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Homomorphic public-key cryptosystems over groups and rings [article]

Dima Grigoriev, Ilia Ponomarenko
2003 arXiv   pre-print
We propose a new homomorphic public-key cryptosystem over arbitrary nonidentity finite group based on the difficulty of the membership problem for groups of integer matrices.  ...  Besides, a homomorphic cryptosystem is designed for the first time over finite commutative rings.  ...  If the inversion of f is efficiently computable and computing of f is a hard computational problem (i.e. f is a trapdoor function), one can design a homomorphic public-key cryptosystem in which an element  ... 
arXiv:cs/0309010v1 fatcat:m5oleeiwpjd4zoimohk4ji3w7i

Quantum Public-Key Cryptosystems [chapter]

Tatsuaki Okamoto, Keisuke Tanaka, Shigenori Uchiyama
2000 Lecture Notes in Computer Science  
This paper proposes a concrete scheme for quantum public-key cryptosystems: a quantum public-key encryption scheme or quantum trapdoor one-way function.  ...  This paper presents a new paradigm of cryptography, quantum public-key cryptosystems.  ...  We can naturally extend the definitions of one-way functions, trapdoor one-way functions, public-key encryption, digital signatures, and the related security notions.  ... 
doi:10.1007/3-540-44598-6_9 fatcat:np2qz66kwfgpjhey6z2rkthazu

Page 1665 of Mathematical Reviews Vol. , Issue 2004b [page]

2004 Mathematical Reviews  
R. (3-WTRL-B; Waterloo, ON); van Trung, Tran [Tran Van Trung] (D-ESSN-EM; Essen) New approaches to designing public key cryptosystems using one-way functions and trapdoors in finite groups.  ...  The paper proposes two approaches to the design of public key cryptosystems based on representing elements of a finite group as products of a restricted form.  ... 

Extended multivariate public key cryptosystems with secure encryption function

HouZhen Wang, HuanGuo Zhang, ZhangYi Wang, Ming Tang
2011 Science China Information Sciences  
Advances in quantum computers pose great threats on the currently used public key cryptographic algorithms such as RSA and ECC.  ...  Thorough analysis shows that our schemes are secure and efficient. Our MPKC gives a positive response to the challenges in multivariate public key cryptography.  ...  Consequently, randomly chosen quadratic equations over finite field F q like (1) is a one-way function.  ... 
doi:10.1007/s11432-011-4262-3 fatcat:xxojpuwgzfaxdhgwfn6tigrcgm

Scytale – An Evolutionary Cryptosystem [article]

Unnikrishnan Menon, Atharva Hudlikar, Divyani Panda
2020 arXiv   pre-print
With the advent of quantum computing, and other advancements in computation and processing capabilities of modern systems, there arises a need to develop new trapdoor functions that will serve as the foundation  ...  This paper explores the possibility of one such potential trapdoor function using concepts stemming from Reversible Cellular Automata (RCA) -- specifically, the Critter's Rule set up in a Margolus Neighborhood  ...  and researchers prodding into AES have found potential ways of cryptanalysis, one of them being a possible key-attack where the operation of a cipher in response to different keys is tracked  ... 
arXiv:2008.05290v1 fatcat:oswgb7xifbf7lnifijmsi4q7ka

Improvement of Lattice-Based Cryptography Using CRT [chapter]

Thomas Plantard, Mike Rose, Willy Susilo
2010 Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering  
In this paper, we first critically analyze two existing latticebased cryptosystems, namely GGH and Micciancio, and identify their drawbacks.  ...  Furthermore, we also propose another cryptosystem optimized for CRT, drawing on the strengths of both cryptosystems. We provide a fair comparison between our scheme and the existing ones.  ...  As a result, new one-way trapdoor functions must be developed that will remain secure after quantum computers become available.  ... 
doi:10.1007/978-3-642-11731-2_34 fatcat:x4adbltnqjgb3beg3secvdpqsy

The Mathematics of Public-Key Cryptography

Martin E. Hellman
1979 Scientific American  
The search for privacy in an age of electronic communications has given rise to new methods of encryption. These methods are more practical than older ones and are mathematically more interesting  ...  Trapdoor one-way functions serve as ba sis of public-key cryptosystems: public key specifies easily computed function, wbich is infea sible to invert unless one knows secret key; tbat key specifies easily  ...  And for the NP problems on which public key cryptosystems have been based it has been possible to build trapdoors into the functions as well.  ... 
doi:10.1038/scientificamerican0879-146 fatcat:7t6pp7s2gveq5cj7vjug6xrdmy

Efficient Design of Certificateless Chameleon Signature from Bilinear Pairing

Tejeshwari Thakur, Neetu Sharma, Birendra Kumar Sharma
2014 International Journal of Database Theory and Application  
Thus, CL-PKC can be seen as a model for the use in public key cryptography. In this paper, we proposed a new certificateless Chameleon signature scheme based on bilinear pairings.  ...  Certificateless public key cryptography (CL-PKC), does not require the use of the certificate to guarantee the authenticity of public keys.  ...  Acknowledgements The first author 1 is thankful to UGC, New Delhi, India for providing Rajiv Gandhi National Fellowship (F1-17.1/2010-13/RGNF-2012-13-ST-CHH-35416) as financial assistance for this Research  ... 
doi:10.14257/ijdta.2014.7.3.03 fatcat:7t46planqzhthog4xrelitdu5q

On a public-key cryptosystem based on iterated morphisms and substitutions

Arto Salomaa, Sheng Yu
1986 Theoretical Computer Science  
A public-key cryptosystem based essentially on ideas coming from L systems was introduced in (Salomaa and Welzl, 1983), see also (Salomaa, 1985) and (Salomaa, 1984) .  ...  In particular, we investigate cryptanalytic approaches and what one can accomplish by preprocessing.  ...  We want to thank the Academy of Finland for a grant making possible this visit.  ... 
doi:10.1016/0304-3975(86)90099-x fatcat:escscmw67fechpwx3tjnfy7qiq

The dual receiver cryptosystem and its applications

Theodore Diament, Homin K. Lee, Angelos D. Keromytis, Moti Yung
2004 Proceedings of the 11th ACM conference on Computer and communications security - CCS '04  
The cryptosystem is simple and efficient yet powerful, as it solves two problems of practical importance whose solutions have proven to be elusive before: (1) A provably secure "combined" public-key cryptosystem  ...  We put forth the notion of a dual receiver cryptosystem and implement it based on bilinear pairings over certain elliptic curve groups.  ...  Our basic design is a cryptosystem that transforms the three-party one-round Diffie-Hellman key exchange proposed by Joux [28] into a dual receiver cryptosystem public key.  ... 
doi:10.1145/1030083.1030128 dblp:conf/ccs/DiamentLKY04 fatcat:5ze6czz44ndwbk5ncqoxxqoidi

A Comparative Study of Homomorphic and Searchable Encryption Schemes for Cloud Computing [article]

B.T. Prasanna, C.B. Akki
2015 arXiv   pre-print
Since in cloud the data is outsourced to third parties, the protection of confidentiality and privacy of user data becomes important.  ...  Different methods for securing the data in cloud have been proposed by researchers including but not limited to Oblivious RAM, Searchable Encryption, Functional Encryption, Homomorphic Encryption etc.  ...  Trapdoor functions are used to secure data in HE. They are one way functions used during encryption and decryption process. Different mathematical constructs are used to create trapdoors.  ... 
arXiv:1505.03263v1 fatcat:6lugnvheqnepfecz2j6mbjqoyu

STUDY OF CRYPTOLOGY AND ITS FORMS IN TODAY'S SECURE WORLD

D KALYANI
2017 International Journal of Advanced Research in Computer Science  
In this paper, we are highlighting the need for security in daily data transmissions and the role of cryptography in order to handle demands of today's secure world.  ...  that is used in daily life as a part of secure communication.  ...  Asymmetric key crypto decryption schemes rely on trapdoor of one-way hash functions.  ... 
doi:10.26483/ijarcs.v8i9.4975 fatcat:dqjzzr3fordmdfwo6w6wwwznnm

Trapdooring Discrete Logarithms on Elliptic Curves over Rings [chapter]

Pascal Paillier
2000 Lecture Notes in Computer Science  
The cryptosystems are based on three specific trapdoor mechanisms allowing the recipient to recover discrete logarithms on different types of curves.  ...  This paper introduces three new probabilistic encryption schemes using elliptic curves over rings.  ...  Without considering all potential applications, this paper focuses on providing and analyzing new discrete log trapdoors and comparing their properties with the ones recently discovered in [8, 9, 11]  ... 
doi:10.1007/3-540-44448-3_44 fatcat:bc6lmplahbcllh3wj3axhgkshm

A Public Key Cryptosystem Based on Non-abelian Finite Groups

Wolfgang Lempken, Trung van Tran, Spyros S. Magliveras, Wandi Wei
2008 Journal of Cryptology  
We present a new approach to designing public-key cryptosystems, based on covers and logarithmic signatures of nonabelian finite groups.  ...  The system is scallable, and the proposed underlying group, represented as a matrix group, affords significant space and time efficiency.  ...  Acknowledgements The third author wishes to express his thanks to the Department of Mathematical Sciences and to the Center for Cryptology and Information Security, Florida Atlantic University, U.S.A.,  ... 
doi:10.1007/s00145-008-9033-y fatcat:vxjm75nru5ajtoy5g7ekuvoerm

Reducing Key Length of the McEliece Cryptosystem [chapter]

Thierry P. Berger, Pierre-Louis Cayrel, Philippe Gaborit, Ayoub Otmani
2009 Lecture Notes in Computer Science  
In this paper we propose a new general way to reduce the public key size through quasi-cyclic codes.  ...  The McEliece cryptosystem is one of the oldest public-key cryptosystem ever designated. It is also the first public-key cryptosystem based on linear error-correcting codes.  ...  Code-Based Cryptography Public-Key Cryptography A public-key cryptosystem uses a trapdoor one-way function E that will serve as the encryption function.  ... 
doi:10.1007/978-3-642-02384-2_6 fatcat:tdu7qveerjhclpbh3l4i4gmilm
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