A new public key scheme based on DRSA and generalized GDLP

2016 ◽  
Vol 08 (04) ◽  
pp. 1650057 ◽  
Author(s):  
Pinkimani Goswami ◽  
Madan Mohan Singh ◽  
Bubu Bhuyan
Keyword(s):  
Multiplicative Group ◽  
Discrete Logarithm ◽  
Randomized Algorithm ◽  
Discrete Logarithm Problem ◽  
Public Key ◽  
Integer Factorization ◽  
New Public ◽  
Encryption Decryption ◽  
Group Modulo

In this paper, we propose a new public key scheme, which is a combination of RSA variant namely the DRSA and the generalization of generalized discrete logarithm problem (generalized GDLP). The security of this scheme depends equally on the integer factorization of [Formula: see text] and the discrete logarithm problem (DLP) on [Formula: see text], where [Formula: see text] is the product of two large primes and [Formula: see text] is the multiplicative group modulo [Formula: see text]. The scheme is a randomized algorithm. It is at least as secure as the DRSA and ElGamal schemes. We also compare the encryption–decryption performance of the proposed scheme with the RSA and DRSA schemes.

A new public key cryptosystem over ℤn2*

2017 ◽  
Vol 09 (06) ◽  
pp. 1750080
Author(s):  
Pinkimani Goswami ◽  
Madan Mohan Singh ◽  
Bubu Bhuyan
Keyword(s):  
Multiplicative Group ◽  
Discrete Logarithm ◽  
Public Key ◽  
Public Key Cryptosystem ◽  
Quadratic Residues ◽  
Diffie Hellman ◽  
New Public ◽  
Intractable Problems ◽  
The One ◽  
Safe Primes

At Eurocrypt ’99, Paillier showed a cryptographic application of the group [Formula: see text], the multiplicative group modulo [Formula: see text] where [Formula: see text] is some RSA modulus. In this paper, we have present a new public key cryptosystem over [Formula: see text] where [Formula: see text] is a product of two safe primes, which is based on two intractable problems namely, integer factorization and partial discrete logarithm problem over [Formula: see text], the group of quadratic residues modulo [Formula: see text]. This scheme is a combination of BCP (Bresson–Catalano–Pointcheval) cryptosystem, proposed by Bresson et al. at Asiacrypt ’03 and the Rabin–Paillier scheme proposed by Galindo et al. at PKC 2003. We will show that the one-wayness of this new scheme equally depends on the Computational Diffie–Hellman assumption and factoring assumption. We will also prove that the proposed scheme is more secure than the BCP cryptosystem and the Rabin–Paillier cryptosystem.

scholarly journals Improved lower bound for Diffie–Hellman problem using multiplicative group of a finite field as auxiliary group

2018 ◽  
Vol 12 (2) ◽  
pp. 101-118 ◽  
Author(s):  
Prabhat Kushwaha
Keyword(s):  
Lower Bound ◽  
Finite Field ◽  
Elliptic Curves ◽  
Multiplicative Group ◽  
Discrete Logarithm ◽  
Discrete Logarithm Problem ◽  
Reduction Algorithm ◽  
Practical Applications ◽  
Diffie Hellman ◽  
Estimate Lower

Abstract In 2004, Muzereau, Smart and Vercauteren [A. Muzereau, N. P. Smart and F. Vercauteren, The equivalence between the DHP and DLP for elliptic curves used in practical applications, LMS J. Comput. Math. 7 2004, 50–72] showed how to use a reduction algorithm of the discrete logarithm problem to Diffie–Hellman problem in order to estimate lower bound for the Diffie–Hellman problem on elliptic curves. They presented their estimates on various elliptic curves that are used in practical applications. In this paper, we show that a much tighter lower bound for the Diffie–Hellman problem on those curves can be achieved if one uses the multiplicative group of a finite field as auxiliary group. The improved lower bound estimates of the Diffie–Hellman problem on those recommended curves are also presented. Moreover, we have also extended our idea by presenting similar estimates of DHP on some more recommended curves which were not covered before. These estimates of DHP on these curves are currently the tightest which lead us towards the equivalence of the Diffie–Hellman problem and the discrete logarithm problem on these recommended elliptic curves.

scholarly journals A Group Law on the Projective Plane with Applications in Public Key Cryptography

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 734
Author(s):  
Raúl Durán Díaz ◽  
Luis Hernández Encinas ◽  
Jaime Muñoz Masqué
Keyword(s):  
Projective Plane ◽  
Multiplicative Group ◽  
Mathematical Problem ◽  
Discrete Logarithm ◽  
Public Key Cryptography ◽  
Public Key ◽  
Arbitrary Field ◽  
Base Field ◽  
Computational Difficulty ◽  
Group Law

In the context of new threats to Public Key Cryptography arising from a growing computational power both in classic and in quantum worlds, we present a new group law defined on a subset of the projective plane F P 2 over an arbitrary field F , which lends itself to applications in Public Key Cryptography and turns out to be more efficient in terms of computational resources. In particular, we give explicitly the number of base field operations needed to perform the mentioned group law. Based on it, we present a Diffie-Hellman-like key agreement protocol. We analyze the computational difficulty of solving the mathematical problem underlying the proposed Abelian group law and we prove that the security of our proposal is equivalent to the discrete logarithm problem in the multiplicative group of the cubic extension of the finite field considered. We present an experimental setup in order to show real computation times along a comparison with the group operation in the group of points of an elliptic curve. Based on current state-of-the-art algorithms, we provide parameter ranges suitable for real world applications. Finally, we present a promising variant of the proposed group law, by moving from the base field F to the ring Z / p q Z , and we explain how the security becomes enhanced, though at the cost of a longer key length.

Public Key-Agreement Schemes Based on the Hidden Discrete Logarithm Problem

2020 ◽  
Vol 26 (10) ◽  
pp. 577-585
Author(s):  
R. S. Fahrutdinov ◽  
◽  
A. Yu. Mirin ◽  
D. N. Moldovyan ◽  
A. A. Kostina ◽  
...  
Keyword(s):  
Key Agreement ◽  
Discrete Logarithm ◽  
Discrete Logarithm Problem ◽  
Public Key
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