Discrete logarithms

 

Are discrete logarithms fundamental to the Digital Signature algorithm (DSA) and the Diffie-Hellman key exchange algorithm?

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Discrete logarithms

The term discrete logarithm is most commonly used in cryptography, although the term “generalized multiplicative order” is sometimes used as well (Schneier 1996, p. 501). In the number theory, the term “index“ is generally used instead (Gauss 1801; Nagell 1951, p. 112). Discrete logarithms are quickly computable in a few special cases. Discrete logarithms are fundamental to a number of public-key algorithms, including Diffie-Hellman key exchange and the digital signature algorithm (DSA) (ORE67 and LEVE90). The Diffie-Hellman (DH) Algorithm is a key-exchange protocol that enables two parties communicating over public channel to establish a mutual secret without it being transmitted over the internet. Digital signature algorithm (DSA) is a type of public-key encryption algorithm, and is used to generate an electronic signature.

purpose the promotion of this type of political-religious behavior through violence (terrorism). A strong imprint on the history of contemporary terrorism was the Hamas Palestinian Islamist group (the name is an acronym of Harakat al-Muqawama al-Islamiyya, or the Islamic Resistance Movement). The general purpose of the organization is the conquest of the Israeli territories of the West Bank and the Gaza Strip, which, according to their claims, represent their historical, political and cultural legacy, which was later “unfairly” given to the State of Israel with its establishment on 14 May 1948.
Regarding the origins of this group, at a closer look there can be strong similarities (ideologically and organizationally) with Muslim Brotherhood-M.B. established in 1920, and with strong activity in Jordan and Egypt. Hamas is therefore classified as a detached group of M.B., which will have the first signs of autonomy around 1967, officially registered in Israel only in 1978 by Sheik Ahmad Yasin. In the early years, the group had the status of a non-governmental organization, so it worked as a good time as a non-profit foundation (the Al-Mudjamma Foundation). This type of organization has brought many adherents to the group, due to cultural and religious concerns (spread of Islam, cultural institutions funding, promotion of various religious circles, and last but not least, social workers) . Transforming the status of a non-governmental group into a terrorist will be progressive. In 1987, on the occasion of the first Intifade led by Ahmad Yasin and Muhammad Taha (who was at that time a distinguished leader of the MB in the Gaza Strip), Hamas is involved in the first violent forms of manifestation through direct participation in street violence and assassinations, Thus gaining a central role in the intifada. Beginning in September 1989, the organization will be outlawed by continued involvement in acts of violence and officially recognized as a terrorist group.
The significant stage of the Hamas expansion took place especially after the Gulf War, when terrorist activities grew both quantitatively (in terms of violence, membership, funding, etc.), m

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