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The security of the RSA cryptosystem and electronic signature

Kotlarz P., Piechowiak M., Dunajewski I.

Image Processing & Communications

2006

Vol. 11, no 1

33-39

Electronic document has a significant use in practice. It should fulfil requirements similar to those of paper document. An essential element of electronic document security is the electronic signature. This article presents the discussion on the security of cryptographic protocol - electronic signature - taking into account the possibilities of an accompanying attack on an asymmetric cryptosystem with an application of factorization and Euler's function. The discussion about potential vulnerabilities in verification of the electronic signature from the point of view of weak and strong RSA keys will be presented as well. This article is taking into account the problem of key length and the quality of the components for the public key. The considerations will be presented from the point of view of an attack on the electronic signature using standalone computer and a group of computers in network. The computation of Euler's function in an algorithm using parallel mode will be presented. In this article we show a relation between investment in security infrastructure and the value of protected information.

The attack on the RSA algorithm with the application of Euler's function

Kotlarz P., Żmudziński P., Dunajewski I.

Image Processing & Communications

2006

Vol. 11, no 1

25-31

The security of present-day asymmetric encryption algorithms is based on certain limitations of modern mathematics. A wide range of applications of asymmetric cryptography in commonly and widely used network protocols poses a question as to what degree such solutions, in a situation where the security of the used algorithm is not given once and for all, are really safe? In the vast majority of instances, a discussion on security involves considerations on the problem of factorization. The attack, derived almost from the definition, is an attack that involves trying many different options to intercept the private key, indispensable for decryption of the encrypted message, on the basis of the intercepted public key. The present work discusses possibilities and the feasibility of an attack on the RSA algorithm using two given methods, factorization and the method that implements Euler's function. The paper presents an analysis of potential costs (time and computational) for both presented methods. The article also includes a discussion on strong and weak keys for the RSA encryption. The quality of the keys is discussed taking into account the aforementioned two algorithms carrying out an attack against the encryption algorithm.