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An Asymptotically Optimal Structural Attack on the ABC Multivariate Encryption Scheme [chapter]

Dustin Moody, Ray Perlner, Daniel Smith-Tone
2014 Lecture Notes in Computer Science  
The attack is a structural key recovery attack which is asymp totically optimal among all known attacks (including algebraic attacks) on the original scheme and its generalizations.  ...  At PQCRYPTO '13 in Limoges, Tao, Diene, Tang, and Ding introduced a promising new multivariate encryption algorithm based on a fundamentally new idea: hiding the structure of a large matrix algebra over  ...  In this article, we present a structural attack which is the asymptotically optimal s+4 attack on this matrix encryption scheme, having a complexity on the order of q , where s is the dimension of the  ... 
doi:10.1007/978-3-319-11659-4_11 fatcat:c246a44cg5bchg474fiuvzbtwu

Improved Attacks for Characteristic-2 Parameters of the Cubic ABC Simple Matrix Encryption Scheme [chapter]

Dustin Moody, Ray Perlner, Daniel Smith-Tone
2017 Lecture Notes in Computer Science  
In the last few years multivariate public key cryptography has experienced an infusion of new ideas for encryption.  ...  One promising approach to cryptanalyzing these schemes has been structural cryptanalysis, based on applying a strategy similar to MinRank attacks to the discrete differential.  ...  Recently, a new framework for developing secure multivariate encryption schemes has surfaces, drawing on the idea that it may impose sufficiently few restrictions on a multivariate map to be merely an  ... 
doi:10.1007/978-3-319-59879-6_15 fatcat:m2sdxehkuvbxfav2xae3ii4uzy

Extension Field Cancellation: A New Central Trapdoor for Multivariate Quadratic Systems [chapter]

Alan Szepieniec, Jintai Ding, Bart Preneel
2016 Lecture Notes in Computer Science  
After applying this transformation, the plaintext can be recovered by solving a linear system. We use the minus and projection modifiers to inoculate our scheme against known attacks.  ...  This paper introduces a new central trapdoor for multivariate quadratic (MQ) public-key cryptosystems that allows for encryption, in contrast to time-tested MQ primitives such as Unbalanced Oil and Vinegar  ...  The authors would like to thank the anonymous reviewers for their helpful comments. This work was supported in part by the Research Council  ... 
doi:10.1007/978-3-319-29360-8_12 fatcat:dl4f6ceagzhibhnnjsmmb6padm

Recent Developments in Multivariate Public Key Cryptosystems [chapter]

Yasufumi Hashimoto
2020 Mathematics for Industry  
On the other hand, there are few multivariate encryption schemes expected to be practical and despite that, various new schemes have been proposed recently.  ...  In the present paper, we summarize multivariate schemes UOV, Rainbow, and (variants of) HFE generating the second round candidates and study the practicalities of several multivariate encryption schemes  ...  Acknowledgements The author would like to thank the anonymous reviewer(s) for reading the previous draft and giving helpful comments.  ... 
doi:10.1007/978-981-15-5191-8_16 fatcat:b62b2eu5mzdjnmvyik2rewbyxu

Security Analysis and Key Modification for ZHFE [chapter]

Ray Perlner, Daniel Smith-Tone
2016 Lecture Notes in Computer Science  
., is one of the few promising candidates for a multivariate public-key encryption algorithm. In this article we extend and expound upon the existing security analysis on this scheme.  ...  We further suggest a modification, ZHF E − , a multivariate encryption scheme which retains the security and performance properties of ZHF E while optimizing key size in this theoretical framework.  ...  In [12] , however, a new and unexpected attack was presented on the ABC simple matrix encryption scheme of [9] .  ... 
doi:10.1007/978-3-319-29360-8_13 fatcat:pzfbzk4nj5hcthtgwqaformwwu

Post-Quantum Cryptography: State of the Art [chapter]

Johannes A. Buchmann, Denis Butin, Florian Göpfert, Albrecht Petzoldt
2016 Lecture Notes in Computer Science  
This paper gives an overview of the alternative public-key schemes that have the capability to resist quantum computer attacks and compares them.  ...  However, as a result of Peter Shor shows, the public-key schemes that are being used today will become insecure once quantum computers reach maturity.  ...  The currently most promising multivariate encryption scheme is the Sim-pleMatrix (or ABC) encryption scheme [71] , which allows very fast en-and decryption.  ... 
doi:10.1007/978-3-662-49301-4_6 fatcat:ylrv42q33fegnidacywmkzmvme

Practical-Sized Instances of Multivariate PKCs: Rainbow, TTS, and ℓIC-Derivatives [chapter]

Anna Inn-Tung Chen, Chia-Hsin Owen Chen, Ming-Shing Chen, Chen-Mou Cheng, Bo-Yin Yang
2008 Lecture Notes in Computer Science  
We present instances of MPKCs (multivariate public key cryptosystems) with design, given the best attacks we know, and implement them on commodity PC hardware.  ...  In fact, they can be up to an order of magnitude faster.  ...  Acknowledgements The authors thank Prof. Jintai Ding and Pei-Yuan Wu for invaluable comments and discussions, and also to National Science Council for sponsorship under Grant 96-2221-E-001-031-MY3.  ... 
doi:10.1007/978-3-540-88403-3_7 fatcat:i7w7nqtljzcejnxtrztk7u57pa

Quantum Computing: A Taxonomy, Systematic Review and Future Directions [article]

Sukhpal Singh Gill, Adarsh Kumar, Harvinder Singh, Manmeet Singh, Kamalpreet Kaur, Muhammad Usman, Rajkumar Buyya
2021 arXiv   pre-print
Quantum computing is an emerging paradigm with the potential to offer significant computational advantage over conventional classical computing by exploiting quantum-mechanical principles such as entanglement  ...  As the quantum devices are expected to steadily scale up in the next few years, quantum decoherence and qubit interconnectivity are two of the major challenges to achieve quantum advantage in the NISQ  ...  Multivariate Encryption/decryption schemes [190] - [193] EFLASH, C* Toy, PFLASH, C*, SFLASH, Hidden Field Equation (HFE), HFE -, ABC, SRP, EFC.  ... 
arXiv:2010.15559v4 fatcat:y6cuttww5fd5jdmvcer352lh4e

GRAFFL: Gradient-free Federated Learning of a Bayesian Generative Model [article]

Seok-Ju Hahn, Junghye Lee
2020 arXiv   pre-print
One of the major benefits is to mitigate the privacy risks as the learning of algorithms can be achieved without collecting or sharing data.  ...  Unlike conventional federated learning algorithms based on gradients, our framework does not require to disassemble a model (i.e., to linear components) or to perturb data (or encryption of data for aggregation  ...  Some theoretical analyses on the relationship between an acceptance threshold value and an asymptotic convergence property of ABC exist [7, 10, 20] ;, it is limited to be applied in a practical setting  ... 
arXiv:2008.12925v1 fatcat:atcgvlttqrba5dyl7e72wwwq5e

Multivariate Public Key Cryptosystem from Sidon Spaces [article]

Netanel Raviv, Ben Langton, Itzhak Tamo
2022 arXiv   pre-print
In particular, it is proved that the two popular attacks on the MinRank problem, the kernel attack, and the minor attack, succeed only with exponentially small probability.  ...  This paper proposes a new public-key cryptosystem of the multivariate type which is based on Sidon spaces, and has the potential to remain secure even if quantum supremacy is attained.  ...  Recently, the so-called ABC cryptosystem [29] , that relies on simple matrix multiplication as the encryption scheme, seems to have been broken by [13] .  ... 
arXiv:2106.07785v3 fatcat:bnv5npc6wnb4hobv2ddplcxhhi

Structure-Preserving Signatures on Equivalence Classes and Constant-Size Anonymous Credentials

Georg Fuchsbauer, Christian Hanser, Daniel Slamanig
2018 Journal of Cryptology  
We also introduce a set-commitment scheme that lets one open subsets of the committed set.  ...  Our ABC system avoids costly zero-knowledge proofs and only requires a short interactive proof to thwart replay attacks.  ...  The work of the second author has been supported by the European Commission through project FP7-MATTHEW (GA No. 610436).  ... 
doi:10.1007/s00145-018-9281-4 fatcat:yo4uxp4sb5aubiosnkp2fbvrja

Practical Functional Encryption for Quadratic Functions with Applications to Predicate Encryption [chapter]

Carmen Elisabetta Zaira Baltico, Dario Catalano, Dario Fiore, Romain Gay
2017 Lecture Notes in Computer Science  
Specifically, our constructions enable the computation of so-called bilinear maps on encrypted vectors.  ...  This significantly improves the O(n 2 ) bound one would get from inner product encryption-based constructions.  ...  This is in sharp contrast with the O(n 2 ) solutions one would get via inner product encryption schemes (e.g., [28] ). An informal description of our FE schemes.  ... 
doi:10.1007/978-3-319-63688-7_3 fatcat:c34wxox2dfdc7kh5f6qe7xemza

Efficient Sorting of Homomorphic Encrypted Data with k-way Sorting Network [article]

Seungwan Hong, Seunghong Kim, Jiheon Choi, Younho Lee, Jung Hee Cheon
2021 IACR Cryptology ePrint Archive  
Fully homomorphic encryption (FHE), an innovative method that facilitates operations on encrypted inputs without decryption, has been developed to turn privacy-preserving computation into reality [24]  ...  In this study, we propose an efficient sorting method for encrypted data using fully homomorphic encryption (FHE).  ...  Then we can set the largest modulus Q to 2 2900 by considering the state-of-the-art attacks for ring LWE encryption schemes for sparse ternary secret [17] .  ... 
dblp:journals/iacr/HongKCLC21 fatcat:b2f7xhmsgren3mpqcqphuhwu4u

Public-Key Encryption, Revisited: Tight Security and Richer Functionalities

Romain Gay
2019 Zenodo  
We also give new functional encryption schemes, whose security relies on well-founded assumptions.  ...  This is necessary when considering widely deployed encryption schemes, where many sessions are performed concurrently, as in the case on the Internet; 2) we consider so-called Functional ENcryption, introduced  ...  Multi-ciphertext CCA-secure Public Key Encryption scheme Our construction We now describe the optimized IND-CCA-secure PKE scheme.  ... 
doi:10.5281/zenodo.3405872 fatcat:ypcfqlzjifephog53uenm4mqm4

Pinocchio: Nearly Practical Verifiable Computation

B. Parno, J. Howell, C. Gentry, M. Raykova
2013 2013 IEEE Symposium on Security and Privacy  
Pinocchio also reduces the worker's proof effort by an additional 19-60×. As an additional feature, Pinocchio generalizes to zero-knowledge proofs at a negligible cost over the base protocol.  ...  The worker then evaluates the computation on a particular input and uses the evaluation key to produce a proof of correctness.  ...  on compiler development; Rosario Gennaro for valuable discussions; and the anonymous reviewers for their helpful comments.  ... 
doi:10.1109/sp.2013.47 dblp:conf/sp/ParnoHG013 fatcat:ilx75lduibccnek4nfreezyx7q
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