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Secure information hiding based on computationally intractable problems

S. Armeni, D. Christodulakis, I. Kostopoulos, Y. C. Stamatiou, M. Xenos
2003 Journal of Discrete Mathematical Sciences and Cryptography  
On another front, there is a vast literature on threshold phenomena in intractable combinatorial problems: it has been experimentally observed that for many of these problems there is a value for some  ...  In [9] , Craver uses the computational intractable Hamiltonian Path problem in order to produce a difficult to discover scrambling of the data to be protected.  ... 
doi:10.1080/09720529.2003.10697958 fatcat:7bdejx4hirgktg2wtl2jbc73p4

Pairing-Based Cryptography: Past, Present, and Future [chapter]

Dan Boneh
2012 Lecture Notes in Computer Science  
While pairings were first introduced in cryptography as a tool to attack the discrete-log problem on certain elliptic curves, they have since found numerous applications in the construction of cryptographic  ...  To this day many problems can only be solved using pairings.  ...  In this talk we survey some of the existing applications of pairings to cryptography, but mostly focus on open problems that cannot currently be solved using pairings.  ... 
doi:10.1007/978-3-642-34961-4_1 fatcat:t37a37zs5bbq5hpsaeeo66c2de

From Algorithms to Cryptography Tutorial [chapter]

Fabrizio Luccio, Linda Pagli
2002 Lecture Notes in Computer Science  
Cryptography and randomization are discussed as non trivial fields of algorithm application. Contents. Six lectures organized as follows:  ...  Tractable and intractable problems. The classes P, NP, NP-hard. 4. The role of randomization. Random sources and random number generators. Hash functions. Randomized algorithms. 5.  ...  Symmetric and asymmetric cryptography. From DES to AES. Public key cryptosystems and RSA. 6. Cryptography on the Web. Identification, authentication, and digital signatures.  ... 
doi:10.1007/3-540-45995-2_7 fatcat:htx5mkvy5zfjpo2apioedakx3y

Untitled Item

Oluyemi Amujo, M.B Hammawa, A.Y. Atumoshi, A. Abdulrahman
intractable.  ...  This paper focuses on quantum cryptography and how it contributes value to a long-time strategy pertaining to completely secure key distribution.  ...  Modern cryptography algorithms are based on the fundamental process of factoring large integers into their primes, which is said to be “intractable”.  ... 
doi:10.6084/m9.figshare.17134601.v1 fatcat:ihx6rf65izdnzmcqsqmx7v65i4

Public Key Encryption in Non-Abelian Groups [article]

Haibo Hong, Jun Shao, Licheng Wang, Haseeb Ahmad, Yixian Yang
2016 arXiv   pre-print
In particular, we firstly investigate the intractability assumptions in the Lie group, including the non-abelian factoring assumption and non-abelian inserting assumption.  ...  [10] developed braid group cryptography based on the intractable assumption of conjugate search problem in braid group.  ...  One of the outstanding properties of noncommutative cryptography is that it can take the advantage of intractable problems in quantum computing, combinatorial group theory and computational complexity  ... 
arXiv:1605.06608v1 fatcat:tdyqzmeoorbp5jwlreslglio3y

A Miniature CCA2 Public key Encryption scheme based on non-Abelian factorization problems in Lie Groups [article]

Haibo Hong, Licheng Wang, Jun Shao, Haseeb Ahmad, Yixian Yang
2016 arXiv   pre-print
Besides, combing with discrete logarithm problem(DLP) and factorization problem(FP), we propose some new intractable assumptions based on exponential mapping.  ...  Moreover, in analog with Boyen's sceme(AsiaCrypt 2007), we disign a public key encryption scheme based on non-Abelian factorization problems in Lie Groups.  ...  [11] developed braid group cryptography based on the intractable assumption of conjugate search problem in braid group.  ... 
arXiv:1605.07168v3 fatcat:25qnzapxozfuhjokmceeiedycq

Cryptography and machine learning [chapter]

Ronald L. Rivest
1993 Lecture Notes in Computer Science  
This paper gives a survey of the relationship between the fields of cryptography and machine learning, with an emphasis on how each field has contributed ideas and techniques to the other.  ...  The primary impact of cryptography on machine learning theory is a natural (but negative) one: showing that certain learning problems are computationally intractable.  ...  Of course, there are other ways in which a learning problem could be intractable; for example, learning the class of all boolean functions is intractable merely because the required number of examples  ... 
doi:10.1007/3-540-57332-1_36 fatcat:tfi6lrc7jnc5dkan6pjwk4mrii

Quantum Cryptography: where do we stand? [article]

Nicolas Gisin
2015 arXiv   pre-print
In the last few years the world in which Quantum Cryptography evolves has deeply changed.  ...  This implies that in order to protect today's data over a few decades, one has to act now and use some quantum-safe cryptography.  ...  The first ones consists in merely replacing the problem on which RSA rests (i.e. factoring) by another problem claimed to be intractable both for classical and for quantum computers, as factoring was claimed  ... 
arXiv:1508.00341v1 fatcat:25heaevf7ng5hhe7ndfl7u3j5u

Authentication Schemes Using Polynomials Over Non-Commutative Rings

Maheswara Rao Valluri
2012 International Journal on Cryptography and Information Security  
The security of the schemes is based on the intractability of the polynomial symmetrical decomposition problem over the given non-commutative ring.  ...  As addressed in [2] , in order to enrich cryptography, there have been many attempts to develop alternative PKC based on different kinds of problems.  ...  CSP (DP, respectively) is intractable.  ... 
doi:10.5121/ijcis.2012.2406 fatcat:cv6v3rpqtzhfffhifehnzgvlae

Elliptic Curves and Their Applications to Cryptography [chapter]

2013 Discrete Mathematics and Its Applications  
Elliptic curves are also used in several integer factorization algorithms that have applications in cryptography.  ...  This paper presents elliptic curves and their application in public-key cryptography, using software Mathematica Wolphram Research.  ...  The security of modern elliptic curve cryptography depends on the intractability of determining l from Q = lP given known values of Q and P.  ... 
doi:10.1201/b14977-4 fatcat:xqpdjlho6na7pg5tqb54h3e7nq

Conjugacy Systems Based on Nonabelian Factorization Problems and Their Applications in Cryptography

Lize Gu, Shihui Zheng
2014 Journal of Applied Mathematics  
To resist known quantum algorithm attacks, several nonabelian algebraic structures mounted upon the stage of modern cryptography.  ...  Recently, Baba et al. proposed an important analogy from the integer factorization problem to the factorization problem over nonabelian groups.  ...  Therefore, our 2nd, 3rd, and 4th hardness assumptions state the intractabilities of the CDH ,ℎ problem, the DDH ,ℎ problem, and the Gap-DH ,ℎ problem, respectively.  ... 
doi:10.1155/2014/630607 fatcat:7jqkwt5exnabdnwjumrwidzaue

Identity-Based Mediated RSA Revisited

Ibrahim Elashry, Yi Mu, Willy Susilo
2013 2013 12th IEEE International Conference on Trust, Security and Privacy in Computing and Communications  
To make the key generation function division intractable, Ding and Tsudik used a division intractable hash function to generate division intractable public keys.  ...  In this paper, we show that using a division intractable hash function does not necessarily mean that the key generation function is division intractable.  ...  to this problem.  ... 
doi:10.1109/trustcom.2013.88 dblp:conf/trustcom/ElashryMS13 fatcat:lbehfega6nfhrpxhpadx4gdlj4

Inapproximability Results for Computational Problems on Lattices [chapter]

Subhash Khot
2009 The LLL Algorithm  
In this article, we present a survey of known inapproximability results for computational problems on lattices, viz.  ...  Most of these problems turn out to be intractable, and even computing approximate solutions remains intractable.  ...  Vallée (eds.), The LLL Algorithm, Information Security and Cryptography, DOI 10.  ... 
doi:10.1007/978-3-642-02295-1_14 dblp:series/isc/Khot10 fatcat:lsgk3bgpp5adzg7zctnydb3ihq

One Way Functions –Conjecture, Status, Applications and Future Research Scope

Amit Sharma, Sunil Kr.
2016 International Journal of Computer Applications  
The conjecture that one way function exists is an open problem, the resolution of which holds the key for the solution of many unsolved problems in mathematics and cryptography.  ...  This paper presents the introduction of one way functions from complexity & modern cryptography theory viewpoint and their significance in cryptographic applications and research.  ...  The security of elliptic curve one way function depends on intractability of determining n if P and Q are known. It is known as elliptic curve discrete logarithmic problem.  ... 
doi:10.5120/ijca2016912126 fatcat:jttkqoy3ercupctqpyqmtyphsu

Quantum cryptography: a view from classical cryptography

Johannes Buchmann, Johannes Braun, Denise Demirel, Matthias Geihs
2017 Quantum Science and Technology  
The corresponding DH instance is secure as long as the discrete logarithm problem (DLP) in ( ) p GF with the chosen p remains intractable.  ...  This means that their security relies on the intractability of certain algorithmic problems. This implies that complexity-based cryptosystems only remain secure for a certain time period.  ... 
doi:10.1088/2058-9565/aa69cd fatcat:dzdpfvfvbbardaqlr3peohxbze
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