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Bonsai Trees, or How to Delegate a Lattice Basis [chapter]

David Cash, Dennis Hofheinz, Eike Kiltz, Chris Peikert
2010 Lecture Notes in Computer Science  
We introduce a new lattice-based cryptographic structure called a bonsai tree, and use it to resolve some important open problems in the area.  ...  Our Results We put forward a new cryptographic notion called a bonsai tree, and give a realization based on hard lattice problems.  ...  The ancient art of bonsai is centered around a tree and the selective control thereof by an arborist, the tree's cultivator and caretaker.  ... 
doi:10.1007/978-3-642-13190-5_27 fatcat:r6f2xojvhvf6xagod4algivijm

Bonsai Trees, or How to Delegate a Lattice Basis

David Cash, Dennis Hofheinz, Eike Kiltz, Chris Peikert
2011 Journal of Cryptology  
We introduce a new lattice-based cryptographic structure called a bonsai tree, and use it to resolve some important open problems in the area.  ...  Our Results We put forward a new cryptographic notion called a bonsai tree, and give a realization based on hard lattice problems.  ...  The ancient art of bonsai is centered around a tree and the selective control thereof by an arborist, the tree's cultivator and caretaker.  ... 
doi:10.1007/s00145-011-9105-2 fatcat:rvpebkwqpjdjnmxkaamfffulbq

Adaptively Secure Identity-Based Identification from Lattices without Random Oracles [chapter]

Markus Rückert
2010 Lecture Notes in Computer Science  
Our scheme uses an ideal-lattice interpretation of the Bonsai tree concept in lattices (EUROCRYPT 2010), which we call convoluted Bonsai trees.  ...  We propose a concurrently secure, identity-based identification scheme from lattices.  ...  [SSTX09] because they show how to generate an ideal lattice together with a basis of short vectors of that lattice. The notion of Bonsai trees on lattices is an analogy to arboriculture.  ... 
doi:10.1007/978-3-642-15317-4_22 fatcat:64z4vtwifbgepix4lkdrj7nfmq

A Lattice-Based Identity-Based Proxy Blind Signature Scheme in the Standard Model

Lili Zhang, Yanqin Ma
2014 Mathematical Problems in Engineering  
A proxy blind signature scheme is a special form of blind signature which allowed a designated person called proxy signer to sign on behalf of original signers without knowing the content of the message  ...  Moreover, lattice-based cryptography is believed to be hard even for quantum computers.  ...  In 2010, Cash et al. put forward a new cryptographic notion called a bonsai tree based on hard lattice [20] .  ... 
doi:10.1155/2014/307637 fatcat:lx7wvv2bxzgh3ilz6egqreytw4

A New Lattice-Based Signature Scheme in Post-Quantum Blockchain Network

Chao-Yang Li, Xiu-Bo Chen, Yu-Ling Chen, Yan-Yan Hou, Jian Li
2019 IEEE Access  
Then, a new lattice-based signature scheme has been proposed, which can be used to secure the blockchain network over existing classical channels.  ...  Meanwhile, the public and private keys are generated by the Bonsai Trees technology with RandBasis algorithm from the root keys, which not only ensure the randomness, but also construct the lightweight  ...  Then, save (A 0 , T A 0 ) as the root lattice basis, and generate the sub-public and private keys by the bonsai tree algorithm [27, Fig. 2] .  ... 
doi:10.1109/access.2018.2886554 fatcat:ej4n4amjejecbhbstjil6tzcqu

Experiment-Calculated Estimate of a LSIC Operation Reliability in order to Ensure Safety of Information under Radiation Influence

Vyacheslav Mihailovich Barbashov, Vitaly Grigorievich Ivanenko, Nikolai Sergeievich Trushkin
2015 Bezopasnostʹ Informacionnyh Tehnologij  
In this paper digital systems safety operation prediction methods under radiation influence, founded on Brower digital automate and a digital systems operation estimate topological probabilistic models  ...  Bonsai trees, or How to delegate a lattice basis. URL: http://www.cc.gatech. edu/~cpeikert/pubs/bonsai.pdf. 6. Kawachi A., Tanaka K., Xagawa K.  ...  A group signature scheme from lattice assumptions. URL: https://eprint.iacr.org/2011/ 060.pdf. 3. Laguillaumie F., Langlois A., Libert B., Stehle D.  ... 
doaj:2a4c1926d43c463ba43fa11134eb2c55 fatcat:hy4a2nsp2nak7or3jglyf63mwy

Strongly Unforgeable Signatures and Hierarchical Identity-Based Signatures from Lattices without Random Oracles [chapter]

Markus Rückert
2010 Lecture Notes in Computer Science  
We propose a variant of the "bonsai tree" signature scheme, a latticebased existentially unforgeable signature scheme in the standard model.  ...  Strong unforgeability demands that the adversary is unable to produce a new message-signature pair (m, s), even if he or she is allowed to see a different signature s for m.  ...  The author is indebted to one of the reviewers, who suggested a simplification for demonstrating that the scheme in [12] is not SU-CMA secure.  ... 
doi:10.1007/978-3-642-12929-2_14 fatcat:r2goh4grkzdl5ek6ddhc4llb3e

Forward-Secure Group Signatures from Lattices [article]

San Ling and Khoa Nguyen and Huaxiong Wang and Yanhong Xu
2019 arXiv   pre-print
To realize this essential building block, we first employ the Bonsai tree structure by Cash et al. (EUROCRYPT 2010) to handle the key evolution process, and then develop Langlois et al.'  ...  At the heart of our construction is a scalable lattice-based key evolving mechanism, allowing users to periodically update their secret keys and to efficiently prove in zero-knowledge that key evolution  ...  To achieve logarithmic overhead, we should think of a way to employ the structure of the Bonsai tree.  ... 
arXiv:1801.08323v2 fatcat:c6bxjqcs7jbklizxbrzey4nb7u

An Efficient Homomorphic Aggregate Signature Scheme Based on Lattice

Zhengjun Jing
2014 Mathematical Problems in Engineering  
In order to design an efficient postquantum secure HAS scheme, we borrow the idea of the lattice-based LHS scheme over binary field in the single-user case, and develop it into a new lattice-based HAS  ...  The security of the proposed scheme is proved by showing a reduction to the single-user case and the signature length remains invariant.  ...  To derive a new short basis of the highdimension lattice Λ ⊥ (A) ⊂ Z , some lemmas about the basis delegation mechanism proposed by Cash et al. in [21] will be employed.  ... 
doi:10.1155/2014/536527 fatcat:ekiaiqrfibaijoqh4u2d74hikm

Efficient Lattice CP-ABE AC Scheme Supporting Reduced-OBDD Structure for CCN/NDN

Affum, Zhang, Wang, Ansuura
2020 Symmetry  
To achieve an efficient scheme, we used an efficient trapdoor technique and the access tree representation of access structure describing the access policies was modified into a new structure, based on  ...  The attribute based encryption (ABE) scheme is a preferable approach, identified to enable cached contents to be self-secured since it has a special property of encryption with policies.  ...  To solve some open issues, a bonsai tree, which is a cryptography structure based on lattice, was proposed by David Cash [27] .  ... 
doi:10.3390/sym12010166 fatcat:3xbp35ztujfa3gxoe4ctgekpei

Constrained Keys for Invertible Pseudorandom Functions [chapter]

Dan Boneh, Sam Kim, David J. Wu
2017 Lecture Notes in Computer Science  
In this paper we show how to constrain an invertible PRF (IPF), which is significantly harder. An IPF is a secure injective PRF accompanied by an inversion algorithm.  ...  A constrained key for an IPF can only be used to evaluate the IPF on a subset S of the domain, and to invert the IPF on the image of S.  ...  Acknowledgments This work was funded by NSF, DARPA, a grant from ONR, and the Simons Foundation.  ... 
doi:10.1007/978-3-319-70500-2_9 fatcat:gusmoqldtzg27m7nylzhsm27ca

Zero-Knowledge Arguments for Lattice-Based Accumulators: Logarithmic-Size Ring Signatures and Group Signatures Without Trapdoors [chapter]

Benoît Libert, San Ling, Khoa Nguyen, Huaxiong Wang
2016 Lecture Notes in Computer Science  
In the lattice setting, currently known instantiations of the primitive are based on Merkle trees, which do not interact well with zero-knowledge proofs.  ...  It has proved useful in the design of numerous privacy-enhancing protocols, in order to handle revocation or simply prove set membership.  ...  have a GPV trapdoor [32] consisting of a short lattice basis.  ... 
doi:10.1007/978-3-662-49896-5_1 fatcat:oyaa6tifrra75jt6dwhgfarm5e

Learning with Errors in the Exponent [chapter]

Özgür Dagdelen, Sebastian Gajek, Florian Göpfert
2016 Lecture Notes in Computer Science  
We put forth the notion of Learning with Errors in the Exponent (LWEE) and rather surprisingly show that various attractive properties known to exclusively hold for lattices carry over.  ...  We initiate the study of a novel class of group-theoretic intractability problems.  ...  Acknowledgements The authors would like to thank Steven Galbraith and Dan Bernstein to point to a bug in a previous version of the paper, and the attendees of the Cryptography Workshop in Oberwolfach for  ... 
doi:10.1007/978-3-319-30840-1_5 fatcat:7i25r2bn6bdgphr3lzqj64zmxq

A Note on the Post-Quantum Security of (Ring) Signatures [article]

Rohit Chatterjee, Kai-Min Chung, Xiao Liang, Giulio Malavolta
2021 arXiv   pre-print
(Crypto'21) proposes a definition trying to capture adversaries with quantum access to the signer.  ...  Moreover, assuming the quantum hardness of LWE, we construct a compiler converting any blind-unforgeable (ordinary) signatures to a ring signature satisfying our definition.  ...  Bonsai trees, or how to delegate a lattice basis. In Gilbert [Gil10], pages 523–552. 14 CHS19. Jan Czajkowski, Andreas Hülsing, and Christian Schaffner.  ... 
arXiv:2112.06078v1 fatcat:potybhcv7nfqbaw4ek5ggiklmu

Digital signature scheme for information non-repudiation in blockchain: a state of the art review

Weidong Fang, Wei Chen, Wuxiong Zhang, Jun Pei, Weiwei Gao, Guohui Wang
2020 EURASIP Journal on Wireless Communications and Networking  
A digital signature scheme is an effective approach to achieve nonrepudiation.  ...  Our works will facilitate to design efficient and secure digital signature algorithms in blockchain.  ...  Acknowledgements We are grateful to the anonymous reviewers who have contributed to the enhancement of the paper's completeness with their valuable suggestions.  ... 
doi:10.1186/s13638-020-01665-w fatcat:wnp4uxzixzfzngxnerlkbewame
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