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Concrete Chosen-Ciphertext Secure Encryption from Subgroup Membership Problems [chapter]

Jaimee Brown, Juan Manuel González Nieto, Colin Boyd
2006 Lecture Notes in Computer Science  
Using three previously studied subgroup membership problems, we obtain new concrete encryption schemes secure against adaptive chosen-ciphertext attack in the standard model, from the Cramer-Shoup and  ...  The hybrid variants are even more efficient, with a smaller number of exponentiations and a shorter ciphertext than the Kurosawa-Desmedt Decisional Diffie-Hellman based scheme.  ...  We present several practical, concrete encryption schemes that are proven CCA-secure in the standard model each based on the difficulty of a particular subgroup membership problem.  ... 
doi:10.1007/11935070_1 fatcat:d2jzap5lezbpza2kwbhufllivy

Symmetric Subgroup Membership Problems [chapter]

Kristian Gjøsteen
2005 Lecture Notes in Computer Science  
We also discuss how chosen ciphertext secure hybrid cryptosystems based on a symmetric subgroup membership can be constructed in the standard model, giving a very efficient cryptosystem whose security  ...  relies solely on the symmetric subgroup membership problem.  ...  The security proofs for many public key cryptosystems essentially rely on subgroup membership problems.  ... 
doi:10.1007/978-3-540-30580-4_8 fatcat:ehxsphcoivcdbdkwatse6f75b4

New probabilistic public-key encryption based on the RSA cryptosystem

Vitalii A. Roman'kov
2015 Groups - Complexity - Cryptology  
AbstractWe propose a novel probabilistic public-key encryption, based on the RSA cryptosystem.  ...  the concrete RSA cryptosystem who chooses and distributes encryption keys among all users.  ...  New probabilistic public-key encryption based on the RSA cryptosystem The objective of this section is to propose a novel probabilistic public-key encryption.  ... 
doi:10.1515/gcc-2015-0016 fatcat:4q5hdm4sdfhgjeme6nqt6wbkw4

A New Security Proof for Damgård's ElGamal [chapter]

Kristian Gjøsteen
2006 Lecture Notes in Computer Science  
Unlike previous security proofs for this cryptosystem, which rely on somewhat problematic assumptions, our computational problem is similar to accepted problems such the Gap and Decision Diffie-Hellman  ...  problems.  ...  The cryptosystem First we describe the cryptosystem based on a subgroup membership problem (G, H, J) and a hash proof system P with projective hash family (G, H, L, L , W, ρ, M ).  ... 
doi:10.1007/11605805_10 fatcat:qywtee7vvjbajb7nosvvyt54ny

Constructions in public-key cryptography over matrix groups [article]

Dimitri Grigoriev, Ilia Ponomarenko
2005 arXiv   pre-print
They rely on difficulty of the conjugacy and membership problems for subgroups of a given group.  ...  solvable groups) and a new homomorphic public-key cryptosystem.  ...  In fact, the security of these cryptosystems was based on the difficulty of the membership problem (see below) for special subgroups of the group G k .  ... 
arXiv:math/0506180v1 fatcat:55lqn7ip4vhkxnn622nax7sjta

Decision and Search in Non-Abelian Cramer-Shoup Public Key Cryptosystem

Delaram Kahrobaei, Michael Anshel
2009 Groups - Complexity - Cryptology  
A method for non-abelian Cramer-Shoup cryptosystem is presented. The role of decision and search is explored, and the platform of solvable / polycyclic group is suggested.  ...  In the process we review recent progress in non-abelian cryptography and post some open problems that naturally arise from this path of research.  ...  In [8] , Cao et al. propose a new method for designing public key cryptosystems based on general non-commutative rings.  ... 
doi:10.1515/gcc.2009.217 fatcat:isdna5jto5c5pc7pmnzkdc7sym

Decision and Search in Non-abelian Cramer Shoup Public Key Cryptosystem [article]

Michael Anshel, Delaram Kahrobaei
2013 arXiv   pre-print
A method for non-abelian Cramer-Shoup cryptosystem is presented. The role of decision and search is explored, and the platform of solvable/polycyclic group is suggested.  ...  In the process we review recent progress in non-abelian cryptography and post some open problems that naturally arise from this path of research.  ...  In [8] , Cao et al. propose a new method for designing public key cryptosystems based on general non-commutative rings.  ... 
arXiv:1309.4519v1 fatcat:avb4yo37lrbwzgzzkjifvuc5bq

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.  ...  In contrast to the cryptosystems based on the factoring problem the first main result of this paper is a new homomorphic public-key cryptosystem over arbitrary nonidentity finite group based on the difficulty  ... 
arXiv:cs/0309010v1 fatcat:m5oleeiwpjd4zoimohk4ji3w7i

Homomorphic Encryption for Multiplications and Pairing Evaluation [chapter]

Guilhem Castagnos, Fabien Laguillaumie
2012 Lecture Notes in Computer Science  
We prove the semantic security under chosen plaintext attack of our scheme under a generalized subgroup membership assumption, and we also prove that it cannot achieve ind-cca1 security.  ...  On the theoretical side, this scheme is an example of cryptosystem which can be naturally implemented with groups of prime order, as the homomorphic properties require only a projecting pairing using Freeman's  ...  Other schemes based on the Symmetric Subgroup Membership Problem and the Splitting Problem are implementations of this construction, such as the scheme of [Gjo05] .  ... 
doi:10.1007/978-3-642-32928-9_21 fatcat:47ac3ta75jdo3f6usc4stnf5oa

Algebraic cryptography: new constructions and their security against provable break

D. Grigoriev, A. Kojevnikov, S. J. Nikolenko
2009 St. Petersburg Mathematical Journal  
It is proved that the cryptosystems based on matrix group invariants and a version of the Anshel-Anshel-Goldfeld key agreement protocol for modular groups are secure against provable break unless NP =  ...  Its security is based on factoring a number into prime divisors, or, more precisely, on the hardness of the so-called "RSA problem": find roots of a given degree modulo a number n = pq, where p and q are  ...  Acknowledgments The authors are grateful to Edward A. Hirsch for valuable discussions and for Remark 2.  ... 
doi:10.1090/s1061-0022-09-01079-6 fatcat:56dpn3v5jvb4bekjg36uj77pfy

KDM-Security via Homomorphic Smooth Projective Hashing [chapter]

Hoeteck Wee
2016 Lecture Notes in Computer Science  
-Using our second framework, we obtain new dual-mode cryptosystems based on the d -linear, quadratic residuocity and decisional composite residuocity assumptions.  ...  Since then, Applebaum et al. [4] presented a scheme under the LWE assumption (which is itself a variant of Regev's cryptosystem [33] ) and Brakerski and Goldwasser [10] presented a BHHO-like scheme based  ...  on multiple keys), -new constructions of dual-mode cryptosystems: (i) a construction based on the d -linear assumption, generalizing the previous construction based on DDH; (ii) a simple construction  ... 
doi:10.1007/978-3-662-49387-8_7 fatcat:uidr6j6yf5chjof46lmsg7acmu

How to make RSA and some other encryptions probabilistic [article]

Vitalii Roman'kov
2016 arXiv   pre-print
A new scheme of probabilistic subgroup-related encryption is introduced. Some applications of this scheme based on the RSA, Diffie-Hellman and ElGamal encryption algorithms are described.  ...  Some algorithmic problems for finite fields and modular rings. In [1] , [2] , we proposed a novel probabilistic public-key encryption, based on the RSA cryptosystem.  ...  This problem is considered by many authors as intractable. A number of cryptographic schemes are based on this intractability, and the famous Goldwasser-Micali cryptosystem is one of them.  ... 
arXiv:1603.02031v1 fatcat:cbbpua4ah5hirpgvowdw2invha

A McEliece cryptosystem using permutation codes [article]

Adarsh Srinivasan, Ayan Mahalanobis
2021 arXiv   pre-print
We study a public-key cryptosystem built using two permutation error-correcting codes. We show that these cryptosystems are insecure.  ...  This paper is an attempt to build a new public-key cryptosystem; similar to the McEliece cryptosystem, using permutation error-correcting codes.  ...  The second author was partially supported by a NBHM research grant. Both authors thank Upendra Kapshikar for stimulating discussions on the topic.  ... 
arXiv:2111.02119v1 fatcat:r5fqjqnkmbas7oksln53kuekau

Towards a Uniform Description of Several Group Based Cryptographic Primitives

María Isabel González Vasco, Consuelo Martínez, Rainer Steinwandt
2004 Designs, Codes and Cryptography  
In particular, a generalization of M ST 2 can be regarded as a unifying framework for several suggested cryptosystems including the ElGamal public key system, a public key system based on braid groups  ...  The public key cryptosystems M ST 1 and M ST 2 make use of certain kinds of factorizations of finite groups.  ...  like (as it is done in [13] , where a general construction for a PIR system based on any subgroup membership problem is given).  ... 
doi:10.1023/b:desi.0000036247.38461.c9 fatcat:gu2fhuhtirfulopkokeblpc32q

The Status of Polycyclic Group-Based Cryptography: A Survey and Open Problems [article]

Jonathan Gryak, Delaram Kahrobaei
2016 arXiv   pre-print
These include key exchanges such as non-commutative ElGamal, authentication schemes based on the twisted conjugacy problem, and secret sharing via the word problem.  ...  Of particular interest is to show that cryptosystems using infinite polycyclic groups are resistant to cryptanalysis on a quantum computer.  ...  Delaram Kahrobaei is partially supported by a PSC-CUNY grant from the CUNY Research Foundation, the City Tech Foundation, and ONR (Office of Naval Research) grant N00014-15-1-2164.  ... 
arXiv:1607.05819v2 fatcat:4nby6gf3xzezfkevvf5xt2xwm4
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