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Threshold Properties of Prime Power Subgroups with Application to Secure Integer Comparisons [chapter]

Rhys Carlton, Aleksander Essex, Krzysztof Kapulkin
2018 Lecture Notes in Computer Science  
Our scheme introduces a novel threshold homomorphic property, which we use to build a two-party protocol for secure integer comparison.  ...  We present a semantically secure somewhat homomorphic public-key cryptosystem working in sub-groups of Z * of prime power order.  ...  In this paper we propose a new approach to secure integer comparison using a novel threshold scalar homomorphic property of subgroups of Z * of prime power order.  ... 
doi:10.1007/978-3-319-76953-0_8 fatcat:6qadqlax3bh3liju7tynif5knm

A Pseudo-Random Pixel Rearrangement Algorithm Based on Gaussian Integers for Image Watermarking

Aleksey Koval, Frank Y. Shih, Boris S. Verkhovsky
2011 Journal of Information Hiding and Multimedia Signal Processing  
In this paper, we propose a new method of rearranging image pixels based on the properties of Gaussian integers.  ...  This paper presents a pseudo-random pixel rearrangement algorithm to improve the security of most image watermarking techniques.  ...  The thresholds for the size of p vary widely with implementation details.  ... 
dblp:journals/jihmsp/KovalSV11 fatcat:dhu2dbonvvckvjk7dhb4joetcq

Efficient Cryptosystems from 2 k -th Power Residue Symbols [chapter]

Marc Joye, Benoît Libert
2013 Lecture Notes in Computer Science  
Further, the cryptosystems described in this paper inherit the useful features of the original cryptosystem (like its homomorphic property) and are shown to be secure under a similar complexity assumption  ...  A number of works followed to address this issue and proposed various modifications. This paper revisits the original Goldwasser-Micali cryptosystem using 2 k -th power residue symbols.  ...  We are grateful to the anonymous reviewers for EUROCRYPT 2013 for their useful comments.  ... 
doi:10.1007/978-3-642-38348-9_5 fatcat:lmczneigqbacpjl5fq4fi7tf6q

Multiparty secret sharing based on hidden multipliers [article]

Vitaly Roman'kov
2021 arXiv   pre-print
This property distinguishes the proposed schemes from the secret sharing schemes known in the literature. The proposed schemes are semantically secure.  ...  From the transferred secret c it is impossible to determine which of the two given secrets m_1 or m_2 was transferred. For concreteness, we give some numerical examples.  ...  These properties show the advantages of the proposed scheme in comparison with the known secret distribution schemes. The proposed schemas are semantically secure.  ... 
arXiv:2108.06967v1 fatcat:n2b6uxmofbef7p6pgzlzpvwnue

A New Approach to Weighted Multi-Secret Sharing

Xukai Zou, Fabio Maino, Elisa Bertino, Yan Sui, Kai Wang, Feng Li
2011 2011 Proceedings of 20th International Conference on Computer Communications and Networks (ICCCN)  
Secret sharing is important in information and network security and has broad applications in the real world.  ...  , the new scheme is able to apply to broader applications involving wireless/sensor networks and pervasive computing.  ...  For each newly generated integer, we need to check if the integer is pairwise co-prime with existing integers. Therefore, the complexity of generating W pairwise co-prime integers is in O(W 2 n 2 ).  ... 
doi:10.1109/icccn.2011.6005766 dblp:conf/icccn/ZouMBSWL11 fatcat:xbefyyiczrauxaq6hpnaijiixy

Removable Weak Keys for Discrete Logarithm Based Cryptography [article]

Michael John Jacobson, Jr., Prabhat Kushwaha
2020 arXiv   pre-print
occurs purely due to parameter choice of p, and hence, can be removed with appropriate value of p.  ...  We describe a novel type of weak cryptographic private key that can exist in any discrete logarithm based public-key cryptosystem set in a group of prime order p where p-1 has small divisors.  ...  Acknowledgements The first author is supported in part by NSERC of Canada. The second author is supported by MeitY, India under the ISEA (Phase II) project.  ... 
arXiv:2011.07483v1 fatcat:3w3p5p42hvb4lngm6assksoq3i

Practical Cryptography in High Dimensional Tori [chapter]

Marten van Dijk, Robert Granger, Dan Page, Karl Rubin, Alice Silverberg, Martijn Stam, David Woodruff
2005 Lecture Notes in Computer Science  
This allows us to apply our results to ElGamal encryption with a small message domain to obtain ciphertexts that are 10% smaller than in previous schemes.  ...  cryptographic applications.  ...  The torus T n is known to be rational when n is either a prime power or a product of two prime powers [30, 12] , and is conjectured to be rational for all n [30] .  ... 
doi:10.1007/11426639_14 fatcat:rvwz5iclj5dcxdsufsyjoldtt4

AN EFFICIENT THRESHOLD SECRET SHARING SCHEME USING FAST FOURIER TRANSFORM

Vanashree Gupta
2022 International Journal of Smart Sensor and Adhoc Network.  
But this impacts on efficiency as degree of polynomial is increased. Either we must adjust the privacy threshold or number of shares needed to reconstruct. There is need of advance technique.  ...  Secret Sharing is a robust key management method which is having applications in password management, secure multi party computation, e-voting etc.  ...  The only requirement is that the length L is a power of 2 and that we can find a generator omegaL of a subgroup of this size.  ... 
doi:10.47893/ijssan.2022.1210 fatcat:gfm4ydayhbb6horsahunn2ig2e

Accountable-subgroup multisignatures

Silvio Micali, Kazuo Ohta, Leonid Reyzin
2001 Proceedings of the 8th ACM conference on Computer and Communications Security - CCS '01  
In essence, ASM schemes enable any subgroup, S, of a given group, G, of potential signers, to sign efficiently a message M so that the signature provably reveals the identities of the signers in S to any  ...  Formal models and security proofs are especially important for multisignatures: in contrast to threshold signatures, no precise definitions were ever provided for such schemes, and some proposals were  ...  Acknowledgements The work of the second author was performed, in part, during his visit to the MIT Laboratory for Computer science.  ... 
doi:10.1145/501983.502017 dblp:conf/ccs/MicaliOR01 fatcat:3pnil6eajrgxnhyzvnt2l6tvke

A Post-Quantum Fuzzy Commitment Scheme for Biometric Template Protection: An Experimental Study

Alawi A. Al-Saggaf
2021 IEEE Access  
Let ∈ Ζ + be a security parameter, be a prime number, while and are positive integers such that , = ( ). : To commit to a message ∈ , draw randomly a vector ∈ ℤ and the output the fuzzy commitment such  ...  Definition 4: A lattice ℒ is a discrete additive subgroup of ℝ whose elements are generated by the integer linear combinations of the basis = { 1 , 2 , … . . , } ⊂ ℝ × .  ... 
doi:10.1109/access.2021.3100981 fatcat:vpc34nzaefcmbi5kectkdbmozm

ECC mod 8^91+5 [article]

Daniel R. L. Brown
2018 IACR Cryptology ePrint Archive  
The field size 8 91 +5 for elliptic curve cryptography offers simplicity, security, and efficiency.  ...  Primes close to a power of two, are generally known to yield efficient modular arithmetic, mainly because computer hardware deals most efficiently with powers of two.  ...  This prime is very close to a power of two: differing just by five.  ... 
dblp:journals/iacr/Brown18 fatcat:vfstnfe6b5fefmquf5haq4oy4a

Practical Threshold RSA Signatures without a Trusted Dealer [chapter]

Ivan Damgård, Maciej Koprowski
2001 Lecture Notes in Computer Science  
The robustness (but not the unforgeability) of our scheme depends on a new intractability assumption, in addition to security of the underlying standard RSA scheme.  ...  that the modulus must be a product of safe primes and that a trusted dealer generates the keys.  ...  Basing threshold schemes on RSA is technically more difficult because we have to work in a group of non-prime and unknown order (Z * n rather than a prime order subgroup of Z * p for a prime p).  ... 
doi:10.1007/3-540-44987-6_10 fatcat:tei4nrjnyjfgxdfq5lfidxeq7i

Accountable-subgroup multisignatures

Silvio Micali, Kazuo Ohta, Leonid Reyzin
2001 Proceedings of the 8th ACM conference on Computer and Communications Security - CCS '01  
The case of more general subgroups S has been, in particular, addressed in [IN83, Har94, LHL94, HMP95]. General subgroups of signers are needed in many applications.  ...  To avoid confusion with other similar notions, we use the term "accountable-subgroup multisignatures" (ASM) to describe the schemes in our model.  ...  Our scheme has the following desirable efficiency properties, when compared to the obvious solution that simply uses multiple single-signer signatures: Comparison with Prior Implementations Implementations  ... 
doi:10.1145/502014.502017 fatcat:nc2jgia7vzeghfgneyyen4gdnu

Secure Threshold Ring Signature Based on SM9

Shuanggen Liu, Kang Chen, Zikang Liu, Teng Wang
2021 IEEE Access  
In order to satisfy different application requirements, researchers have proposed threshold ring signatures with different properties, such as solving the problem of attribute key escrow [5] , implementing  ...  With the wide application of SM9 in various fields, its security issues have received close attention. The security of SM9 is based on the premise of the security of the private key.  ... 
doi:10.1109/access.2021.3094902 fatcat:ljxfcbdnrff6vpnmlu44pqqgci

Practical Threshold RSA Signatures Without a Trusted Dealer

Ivan B. Damgård, Maciej Koprowski
2000 BRICS Report Series  
, namely that the modulus must be a product of safe primes<br />and that a trusted dealer generates the keys.  ...  We propose a threshold RSA scheme which is as efficient as the fastest previous<br />threshold RSA scheme (by Shoup), but where two assumptions needed in Shoup's and in<br />previous schemes can be dropped  ...  Basing threshold schemes on RSA is technically more difficult because we have to work in a group of non-prime and unknown order (Z * n rather than a prime order subgroup of Z * p for a prime p).  ... 
doi:10.7146/brics.v7i30.20164 fatcat:m53olpfbbbdgxf4itbwtcnai34
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