• Corpus ID: 11023027


  author={Dan Boneh},
  journal={Notices of the American Mathematical Society},
  • D. Boneh
  • Published 1999
  • Computer Science, Mathematics
  • Notices of the American Mathematical Society
Introduction The RSA cryptosystem, invented by Ron Rivest, Adi Shamir, and Len Adleman [18], was first publicized in the August 1977 issue of Scientific American. The cryptosystem is most commonly used for providing privacy and ensuring authenticity of digital data. These days RSA is deployed in many commercial systems. It is used by Web servers and browsers to secure Web traffic, it is used to ensure privacy and authenticity of e-mail, it is used to secure remote login sessions, and it is at… 
Cryptanalysis of RSA: A Survey
A survey of the main methods used in attacks against the RSA cryptosystem, which describes the main factoring methods, attacks on the underlying mathematical function, as well as attacks that exploit details in implementations of th e algori thm.
Cryptanalytic Attacks on Rivest, Shamir, and Adleman (RSA) Cryptosystem: Issues and Challenges
The issues and challenges on some key aspects of cryptanalytic attacks on RSA algorithm are presented and the perceived vulnerabilities of implementing RSA algorithm which can render a cryptanalyst easier means of attack are explored.
Thirty Years of Attacks on the RSA Cryptosystem
A survey on RSA attacks is intended to cover the attacks enabled by the weak private exponent, the weak public exponent,The partial key exposure and the implementation details of RSA respectively.
On the security of some variants of rsa
  • M. Hinek
  • Computer Science, Mathematics
  • 2007
This thesis provides detailed analyses of the best known algebraic attacks on instances of RSA with certain special private exponents, multiple instance of RSA sharing a common small private exponent, Multi-prime RSA, Common Prime RSA and Dual RSA.
A security enhancement on the RSA cryptosystem is introduced that will make the RSA semantically secure, this means that an attacker cannot distinguish two encryptions from each other even if the attacker knows (or has chosen) the corresponding plaintexts.
A-RSA: Augmented RSA
This paper design and implement a swift and secure variant of RSA based on Rabin and Huffman coding called Augmented RSA (A-RSA) to solve aforementioned limitations of the basic RSA.
A Study of RSA Algorithm in Cryptography
Being the first example in history of the public key cryptosystem and, worth nothing, the only type that has withstood more than three decades of attacks, the RSA has become the choice algorithm for functions such as authenticating phonecalls, encrypting credit-card transactions over the Internet, Security e-mail and providing numerous other Internet security functions.
On the Analysis of Public-Key Cryptologic Algorithms
It is shown that integrating state-of-the-art NFS software packages with GPU software can lead to a speed-up of 50% in the case of elliptic and hyperelliptic curves for cryptographic use, and the best published method to solve the Pollard rho algorithm.
Comparative Analysis of Encryption and Decryption Techniques Using Mersenne Prime Numbers and Phony Modulus to Avoid Factorization Attack of RSA
This paper presents a methodology which is more secure than RSA algorithm by doing some modifications in it and it is constructed by Mersenne prime numbers to provide more efficiency and security.
Diophantine and Lattice Cryptanalysis of the RSA Cryptosystem
  • Abderrahmane Nitaj
  • Computer Science, Mathematics
    Artificial Intelligence, Evolutionary Computing and Metaheuristics
  • 2013
A survey of the mathematics of the RSA cryptosystem focussing on the cryptanalysis of RSA using a variety of diophantine methods and lattice-reduction based techniques is given.


Timing Attacks on Implementations of Diffie-Hellman, RSA, DSS, and Other Systems
  • P. Kocher
  • Computer Science, Mathematics
  • 1996
By carefully measuring the amount of time required tm perform private key operalions, attackers may be able to find fixed Diffie-Hellman exponents, factor RSA keys, and break other cryptosystems.
Cryptanalysis of short RSA secret exponents
  • M. Wiener
  • Computer Science, Mathematics
    IEEE Trans. Inf. Theory
  • 1990
A cryptanalytic attack on the use of short RSA secret exponents is described, which poses no threat to the normal case of RSA where the secret exponent is approximately the same size as the modulus.
A Chosen Text Attack on the RSA Cryptosystem and Some Discrete Logarithm Schemes
A new attack on the RSA cryptosystem is presented, which is considerably more efficient than the best algorithms that are known for factoring the public modulus.
On the importance of securing your bins: the garbage-man-in-the-middle attack
This paper exploits weak error-handling methods and attacks RSA, Rabin, LUC, KMOV, Demytko, ElGamal and its analogues, 3-pass system, knapsack scheme, etc.
A method for obtaining digital signatures and public-key cryptosystems
An encryption method is presented with the novel property that publicly revealing an encryption key does not thereby reveal the corresponding decryption key, soriers or other secure means are not needed to transmit keys.
Chosen Ciphertext Attacks Against Protocols Based on the RSA Encryption Standard PKCS #1
A new adaptive chosen ciphertext attack against certain protocols based on RSA is introduced if the attacker has access to an oracle that returns only one bit telling whether the ciphertext corresponds to some unknown block of data encrypted using PKCS #1.0.
Optimal Asymmetric Encryption
A slightly enhanced scheme is shown to have the property that the adversary can create ciphertexts only of strings for which she “knows” the corresponding plaintexts—such a scheme is not only semantically secure but also non-malleable and secure against chosen-ciphertext attack.
Attacks on Some RSA Signatures
Two simple redundancy schemes are shown to be inadequate in securing RSA signatures against attacks based on multiplicative properties. The schemes generalize the requirement that each valid message
Small Solutions to Polynomial Equations, and Low Exponent RSA Vulnerabilities
It is shown how to find sufficiently small integer solutions to a polynomial in a single variable modulo N, and to a Poole's inequality in two variables over the integers.
Solving Simultaneous Modular Equations of Low Degree
  • J. Håstad
  • Mathematics, Computer Science
    SIAM J. Comput.
  • 1988
It is shown that a protocol by Broder and Dolev is insecure if RSA with a small exponent is used and the RSA cryptosystem used with asmall exponent is not a good choice to use as a public-key cryptos system in a large network.