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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.  ...  We then show that bonsai trees resolve some central open questions in lattice-based cryptography: to summarize, they remove the need for random oracles in many important applications, and facilitate delegation  ...  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.  ...  We then show that bonsai trees resolve some central open questions in lattice-based cryptography: to summarize, they remove the need for random oracles in many important applications, and facilitate delegation  ...  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

Expressive Encryption Systems from Lattices [chapter]

Xavier Boyen
2011 Lecture Notes in Computer Science  
In this survey, we review a number of the many "expressive" encryption systems that have recently appeared from lattices, and explore the innovative techniques that underpin them.  ...  Given a good basis T A for an Ajtai lattice Λ ⊥ (A), they show how to create a (slightly less) good basis T B for another lattice Λ ⊥ (B), whose defining matrix B has the same dimension as A and can be  ...  used to reconstruct the delegator basis).  ... 
doi:10.1007/978-3-642-25513-7_1 fatcat:pzyrmvtkpjhcjk6gq6yhcjm3xq

Lattice Basis Delegation in Fixed Dimension and Shorter-Ciphertext Hierarchical IBE [chapter]

Shweta Agrawal, Dan Boneh, Xavier Boyen
2010 Lecture Notes in Computer Science  
We present a technique for delegating a short lattice basis that has the advantage of keeping the lattice dimension unchanged upon delegation.  ...  The resulting systems are very different from earlier lattice-based HIBEs and in some cases result in shorter ciphertexts and private keys. We prove security from classic lattice hardness assumptions.  ...  Randomizing a basis: Cash et al. [CHKP10] show how to randomize a lattice basis (see also [GN08, Sec. 2.1]).  ... 
doi:10.1007/978-3-642-14623-7_6 fatcat:vcvolzneufcq5hcwkiziswxlaq

Cryptanalysis of a lattice-based proxy signature scheme [article]

Miaomiao Tian, Liusheng Huang
2012 arXiv   pre-print
A proxy signature scheme allows a proxy signer to sign messages on behalf of an original signer.  ...  However, in this paper, we disprove their claim and show that an original signer is able to forge a proxy signature on any message.  ...  Trapdoor functions and lattice basis delegation Let A ∈ Z n×m q be a uniformly random matrix. Gentry et al.  ... 
arXiv:1110.4196v2 fatcat:ze76qwr7cfamfntx5mmtlscspe

Ring Signature Schemes from Lattice Basis Delegation [chapter]

Jin Wang, Bo Sun
2011 Lecture Notes in Computer Science  
In this paper, we propose a set of ring signature (RS) schemes using the lattice basis delegation technique due to [6, 7, 12] .  ...  Our proposed schemes fit with ring trapdoor functions introduced by Brakerski and Kalai [18] , and we obtain the first lattice-based ring signature scheme in the random oracle model.  ...  [6, 7, 12] who constructed a basis delegation technique that allows one to derive a short basis of a given lattice using a short basis of a related lattice.  ... 
doi:10.1007/978-3-642-25243-3_2 fatcat:qtyh4zxl75cptbptiz7x3clefi

Page 6319 of Mathematical Reviews Vol. , Issue 2002H [page]

2002 Mathematical Reviews  
To solve this system of equa- tions is essentially to find a “small” solution to these equations, which can be tackled using Babai’s polynomial time algorithm that finds a close lattice vector to a given  ...  Summary: “We propose two trapdoors for the closest-vector prob- lem in lattices related to the lattice tensor product.  ... 

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.  ...  Give an integer , a matrix ∈ × , a syndrome ∈ , and a real , to find an integer vector ∈ , such that = mod and ‖ ‖ 2 ≤ . Trapdoor and Basis Delegation Functions for Lattices.  ... 
doi:10.1155/2014/307637 fatcat:lx7wvv2bxzgh3ilz6egqreytw4

Lattice Mixing and Vanishing Trapdoors: A Framework for Fully Secure Short Signatures and More [chapter]

Xavier Boyen
2010 Lecture Notes in Computer Science  
We extend this idea to make the simulation trapdoors cancel not for a specic target but on a non-negligible subset of the possible challenges.  ...  We propose a framework for adaptive security from hard random lattices in the standard model.  ...  Elementary Delegation There are several ways to delegate a short basis for Λ ⊥ (A) into one for Λ ⊥ ([A|B]).  ... 
doi:10.1007/978-3-642-13013-7_29 fatcat:ndevagf73fff7ncjr75u2qv54u

Lattice-Based Hierarchical Inner Product Encryption [chapter]

Michel Abdalla, Angelo De Caro, Karina Mochetti
2012 Lecture Notes in Computer Science  
To achieve this goal, we extend the lattice-based IPE scheme by Agrawal, Freeman, and Vaikuntanathan (Asiacrypt'11) to the hierarchical setting by employing basis delegation technics by Peikert et al.  ...  In its hierarchical version, first proposed by Okamoto and Takashima (Asiacrypt'09), there exists an additional delegation mechanism which allows users to delegate their decryption capabilities to other  ...  [10] shows how to construct a basis for Λ ⊥ q (A B C) from a basis for Λ ⊥ q (B). Theorem 7. For i = 1, 2, 3 let A i be a matrix in Z n×mi q and let A := (A 1 A 2 A 3 ).  ... 
doi:10.1007/978-3-642-33481-8_7 fatcat:jffruusx3jgj7hteeae47mhd6q

Trapdoors for Lattices: Simpler, Tighter, Faster, Smaller [chapter]

Daniele Micciancio, Chris Peikert
2012 Lecture Notes in Computer Science  
Our methods involve a new kind of trapdoor, and include specialized algorithms for inverting LWE, randomly sampling SIS preimages, and securely delegating trapdoors.  ...  We give new methods for generating and using "strong trapdoors" in cryptographic lattices, which are simultaneously simple, efficient, easy to implement (even in parallel), and asymptotically optimal with  ...  LWE Inversion Algorithm 2 below shows how to use a trapdoor to solve LWE relative to A.  ... 
doi:10.1007/978-3-642-29011-4_41 fatcat:xykbsklp2vasbl3ybrt5hxyudy

Blind topological measurement-based quantum computation

Tomoyuki Morimae, Keisuke Fujii
2012 Nature Communications  
Blind quantum computation is a novel secure quantum-computing protocol that enables Alice, who does not have sufficient quantum technology at her disposal, to delegate her quantum computation to Bob, who  ...  has a fully fledged quantum computer, in such a way that Bob cannot learn anything about Alice's input, output and algorithm.  ...  (a) The elementary cell of the RHG lattice L. (b) The elementary cell of the decorated RHG lattice L′. How the decorated lattice works.  ... 
doi:10.1038/ncomms2043 pmid:22948818 pmcid:PMC3658012 fatcat:proz5gjpq5drxc2zirl4n4g5xq

Revocable attribute-based proxy re-encryption

Fucai Luo, Saif Al-Kuwari
2021 Journal of Mathematical Cryptology  
Then, we propose a lattice-based instantiation of revocable ABPRE.  ...  Attribute-based proxy re-encryption (ABPRE), which combines the notions of proxy re-encryption (PRE) and attribute-based encryption (ABE), allows a semi-trusted proxy with re-encryption key to transform  ...  However, in the traditional PRE systems, the communication model is one-to-one (i.e., one delegator to one delegatee), which means that a message can be re-encrypted for only a single public key.  ... 
doi:10.1515/jmc-2020-0039 fatcat:rxdopwunbzaczoz27uan7g3oyq

Lattice Based Forward-Secure Identity Based Encryption Scheme with Shorter Ciphertext

Kunwar Singh, C. Pandurangan, A. K. Banerjee
2013 Journal of Internet Services and Information Security  
We have reduced size of the ciphertext C from (m(i + 2) + 1) × Z q to (m + 1) × Z q where Z q is number of bits required to represent an element of Z q .  ...  In this paper we propose lattice based forward-secure identity based encryption scheme with shorter ciphertext in the random oracle model.  ...  Basis Delegation with Constant Dimension [2] We briefly explain Agrawal et al [2] ' basis delegation technique. Let T L = {l 1 , ..., l m } be a short basis of lattice L in Z m .  ... 
doi:10.22667/jisis.2013.02.31.005 dblp:journals/jisis/SinghPB13 fatcat:p57mmg2zbjaero3es6xhfg4nju

A Bloom Filter Based Model for Decentralized Authorization

Simon N. Foley, Guillermo Navarro-Arribas
2013 International Journal of Intelligent Systems  
A decentralised authorisation mechanism is proposed that uses Bloom filters to implement authorization delegation.  ...  This lightweight mechanism is unlike conventional approaches that typically rely on public key certificates to implement distributed delegation.  ...  The delegation mechanism works on the basis that it is not feasible for a principal to compute a Bloom permission B(⌈x⌉) unless the principal holds (has been delegated) the value for some B(⌈y⌉), where  ... 
doi:10.1002/int.21593 fatcat:yrj2rihzejfk5o2h3zll5vipyy
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