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The Twin Diffie–Hellman Problem and Applications

David Cash, Eike Kiltz, Victor Shoup
2009 Journal of Cryptology  
Moreover, the twin Diffie-Hellman problem is at least as hard as the ordinary Diffie-Hellman problem.  ...  We propose a new computational problem called the twin Diffie-Hellman problem.  ...  This follows by observing that the public key and challenge ciphertext are computed correctly, and that the decryption consistency check works as before. Then we have that  ... 
doi:10.1007/s00145-009-9041-6 fatcat:zgy7rrv7ivcjbchgdbbemcacjq

The Twin Bilinear Diffie-Hellman Inversion Problem and Applications [chapter]

Yu Chen, Liqun Chen
2011 Lecture Notes in Computer Science  
We propose a new computational problem and call it the twin bilinear Diffie-Hellman inversion (BDHI) problem.  ...  Inspired by the technique proposed by Cash, Kiltz and Shoup, we have developed a new trapdoor test which enables us to prove that the twin BDHI problem is at least as hard as the ordinary BDHI problem  ...  We would like to thank Eike Kiltz for helpful discussions, and to the anonymous reviewers for their valuable suggestions.  ... 
doi:10.1007/978-3-642-24209-0_8 fatcat:vfxt7tda2vao7e3d5q53mtdjwa

The Twin Diffie-Hellman Problem and Applications [chapter]

David Cash, Eike Kiltz, Victor Shoup
Advances in Cryptology – EUROCRYPT 2008  
Moreover, the twin Diffie-Hellman problem is at least as hard as the ordinary Diffie-Hellman problem.  ...  We propose a new computational problem called the twin Diffie-Hellman problem.  ...  Acknowledgments We thank Masayuki Abe and Tatsuaki Okamoto for interesting discussions.  ... 
doi:10.1007/978-3-540-78967-3_8 dblp:conf/eurocrypt/CashKS08 fatcat:x4hwquza3vh3toezug44e7fjvi

The Twin Conjugacy Search Problem and Applications [article]

Xiaoming Chen and Weiqing You and Wenxi Li
2018 arXiv   pre-print
However, our new problem is at least hard as the conjugacy search problem. Moreover, the twin conjugacy search problem have many applications.  ...  We propose a new computational problem over the noncommutative group, called the twin conjugacy search problem.  ...  David propose a new computational problem called the twin Diffie-Hellman problem, and its applications [18] , it has solved important problems on the security proofs of the Diffie-Hellman problem.  ... 
arXiv:1806.03078v1 fatcat:6qa3i4wy25h4jpngw2i2fwhz3u

Random Oracle Reducibility [chapter]

Paul Baecher, Marc Fischlin
2011 Lecture Notes in Computer Science  
As a positive example, we consider the twin Diffie-Hellman (DH) encryption scheme of Cash et al.  ...  We discuss a reduction notion relating the random oracles in two cryptographic schemes A and B.  ...  Both authors are supported by grants Fi 940/2-1 and Fi 940/4-1 of the German Research Foundation (DFG). This work was also supported by CASED (www.cased.de).  ... 
doi:10.1007/978-3-642-22792-9_2 fatcat:dlrmijugf5hfpgmawwytrpphva

Twin-Schnorr: A Security Upgrade for the Schnorr Identity-Based Identification Scheme

Ji-Jian Chin, Syh-Yuan Tan, Swee-Huay Heng, Raphael Chung-Wei Phan
2015 The Scientific World Journal  
In this paper, we upgrade the Schnorr-IBI scheme to be secure against impersonation under active and concurrent attacks using only the classical discrete logarithm assumption.  ...  Furthermore, most of these IBI schemes are proven to be secure against impersonation under active and concurrent attacks using interactive assumptions such as the one-more RSA inversion assumption or the  ...  - ation under active and concurrent attack, DLP: discrete logarithm problem, OMDL: one-more discrete logarithm problem, and DDHP: decisional Diffie- Hellman problem, = log 2 .  ... 
doi:10.1155/2015/237514 pmid:25692179 pmcid:PMC4322307 fatcat:cwiqfkew5fe7lm6a4ykinwti6a

The n-Diffie-Hellman Problem and Its Applications [chapter]

Liqun Chen, Yu Chen
2011 Lecture Notes in Computer Science  
On the one hand, the twin Diffie-Hellman (twin DH) problem proposed by Cash, Kiltz and Shoup is extended to the n-Diffie-Hellman (n-DH) problem for an arbitrary integer n, and this new problem is shown  ...  bilinear Diffie-Hellman (BDH) assumption respectively, in the random oracle model.  ...  Introduction In EUROCRYPT 2008 [6] , Cash, Kiltz and Shoup proposed a new computational problem and named it the twin Diffie-Hellman (twin DH) problem with the meaning that given a random triple of the  ... 
doi:10.1007/978-3-642-24861-0_9 fatcat:gcehnv6b4nbhrbudligu52f4sy

Compact CCA-Secure Encryption for Messages of Arbitrary Length [chapter]

Masayuki Abe, Eike Kiltz, Tatsuaki Okamoto
2009 Lecture Notes in Computer Science  
The security is proven based on the strong Diffie-Hellman assumption in the random oracle model. However, the major drawback of the ElGamal scheme is its relatively poor security.  ...  The ciphertext overhead (i.e., the difference between ciphertext and plaintext) is one group element only.  ...  The Strong Twin Diffie-Hellman (STDH) assumption [9] is as follows.  ... 
doi:10.1007/978-3-642-00468-1_21 fatcat:nnhsscb3qba7tejfvmtdpxl3xa

Short CCA-Secure Attribute-Based Encryption

Hiroaki Anada, Seiko Arita
2018 Advances in Science, Technology and Engineering Systems  
Our modification works in the setting that the Diffie-Hellman tuple to be verified in decryption is in the target group of a bilinear map.  ...  The employed techniques result in expansion of the secret-key length and the decryption cost by a factor of four, while the public-key and the ciphertext lengths and the encryption cost remain almost the  ...  In Section 3, we revisit the concept, the algorithm and the security of the twin Diffie-Hellman technique.  ... 
doi:10.25046/aj030132 fatcat:glq6lvmpdvcidou2sxw6qaxy4q

Strongly Secure Certificateless Key Agreement [chapter]

Georg Lippold, Colin Boyd, Juan Gonzalez Nieto
2009 Lecture Notes in Computer Science  
We provide the first one-round CL-AKE scheme proven secure in the random oracle model. We introduce two variants of the Diffie-Hellman trapdoor introduced by [CKS08].  ...  [XWSX08], Wang, Cao and Wang [WCW06], and Shao Zu-hua [Zh05] , but the respective authors gave only heuristic arguments as to why their schemes would be secure.  ...  Diffie-Hellman problem or the computational bilinear Diffie-Hellman problem.  ... 
doi:10.1007/978-3-642-03298-1_14 fatcat:7mia5g3bw5dopksrbqopvti5ni

The Group of Signed Quadratic Residues and Applications [chapter]

Dennis Hofheinz, Eike Kiltz
2009 Lecture Notes in Computer Science  
That is, in this group the Diffie-Hellman problem is hard, even in the presence of a Decisional Diffie-Hellman oracle.  ...  It is known that, in the random oracle model, the scheme is chosenciphertext (CCA) secure under the Strong Diffie-Hellman assumption and hence, by our results, under the standard factoring assumption.  ...  We thank Victor Shoup and the anonymous reviewers for useful comments.  ... 
doi:10.1007/978-3-642-03356-8_37 fatcat:5j7bx5g6jfejtngcbngeuskpc4

Some facets of complexity theory and cryptography: A five-lecture tutorial

Jörg Rothe
2002 ACM Computing Surveys  
Particular attention is paid to cryptographic protocols and the problem of constructing key components of protocols such as one-way functions.  ...  We give a brief overview of the history and the foundations of classical cryptography, and then move on to modern public-key cryptography.  ...  Keitele to me and my family during the summer school.  ... 
doi:10.1145/592642.592646 fatcat:qogelhnxlzerhmyeru6q3xcioa

Efficient Chosen-Ciphertext Security via Extractable Hash Proofs [chapter]

Hoeteck Wee
2010 Lecture Notes in Computer Science  
Computational Diffie-Hellman (CDH) problem.  ...  We show how to instantiate extractable hash proof system for hard search problems, notably factoring and computational Diffie-Hellman.  ...  I thank the anonymous Crypto 2010 reviewers for pointing out that our framework applies to the constructions in [7, 27, 28] , for suggesting the name "adaptive trapdoor relations", and for many helpful  ... 
doi:10.1007/978-3-642-14623-7_17 fatcat:gy2trq7ypbb6ddz4ywaole7zya

Invalid-curve attacks on (hyper)elliptic curve cryptosystems

Berkant Ustaoglu, Koray Karabina
2010 Advances in Mathematics of Communications  
We also show that invalid singular (hyper)elliptic curves can be used in mounting invalid-curve attacks on (hyper)elliptic curve cryptosystems, and make quantitative estimates of the practicality of these  ...  We extend the notion of an invalid-curve attack from elliptic curves to genus 2 hyperelliptic curves.  ...  Acknowledgements The authors thank Alfred Menezes for his careful and critical reading of the draft, and also for his suggestions and corrections.  ... 
doi:10.3934/amc.2010.4.307 fatcat:raf62pwtkvgunbkd7wf2jgfae4

A lightweight and efficient Secure Hybrid RSA (SHRSA) messaging scheme with four-layered authentication stack

A. Bhattacharjya, X. Zhong, X. Li
2019 IEEE Access  
The scheme is resolving the problem of asymptotic very low speed of decryption of RSA, the computational modular exponentiation complexity and partial key exposure vulnerability issues of RSA, and many  ...  We have found that in evolutions and analysis of the scheme, it is not only resolving various scientific problems of RSA but also occupying 2%-4% less CPU than main RSA and occupying 1%-3% less memory  ...  ACKNOWLEDGMENT The authors would like to convey their gratitude and tribute to Late Prof. Wang Jing for his constant supervision and encouragement for this project.  ... 
doi:10.1109/access.2019.2900300 fatcat:3pr4j5coevfhld35pv54iegjxu
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