V. Signature Schemes Based on the Strong RSA Assumption. ACM Transactions on Information and System Security. 2000, Vol. 3 (No. 3), p. 161-185.
[27] Boneh D., Lynn B., Shacham H. Short Signatures from the Weil Pairing. Advances in Cryptology — ASIACRYPT 2001. Gold Coast, 2001-12-09, p. 514-532.
[28] Choon J.C., Hee Cheon J. An Identity-Based Signature from Gap Diffie-Hellman Groups. Public Key Cryptography — PKC 2003. Miami, 2003-01-06, p. 18-30.
[29] Hess F. Efficient Identity Based Signature Schemes Based on Pairings. Selected Areas in Cryptography. St. John's, 2002-08-15, p. 310-324.
[30] Al-Riyami S.S., Paterson K.G. Certificateless Public Key Cryptography. Advances in Cryptology - ASIACRYPT 2003. Taipei, 2003-11-30, p. 452-473.
[31] Cheng Z., Chen L. Certificateless Public Key Signature Schemes from Standard Algorithms. Information Security Practice and Experience. Tokyo, 2018-09-25, p. 45-62.
[32] Goldreich O., Goldwasser S., Halevi S. Public-key cryptosystems from lattice reduction problems. Advances in Cryptology — CRYPTO '97. Santa Barbara, 1997-08-17, p. 112-131.
[33] Hoffstein J., Howgrave-Graham N., Pipher J., Silverman J.H., Whyte W. NTRUSign: Digital Signatures Using the NTRU Lattice. Topics in Cryptology — CT RSA 2003. San Francisco, 2003-04-13, p. 122-140.
[34] Gentry C., Peikert C., Vaikuntanathan V. Trapdoors for Hard Lattices and New Cryptographic Constructions. Proceedings of the 40th ACM Symposium on Theory of Computing. Victoria, 2008-05-17, p. 197-206.
[35] Ducas L., Durmus A., Lepoint T., Lyubashevsky V. Lattice Signatures and Bimodal Gaussians. Advances in Cryptology – CRYPTO 2013. Santa Barbara, 2013-08-18, p. 117-131.
[36] Ducas L., Kiltz E., Lepoint T., Lyubashevsky V., Schwabe P., Seiler G., Stehlé D. CRYSTALS Dilithium: A Lattice-Based Digital Signature Scheme. IACR Transactions on Cryptographic Hardware and Embedded Systems. 2018, Vol. 2018 (No. 1), p. 238-268.
[37] Information on: https://csrc.nist.gov/projects/post-quantum-cryptography
[38] Menezes A. J., van Oorschot P. C., Vanstone S. A. *Handbook of Applied Cryptography*. Boca Raton, FL, USA: CRC Press, 1996.
[39] D. Demirel, D. Derler, C. Hanser, H. C. Pöhls, D. Slamanig, G. Traverso, “PRISMACLOUD D4.4: Overview of Functional and Malleable Signature Schemes,” PRISMACLOUD Project Deliverable D4.4, H2020 Project 644962, Vienna, Austria: PRISMACLOUD Consortium, 2015. [Online]. Available: https://www.prismacloud.eu/deliverables/ [Accessed: Sep. 15, 2023].
[40] Chaum D. Blind Signatures for Untraceable Payments. Advances in Cryptology. Santa Barbara, 1983-08-22, p. 199-203.
[41] Itakura K., Nakamura K. A Public-Key Cryptosystem Suitable for Digital Multisignatures. NEC Research and Development. 1983, Vol. 71, p. 1-8.
[42] Boneh D., Gentry C., Lynn B., Shacham H. Aggregate and Verifiably Encrypted Signatures from Bilinear Maps. Advances in Cryptology — EUROCRYPT 2003. Warsaw, 2003-05-04, p. 51-65.
[43] Lysyanskaya A., Micali S., Reyzin L., Shacham H. Sequential Aggregate Signatures from Trapdoor Permutations. Advances in Cryptology — EUROCRYPT 2004. Interlaken, 2004-05-02, p. 89-104.
[44] Desmedt Y. Society and Group Oriented Cryptography: A New Concept. Advances in Cryptology— CRYPTO ’87. Santa Barbara, 1987-08-16, p. 120-135.
[45] Chaum D., van Antwerpen H. Undeniable Signatures. Advances in Cryptology — CRYPTO’ 89 Proceedings. Santa Barbara, 1989-08-20, p. 212-227.
[46] Pfitzmann B. Fail-Stop Signatures; Principles and Applications. Proc. COMPSEC'91, 8th World Conference on Computer Security, Audit and Control. London, 1991-09-15, p. 125-134.
[47] Chaum D., van Heyst E. Group Signatures. Advances in Cryptology — EUROCRYPT ’91. Brighton, 1991-04-08, p. 257-265.
[48] Kiayias A., Tsiounis Y., Yung M. Traceable Signatures. Advances in Cryptology - EUROCRYPT 2004. Interlaken, 2004-05-02, p. 189-204.
[49] Kohlweiss M., Miers I. Accountable Metadata Hiding Escrow: A Group Signature Case Study. Proceedings on Privacy Enhancing Technologies. 2015, Vol. 2015 (No. 2), p. 206-221.
[50] Chaum D. Designated confirmer signatures. In: De Santis A. (eds) Advances in Cryptology — EUROCRYPT'94. Perugia, 1994-05-09, p. 86-91.
[51] Mambo M., Usuda K., Okamoto E. Proxy Signatures: Delegation of The Power to Sign Messages. IEICE Transactions on Fundamentals. 1996, Vol. E79-A (No. 9), p. 1338-1354.
[52] Jakobsson M., Sako K., Impagliazzo R. Designated Verifier Proofs and Their Applications. Advances in Cryptology — EUROCRYPT ’96. Zaragoza, 1996-05-12, p. 143-154.
[53] Zheng Y. Digital Signcryption or How to Achieve Cost(Signature & Encryption) << Cost(Signature) +Cost(Encryption). Advances in Cryptology — CRYPTO '97. Santa Barbara, 1997-08-17, p. 165-179.
[54] Rivest R.L., Shamir A., Tauman Y. How to Leak a Secret. Advances in Cryptology — ASIACRYPT 2001. Gold Coast, 2001-12-09, p. 552-565.
[55] Bresson E., Stern J., Szydlo M. Threshold Ring Signatures and Applications to Ad-hoc Groups. Advances in Cryptology — CRYPTO 2002. Santa Barbara, 2002-08-18, p. 465-480.
[56] Liu J.K., Wong D.S. Linkable Ring Signatures: Security Models and New Schemes. Computational Science and Its Applications – ICCSA 2005. Singapore, 2005-05-09, p. 614-623.
[57] Fujisaki E., Suzuki K. Traceable Ring Signature. Public Key Cryptography – PKC 2007. Beijing, 2007-04-16, p. 181-200.
[58] Boyen X. Mesh Signatures. Advances in Cryptology - EUROCRYPT 2007. Barcelona, 2007-05-20, p. 210-227.
[59] Camenisch J., Lysyanskaya A. A Signature Scheme with Efficient Protocols. Security in Communication Networks. Amalfi, 2002-09-11, p. 268-289.
[60] Brickell E., Camenisch J., Chen L. Direct Anonymous Attestation. Proceedings of the 11th ACM Conference on Computer and Communications Security. Washington, D.C., 2004-10-25, p. 132-145.
[61] Johnson R., Molnar D., Song D., Wagner D. Homomorphic Signature Schemes. Topics in Cryptology — CT-RSA 2002. San Francisco, 2002-02-18, p. 244-262.
[62] Steinfeld R., Bull L., Zheng Y. Content Extraction Signatures. Information Security and Cryptology — ICISC 2001. Seoul, 2001-12-06, p. 285-304.
[63] Boneh D., Freeman D., Katz J., Waters B. Signing a Linear Subspace: Signature Schemes for Network Coding. Public Key Cryptography – PKC 2009. Irvine, 2009-03-18, p. 68-87.
[64] Boneh D., Freeman D.M. Homomorphic Signatures for Polynomial Functions. Advances in Cryptology – EUROCRYPT 2011. Tallinn, 2011-05-15, p. 149-168.
[65] Bellare M., Goldreich O., Goldwasser S. Incremental Cryptography: The Case of Hashing and Signing. Advances in Cryptology — CRYPTO ’94. Santa Barbara, 1994-08-21, p. 216-233.
[66] Micali S., Rivest R.L. Transitive Signature Schemes. Topics in Cryptology — CT-RSA 2002. San Francisco, 2002-02-18, p. 236-243.
[67] Ateniese G., Chou D.H., de Medeiros B., Tsudik G. Sanitizable Signatures. Computer Security – ESORICS 2005. Milan, 2005-09-12, p. 159-177.
[68] Kiltz E., Mityagin A., Panjwani S., Raghavan B. Append-Only Signatures. Automata, Languages and Programming. Lisbon, 2005-07-11, p. 506-518.
[69] Derler D., Hanser C., Slamanig D. Blank Digital Signatures: Optimization and Practical Experiences. Privacy and Identity Management for the Future Internet. Vienna, 2014-09-17, p. 45-63.
[70] Krenn S., Pöhls H.C., Samelin K., Slamanig D. Protean Signature Schemes. In: Camenisch J., Papadimitratos P. (eds) Cryptology and Network Security. CANS 2018. Naples, 2018-09-30, p. 189-209.
[71] ISO/IEC 23264-2:2018 IT Security Techniques — Redaction of Authentic Data – Part 2: Redactable Signature Schemes Based on Asymmetric Mechanisms. Working Draft. ISO, Switzerland 2018.
[72] Fuchsbauer G. Commuting Signatures and Verifiable Encryption. Advances in Cryptology – EUROCRYPT 2011. Tallinn, 2011-05-15, p. 234-251.
[73] Chen L., Kudla C., Paterson K.G. Concurrent Signatures. Advances in Cryptology - EUROCRYPT 2004. Interlaken, 2004-05-02, p. 287-305.
[74] Yang G., Wong D.S., Deng X., Wang H. Anonymous Signature Schemes. Public Key Cryptography - PKC 2006. New York, 2006-04-24, p. 347-363.
[75] Chase M., Lysyanskaya A. On Signatures of Knowledge. Advances in Cryptology - CRYPTO 2006. Santa Barbara, 2006-08-20, p. 78-96.
[76] Abe M., Fuchsbauer G., Groth J., Haralambiev K., Ohkubo M. Structure-Preserving Signatures and Commitments to Group Elements. Advances in Cryptology – CRYPTO 2010. Santa Barbara, 2010-08-15, p. 209-236.
[77] Maji H.K., Prabhakaran M., Rosulek M. Attribute-Based Signatures. Topics in Cryptology – CT-RSA 2011. San Francisco, 2011-02-14, p. 376-392.
[78] Bellare M., Fuchsbauer G. Policy-Based Signatures. Public-Key Cryptography – PKC 2014. Buenos Aires, 2014-03-26, p. 520-537.
[79] Boyle E., Goldwasser S., Ivan I. Functional Signatures and Pseudorandom Functions. Public Key Cryptography – PKC 2014. Buenos Aires, 2014-03-26, p. 501-519.
[80] FIPS PUB 186-2: Digital Signature Standard (DSS). NIST, America 2000.
[81] Moriarty K., Kaliski B., Jonsson J., Rusch A. PKCS #1: RSA Cryptography Specifications Version 2.2. RFC 8017. Internet Engineering Task Force, 2016-11-01.
[82] Josefsson S., Liusvaara I. Edwards-Curve Digital Signature Algorithm (EdDSA). RFC 8032. Internet Research Task Force, 2017-01-01.
[83] Rescorla E. The Transport Layer Security (TLS) Protocol Version 1.3. RFC 8446. Internet Engineering Task Force, 2018-08-01.
[84] GOST R 34.10-94, Information Technology. Cryptographic Data Security. Procedures for Generation and Verification of Electronic Digital Signatures Based on Asymmetric Cryptographic Algorithm. Moscow, Russia: State Standard of the Russian Federation, 1994. (In Russian).
[85] GOST R 34.10-94, Information Technology. Cryptographic Data Security. Procedures for Generation and Verification of Electronic Digital Signatures Based on Asymmetric Cryptographic Algorithm. Moscow, Russia: State Standard of the Russian Federation, 1994. (In Russian).
[86] GOST R 34.10-2001, Information Technology. Cryptographic Data Security. Signature and Verification Processes of Electronic Digital Signatures. Moscow, Russia: State Standard of the Russian Federation, 2001. (In Russian).
[87] [Online]. Available: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.99.8398 [Accessed: Sep. 15, 2023].
[88] TTAK.KO-12.0015/R2. Digital Signature Mechanism with Appendix - Part 3: Korean Certificate-based Digital Signature Algorithm using Elliptic Curves EC KCDSA. Korean 2014.
[89] TTAK.KO-12.0001/R3. Digital Signature Mechanism with Appendix - Part 2: Korean Certificate-based Digital Signature Algorithm KCDSA. Korean 2014.
[90] Erwin H., Pascale S. Digital Signature Scheme EC-GDSA. German Federal Office for Information Security, Germany 2005.
[91] GM/T 0003.2-2012, SM2 Elliptic Curve Public Key Cryptographic Algorithm—Part 2: Digital Signature. Beijing, China: State Cryptography Administration, 2012. (In Chinese).
[92] GM/T 0044.2-2016, SM9 Identity-Based Cryptography—Part 2: Digital Signature Algorithm. Beijing, China: State Cryptography Administration of China, 2016. (In Chinese).
[93] ISO/IEC 9796-2:2010 Information Technology — Security Techniques — Digital Signature Schemes Giving Message Recovery — Part 2: Integer Factorization Based Mechanisms. ISO, Switzerland 2010.
[94] ISO/IEC 9796-3:2006 Information Technology — Security Techniques — Digital Signature Schemes Giving Message Recovery — Part 3: Discrete Logarithm Based Mechanisms. ISO, Switzerland 2006.
[95] ISO/IEC 14888-2:2008 Information Technology — Security Techniques — Digital Signatures with Appendix — Part 2: Integer Factorization Based Mechanisms. ISO, Switzerland 2008.
[96] ISO/IEC 14888-3:2018 IT Security Techniques — Digital Signatures with Appendix — Part 3: Discrete Logarithm Based Mechanisms. ISO, Switzerland 2018.
[97] ISO/IEC 20008-2:2013 Information Technology — Security Techniques — Anonymous Digital Signatures — Part 2: Mechanisms Using A Group Public Key. ISO, Switzerland 2013.
[98] ISO/IEC 18370-2:2016 Information Technology — Security Techniques — Blind Digital Signatures — Part 2: Discrete Logarithm Based Mechanisms. ISO, Switzerland 2016.
[99] ISO/IEC 13888-2:2010 Information Technology — Security Techniques — Non-Repudiation — Part 2: Mechanisms Using Symmetric Techniques. ISO, Switzerland 2010.
[100] ISO/IEC 13888-3:2009 Information Technology — Security Techniques — Non-Repudiation — Part 3: Mechanisms Using Asymmetric Techniques. ISO, Switzerland 2009.
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