Short Signatures from the Weil Pairing

We introduce a short signature scheme based on the Computational Diffie-Hellman assumption on certain elliptic and hyperelliptic curves. The signature length is half the size of a DSA signature for a similar level of security. Our short signature scheme is designed for systems where signatures are typed in by a human or signatures are sent over a low-bandwidth channel.

[1]  S. Lang,et al.  Abelian varieties over finite fields , 2005 .

[2]  Don Coppersmith,et al.  Fast evaluation of logarithms in fields of characteristic two , 1984, IEEE Trans. Inf. Theory.

[3]  Silvio Micali,et al.  A Digital Signature Scheme Secure Against Adaptive Chosen-Message Attacks , 1988, SIAM J. Comput..

[4]  Alfred Menezes,et al.  Reducing elliptic curve logarithms to logarithms in a finite field , 1991, STOC '91.

[5]  David Chaum,et al.  Wallet Databases with Observers , 1992, CRYPTO.

[6]  Alfred Menezes,et al.  Reducing elliptic curve logarithms to logarithms in a finite field , 1993, IEEE Trans. Inf. Theory.

[7]  Mihir Bellare,et al.  Random oracles are practical: a paradigm for designing efficient protocols , 1993, CCS '93.

[8]  Ueli Maurer,et al.  Towards the Equivalence of Breaking the Diffie-Hellman Protocol and Computing Discrete Logarithms , 1994, CRYPTO.

[9]  Rainer A. Rueppel,et al.  Message Recovery for Signature Schemes Based on the Discrete Logarithm Problem , 1994, EUROCRYPT.

[10]  Alfred Menezes,et al.  Handbook of Applied Cryptography , 2018 .

[11]  Rainer A. Rueppel,et al.  Message Recovery for Signature Schemes Based on the Discrete Logarithm Problem , 1994, Des. Codes Cryptogr..

[12]  Oliver Schirokauer,et al.  Discrete Logarithms: The Effectiveness of the Index Calculus Method , 1996, ANTS.

[13]  Mihir Bellare,et al.  The Exact Security of Digital Signatures - HOw to Sign with RSA and Rabin , 1996, EUROCRYPT.

[14]  Alfred Menezes,et al.  Elliptic curve public key cryptosystems , 1993, The Kluwer international series in engineering and computer science.

[15]  Mihir Bellare,et al.  Fast Batch Verification for Modular Exponentiation and Digital Signatures , 1998, IACR Cryptol. ePrint Arch..

[16]  Neal Koblitz,et al.  An Elliptic Curve Implementation of the Finite Field Digital Signature Algorithm , 1998, CRYPTO.

[17]  R. Balasubramanian,et al.  The Improbability That an Elliptic Curve Has Subexponential Discrete Log Problem under the Menezes—Okamoto—Vanstone Algorithm , 1998, Journal of Cryptology.

[18]  Ian F. Blake,et al.  Elliptic Curves in Cryptography: Preface , 1999 .

[19]  Gerhard Frey,et al.  The Tate pairing and the discrete logarithm applied to elliptic curve cryptosystems , 1999, IEEE Trans. Inf. Theory.

[20]  Steven D. Galbraith,et al.  A Cryptographic Application of Weil Descent , 1999, IMACC.

[21]  N. Smart.  The Algorithmic Resolution of Diophantine Equations , 1999 .

[22]  Jean-Sébastien Coron,et al.  On the Exact Security of Full Domain Hash , 2000, CRYPTO.

[23]  S. Vanstone,et al.  Postal Revenue Colle tion in the Digital , 2000 .

[24]  Scott A. Vanstone,et al.  Postal Revenue Collection in the Digital Age , 2000, Financial Cryptography.

[25]  Jacques Stern,et al.  Signing on a Postcard , 2000, Financial Cryptography.

[26]  A. Joux,et al.  Separating Decision Diffie-Hellman from Diffie-Hellman in cryptographic groups , 2001, IACR Cryptol. ePrint Arch..

[27]  Steven D. Galbraith,et al.  Supersingular Curves in Cryptography , 2001, ASIACRYPT.

[28]  Eric R. Verheul,et al.  Self-Blindable Credential Certificates from the Weil Pairing , 2001, ASIACRYPT.

[29]  Nigel P. Smart,et al.  Constructive and destructive facets of Weil descent on elliptic curves , 2002, Journal of Cryptology.

[30]  A. Miyaji,et al.  New Explicit Conditions of Elliptic Curve Traces for FR-Reduction , 2001 .

[31]  Jean-Sébastien Coron,et al.  Optimal Security Proofs for PSS and Other Signature Schemes , 2002, EUROCRYPT.

[32]  Louis Goubin,et al.  QUARTZ, 128-Bit Long Digital Signatures , 2001, CT-RSA.

[33]  David Pointcheval,et al.  The Gap-Problems: A New Class of Problems for the Security of Cryptographic Schemes , 2001, Public Key Cryptography.

[34]  Steven D. Galbraith,et al.  Implementing the Tate Pairing , 2002, ANTS.

[35]  Alexandra Boldyreva,et al.  Efficient threshold signature, multisignature and blind signature schemes based on the Gap-Diffie-Hellman-group signature scheme , 2002, IACR Cryptol. ePrint Arch..

[36]  Paulo S. L. M. Barreto,et al.  Constructing Elliptic Curves with Prescribed Embedding Degrees , 2002, SCN.

[37]  Alice Silverberg,et al.  Supersingular Abelian Varieties in Cryptology , 2002, CRYPTO.

[38]  C. Diem.  The GHS-attack in odd characteristic , 2003 .

[39]  Jonathan Katz,et al.  Efficiency improvements for signature schemes with tight security reductions , 2003, CCS '03.

[40]  Alexandra Boldyreva,et al.  Threshold Signatures, Multisignatures and Blind Signatures Based on the Gap-Diffie-Hellman-Group Signature Scheme , 2003, Public Key Cryptography.

[41]  Matthew K. Franklin,et al.  Identity-Based Encryption from the Weil Pairing , 2001, CRYPTO.

[42]  Antoine Joux,et al.  Separating Decision Diffie–Hellman from Computational Diffie–Hellman in Cryptographic Groups , 2003, Journal of Cryptology.

[43]  Magnus Daum,et al.  On the Security of HFE, HFEv- and Quartz , 2003, Public Key Cryptography.

[44]  Hovav Shacham,et al.  Aggregate and Verifiably Encrypted Signatures from Bilinear Maps , 2003, EUROCRYPT.

[45]  Stanislaw Jarecki,et al.  A Signature Scheme as Secure as the Diffie-Hellman Problem , 2003, EUROCRYPT.

[46]  Craig Gentry,et al.  How to Compress Rabin Ciphertexts and Signatures (and More) , 2004, CRYPTO.

[47]  D. Boneh,et al.  Short Signatures from the Weil Pairing , 2001, Journal of Cryptology.

[48]  Antoine Joux,et al.  A One Round Protocol for Tripartite Diffie–Hellman , 2000, Journal of Cryptology.

[49]  Eric R. Verheul,et al.  Evidence that XTR Is More Secure than Supersingular Elliptic Curve Cryptosystems , 2004, Journal of Cryptology.

[50]  Paulo S. L. M. Barreto,et al.  Efficient Implementation of Pairing-Based Cryptosystems , 2004, Journal of Cryptology.

[51]  Victor S. Miller,et al.  The Weil Pairing, and Its Efficient Calculation , 2004, Journal of Cryptology.

[52]  Andreas Enge,et al.  Building Curves with Arbitrary Small MOV Degree over Finite Prime Fields , 2004, Journal of Cryptology.

[53]  A. Weng,et al.  Elliptic Curves Suitable for Pairing Based Cryptography , 2005, Des. Codes Cryptogr..

[54]  Benoît Chevallier-Mames,et al.  An Efficient CDH-Based Signature Scheme with a Tight Security Reduction , 2005, CRYPTO.

[55]  N. Smart,et al.  On Computable Isomorphisms in Efficient Pairing Based Systems ⋆ , 2005 .

[56]  Hugo Krawczyk,et al.  Secure Distributed Key Generation for Discrete-Log Based Cryptosystems , 1999, Journal of Cryptology.

[57]  P. Stevenhagen,et al.  ELLIPTIC FUNCTIONS , 2022 .