# Cryptanalysis of RSA with Small Prime Difference

@article{Weger2002CryptanalysisOR, title={Cryptanalysis of RSA with Small Prime Difference}, author={Benne de Weger}, journal={Applicable Algebra in Engineering, Communication and Computing}, year={2002}, volume={13}, pages={17-28} }

We show that choosing an RSA modulus with a small difference of its prime factors yields improvements on the small private exponent attacks of Wiener and Boneh-Durfee.

## Figures and Topics from this paper

## 107 Citations

An algorithm to obtain an RSA modulus with a large private key

- Mathematics, Computer ScienceIACR Cryptol. ePrint Arch.
- 2003

Sufficient conditions are obtained on the prime factors of an RSA modulus in order to avoid Wiener and Boneh-Durfee attacks. The public exponent can be chosen arbitrarily.

Small Private-Exponent Attack on RSA with Primes Sharing Bits

- Computer ScienceISC
- 2007

We show in this paper that if the primes share their some bits (e.g. Least-Significant bits), RSA system with small private-exponent is much more vulnerable to the Boneh-Durfee Attack.

Cryptanalysis of RSA with Small Prime Difference using Unravelled Linearization

- Mathematics
- 2013

In 2002, de Weger showed that choosing an RSA modulus with a small difference of primes improves the attack given by Boneh-Durfee. For this attack, de Weger used the complicated geometrical…

De Weger ’ s attack on RSA small prime difference :

- 2013

In 2002, de Weger showed that choosing an RSA modulus with a small difference of primes improves the attack given by Boneh-Durfee. For this attack, de Weger used the complicated geometrical…

Partial Key Exposure Attacks on RSA up to Full Size Exponents

- Computer Science, MathematicsEUROCRYPT
- 2005

These new attacks on RSA are the first attacks of this type that work up to full size public or private exponent, and factor the modulus in polynomial time.

Publishing Upper Half of RSA Decryption Exponent

- Computer ScienceIWSEC
- 2010

This paper proposes certain schemes to exploit the top half of the decryption exponent d, which can be narrowed down within a small search space, towards efficient RSA decryption.

Factoring RSA moduli when a message is close to a multiple of the primes

- Computer Science, MathematicsInt. J. Comput. Math. Comput. Syst. Theory
- 2018

It is shown that it is possible to factor N in polynomial time in when a low public exponent is used.

Factoring multi power RSA moduli with a class of secret exponents

- Mathematics
- 2015

Abstract In this paper, we consider the RSA variant based on the key equation ed ≡ 1 (mod φ(N)) where N = prq, r ≥ 2. We show that if the secret exponent d is close to any multiple of the prime…

The Monte Carlo Type Method of Attack on the RSA Cryptosystem

- Computer Science2020 10th International Conference on Advanced Computer Information Technologies (ACIT)
- 2020

The possibility of determination of the secret key of an RSA cryptosystem by means of the Monte Carlo method applied to the continued fraction method is studied.

Factoring RSA moduli with primes sharing bits in the middle

- Mathematics, Computer ScienceApplicable Algebra in Engineering, Communication and Computing
- 2017

This work addresses the problem of factoring a large RSA modulus $$N=pq$$N= pq with p and q sharing a portion of bits in the middle and suggests that such integers are not appropriate for cryptographic purposes.

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