Toward Quantum-Resistant Strong Designated Verifier Signature from Isogenies

@article{Sun2012TowardQS,
  title={Toward Quantum-Resistant Strong Designated Verifier Signature from Isogenies},
  author={Xi Sun and Haibo Tian and Yumin Wang},
  journal={2012 Fourth International Conference on Intelligent Networking and Collaborative Systems},
  year={2012},
  pages={292-296}
}
  • Xi Sun, Haibo Tian, Yumin Wang
  • Published 19 September 2012
  • Computer Science, Mathematics
  • 2012 Fourth International Conference on Intelligent Networking and Collaborative Systems
This paper proposes a strong designated verifier signature (SDVS) based on a recently proposed mathematical problem. It consists in searching for an isogeny between super singular elliptic curves. The problem is hypothetically strong against a quantum computer. This makes our proposal the first SDVS scheme that may be secure against a quantum computer. 
Toward quantum-resistant strong designated verifier signature
TLDR
Two Strong Designated Verifier Signature SDVS schemes based on two post-quantum key agreement protocols are proposed, the first instantiations of a basic design idea about SDVS that are potentially secure against a quantum computer.
Isogeny-Based Quantum-Resistant Undeniable Signatures
We propose an undeniable signature scheme based on elliptic curve isogenies, and prove its security under certain reasonable number-theoretic computational assumptions for which no efficient quantum
Isogeny-based Quantum-resistant Undeniable Blind Signature Scheme
TLDR
This paper formalizes the notion of a Undeniable Blind Signature scheme by giving the formal definition, and states the isogeny problems in a more general form and discusses their computational hardnesses.
A Post-quantum Digital Signature Scheme Based on Supersingular Isogenies
TLDR
This scheme is an application of Unruh’s construction of non-interactive zero- knowledge proofs to an interactive zero-knowledge proof proposed by De Feo, Jao, and Plut.
Supersingular Isogeny-Based Designated Verifier Blind Signature
TLDR
A quantum-resistant designated verifier blind signature (DVBS) scheme based on supersingular isogenies from the proposed generic construction of a DVS from hard homogeneous spaces is realized.
Signature Schemes Based On Supersingular Isogeny Problems
TLDR
The first signature schemes whose security relies on computational assumptions relating to isogeny graphs of supersingular elliptic curves and which lead to signatures that are existentially unforgeable under chosen message attacks are presented.
Loop-Abort Faults on Supersingular Isogeny Cryptosystems
TLDR
It appears that the iterative structure of the secret isogeny computation renders these schemes vulnerable to loop-abort attacks, which means implementing additional countermeasures seems unavoidable for applications where physical attacks are relevant.
Advances Towards Practical Implementations of Isogeny Based Signatures
TLDR
This dissertation explores two different modifications to the implementation of an isogeny-based signature scheme built on top of SIDH, one with the intent of improving temporal performance, and another with theintent of reducing signature sizes.
Fault Attack on Supersingular Isogeny Cryptosystems
  • Y. Ti
  • Computer Science, Mathematics
    PQCrypto
  • 2017
TLDR
The first fault attack on cryptosystems based on supersingular isogenies, which aims to change the base point to a random point on the curve via a fault injection, demonstrates the need to incorporate checks in implementations of the cryptos system.
On the Non-repudiation of Isogeny Based Signature Scheme
TLDR
A successful key substitution attack on GPS signature which threaten the non-repudiation of GPS signature is presented and how to prevent key substitution attacked in general as well as the attack is suggested.
...
...

References

SHOWING 1-10 OF 13 REFERENCES
An Efficient Strong Designated Verifier Signature Scheme
TLDR
This paper proposes a designated verifier signature scheme based on the Schnorr signature and the Zheng signcryption schemes that achieves the “strong designated verifiers” property without encrypting any part of the signatures.
Towards Quantum-Resistant Cryptosystems from Supersingular Elliptic Curve Isogenies
TLDR
The main technical idea in this scheme is that the images of torsion bases under the isogeny are transmitted in order to allow the two parties to arrive at a common shared key despite the noncommutativity of the endomorphism ring.
Efficient Strong Designated Verifier Signature Schemes without Random Oracles or Delegatability
TLDR
A highly efficient SDVS scheme based on pseudorandom functions, which is proved to be secure in the standard model and shows that it is secure based on discrete logarithm assumption and gap Diffie-Hellman assumption in the random oracle model.
Short Designated Verifier Signature Scheme and Its Identity-based Variant
TLDR
This paper proposes the first construction of short strong designated verifier signature scheme, and extends it to the short identity-based strong designate verifier scheme and provides formal security proofs for the schemes based on the random oracle model.
Designated Verifier Signatures: Anonymity and Efficient Construction from Any Bilinear Map
TLDR
The notion of privacy of signer's identity is formalized which captures the strong designated verifier property investigated in their paper and a variant of the pairing-based DVS scheme introduced at Asiacrypt'03 by Steinfeld, Bull, Wang and Pieprzyk is proposed.
Efficient strong designated verifier signature schemes without random oracle or with non-delegatability
TLDR
Two new SDVS schemes are proposed, one of which is efficient and provably secure in the random oracle model based on the discrete logarithm assumption and Gap Diffie–Hellman assumption and the second is the first SDVS supporting non-delegatability.
Constructing elliptic curve isogenies in quantum subexponential time
TLDR
This work gives a new subexponential-time quantum algorithm for constructing nonzero isogenies between two such elliptic curves, assuming the Generalized Riemann Hypothesis (but with no other assumptions).
Public-Key Cryptosystem Based on Isogenies
TLDR
The paper describes theoretical background and a publickey encryption technique, followed by security analysis and consideration of cryptosystem parameters selection, and proposes ElGamal public-key encryption and Diffie-Hellman key agreement for an isogeny Cryptosystem.
Quantum Cryptanalysis of Hidden Linear Functions (Extended Abstract)
TLDR
It is shown that any cryptosystem based on what is referred to as a ‘hidden linear form’ can be broken in quantum polynomial time and the notion of ‘junk bits’ is introduced which are helpful when performing classical computations that are not injective.
Constructing public-key cryptographic schemes based on class group action on a set of isogenous elliptic curves
  • A. Stolbunov
  • Mathematics, Computer Science
    Adv. Math. Commun.
  • 2010
TLDR
This work proposes a public-key encryption scheme and key agreement protocols based on a group action on a set and introduces a novel way of using elliptic curves for constructing asymmetric cryptography.
...
...