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### RSA with Balanced Short Exponents and Its Application to Entity Authentication [chapter]

Hung-Min Sun, Cheng-Ta Yang
2005 Lecture Notes in Computer Science
Based on our RSA variants, an application to entity authentication for defending the stolen-secret attack is presented.  ...  In this paper, we focus on designing a new RSA variant with balanced d and e, and balanced p and q in order to make such an RSA variant more secure.  ...  Acknowledgements The authors wish to acknowledge the anonymous reviewers for valuable comments and thank helpful discussions with Chiung-Hsun Chen, Mu-En Wu and Ting-Yao Lin on several points in the paper  ...

### RSA, DH, and DSA in the Wild [article]

2022 IACR Cryptology ePrint Archive
RSA Primes with Shared or Predictable Bits Heninger et al. [HDWH12] and Bernstein et al.  ...  using a 512-bit prime, signed with the server's certificate private key.  ...

### New Attacks on RSA with Moduli N = p r q [chapter]

Abderrahmane Nitaj, Tajjeeddine Rachidi
2015 Lecture Notes in Computer Science
We present three attacks on the Prime Power RSA with modulus N = p r q. In the first attack, we consider a public exponent e satisfying an equation ex − φ(N )y = z where φ(N ) = p r−1 (p − 1)(q − 1).  ...  The third attack enables us to factor two Prime Power RSA moduli N1 = p r 1 q1 and N2 = p r 2 q2 when p1 and p2 share a suitable amount of their most significant bits, namely, |p1 − p2| < p 1 2rq 1 q 2  ...  The Second Attack on Prime Power RSA using Two Decryption Exponents In this section, we present an attack on the Prime Power RSA when two private exponents d 1 and d 2 share an amount of their most significant  ...

### Cryptanalysis of Short Exponent RSA with Primes Sharing Least Significant Bits [chapter]

Hung-Min Sun, Mu-En Wu, Ron Steinfeld, Jian Guo, Huaxiong Wang
2008 Lecture Notes in Computer Science
LSBS-RSA denotes an RSA system with modulus primes, p and q, sharing a large number of least signi...cant bits. In ISC 2007, Zhao and Qi analyzed the security of short exponent LSBS-RSA.  ...  In conclusion, it is a trade-o¤ between the number of sharing bits and the security level in LSBS-RSA. One should be more careful when using LSBS-RSA with short exponents.  ...  Moreover, compared with the Boneh-Durfee attack  ,  and de Weger's attack on RSA with small prime di¤erence  , our result yields an improvement when primes sharing a large number of least  ...

### Another Look at Small RSA Exponents [chapter]

M. Jason Hinek
2006 Lecture Notes in Computer Science
In particular, we show that it is possible to have private exponents smaller than N 1/4 which are resistant to all known small private exponent attacks.  ...  This allows for instances of RSA with short CRT-exponents and short public exponents.  ...  As will be shown later, this restriction on the small private exponent is weakened in common prime RSA.  ...

### A Hybrid Encryption Algorithm Based on RSA Small-e and Efficient-RSA for Cloud Computing Environments

Faraz Fatemi Moghaddam, Maen T. Alrashdan, Omidreza Karimi
2013 Journal of Advances in Computer Networks
Accordingly, this schema presents a Hybrid Encryption algorithm that is based on RSA Small-e and Efficient RSA (HE-RSA) for improving the reliability in cloud computing environments.  ...  Moreover, some of the common attacks against RSA algorithm have been analysed to detect the resistance of the proposed algorithm against possible attacks.  ...  RSA SMALL-RSA Small-e is an algorithm based on original RSA except that the public exponent is much smaller than .  ...

### Digital signature and public key cryptosystem in a prime order subgroup of Zn* [chapter]

Colin Boyd
1997 Lecture Notes in Computer Science
There are similarities with the best known digital signatures and public key cryptosystems (RSA and discrete logarithm based schemes) in terms of the mathematical structure.  ...  With regard to computational requirements the new schemes are competitive and, in particular, are more e cient than the best known schemes when averaged over both public and private key computations.  ...  The proposed scheme compares quite well and, in particular, shares a useful property with the DSS of having a small private key.  ...

### Improvement over Public Key Cryptographic Algorithm

Deepak Garg, Seema Verma
2009 2009 IEEE International Advance Computing Conference
in cryptography in the last 300-Generate two large random primes of n/2 bits 400 years.  ...  over a non-secure communication length, e.g. 1024 bits channel without having to share a secret key, e.g  ...  Therefore, one might be tempted to is to perform the RSA private-key operation given only use small secret exponents to speed up the the public key.  ...

### Secure RSA Variant System to Avoid Factorization Attack using Phony Modules and Phony Public Key Exponent

2019 VOLUME-8 ISSUE-10, AUGUST 2019, REGULAR ISSUE
Effectiveness of RSA Algorithm for the most part relies upon how adequately public key segments is shared i.e. common modulus n and public key exponent e.  ...  RSA is considered as one of the effective algorithm in public key cryptography.  ...  Also by introducing the concept of phony exponents and phony modulus attacks on RSA such as low private key exponent  , low public key exponent  , Wiener's attack  , Common modulus attack  ...

### Modified Multi Prime RSA Cryptosystem

M Ghazali Kamardan, N Aminudin, Norziha Che-Him, Suliadi Sufahani, Kamil Khalid, Rozaini Roslan
2018 Journal of Physics, Conference Series
Furthermore, in modified Multi prime RSA another secret key is introduced to increase the obstacle to the attacker.  ...  RSA  is one of the mostly used cryptosystem in securing data and information.  ...  Acknowledgments Authors would like to thank Universiti Tun Hussein Onn Malaysia (UTHM) and Office for Research, Innovation, Commercialization and Consultancy Management (ORICC), UTHM for kindly providing us with  ...

### Server-Aided Public Key Generation Protocols on Low-power Devices for Ad-hoc Networks

Yun Chen, Weijian Chen, Yi Mu, Xin Chen, Min Liu
2006 2006 6th International Conference on ITS Telecommunications
The protocols are secure against some passive attacks, such as "collusion attack" and "the third party attack".  ...  In addition, efficiency of primality test on low-power devices is improved in this paper.  ...  In result, the servers shall know nothimg about user's private key even if they could share information with one anothea.  ...

### Key Generation Using Generalized Pell's Equation in Public Key Cryptography Based on the Prime Fake Modulus Principle to Image Encryption and Its Security Analysis

K. R. Raghunandan, Aithal Ganesh, Shetty Surendra, K. Bhavya
2020 Cybernetics and Information Technologies
It is explored in the results that RSA is prone to factorization problem, since it is sharing common modulus and public key exponent.  ...  Using generalized Pell's equation it is explored that public key exponent depends on several parameters, hence obtaining private key parameter itself is a big challenge.  ...   , common modulus attack  , low private key exponent attack  and B l ö m e r and M a y in  are presented as an extension work of Wiener's attack on small RSA secret decryption exponents  ...

### Eight Prime Numbers of Modified RSA Algorithm Method for More Secure Single Board Computer Implementation

Nanang Triagung Edi Hermawan, Edi Winarko, Ahmad Ashari
2021 International Journal on Advanced Science, Engineering and Information Technology
This research proposes an EPNR (Eight Prime Numbers of Modified RSA) method, a modified double RSA based on eight prime numbers combined with the CRT method, to speed up the random key generation and decryption  ...  To ensure data security, a recommendation to use a key size longer than 2048 bits generates challenges for implementing RSA in the SBC.  ...  The method also implements the CRT method with eight private key exponents on Alice's side and two private key exponents on Bob's side.  ...

### A Modified and Secured RSA Public Key Cryptosystem Based on "n" Prime Numbers

Muhammad Ariful Islam, Md. Ashraful Islam, Nazrul Islam, Boishakhi Shabnam
2018 Journal of Computer and Communications
This paper proposed an enhanced and modified approach of RSA cryptosystem based on "n" distinct prime number.  ...  Experiment on a set of a random number provided that the key generation time, analysis of variable "N", encryption and decryption will take a long time compared to traditional RSA.  ...  The weakness of RSA algorithm is the use of two prime numbers, small encryption exponent and use the same key for encryption and signing.  ...

### The Comparative Study on Public Key Algorithm using RSA AND OAEP

E. Vinithra
2016 International Journal Of Engineering And Computer Science
The core idea is enhance the security of RSA algorithm. In this dissertation public key algorithm RSA and enhanced RSA are compared analysis is made on time based on execution time.  ...  Systems that allow users to share moduli are using RSAEP/RSADP inappropriately. 4. Using a small private exponent d. It may be tempting to use a small private exponent d for reasons of efficiency.  ...  A small private exponent d should not be used. 5. Using a low public exponent e. Some progress has been made  on exploiting the use of a low public exponent.  ...
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