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Discrete Logarithms in Finite Fields and Their Cryptographic Significance
, 1984
"... Given a primitive element g of a finite field GF(q), the discrete logarithm of a nonzero element u GF(q) is that integer k, 1 k q  1, for which u = g k . The wellknown problem of computing discrete logarithms in finite fields has acquired additional importance in recent years due to its appl ..."
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Given a primitive element g of a finite field GF(q), the discrete logarithm of a nonzero element u GF(q) is that integer k, 1 k q  1, for which u = g k . The wellknown problem of computing discrete logarithms in finite fields has acquired additional importance in recent years due to its applicability in cryptography. Several cryptographic systems would become insecure if an efficient discrete logarithm algorithm were discovered. This paper surveys and analyzes known algorithms in this area, with special attention devoted to algorithms for the fields GF(2 n ). It appears that in order to be safe from attacks using these algorithms, the value of n for which GF(2 n ) is used in a cryptosystem has to be very large and carefully chosen. Due in large part to recent discoveries, discrete logarithms in fields GF(2 n ) are much easier to compute than in fields GF(p) with p prime. Hence the fields GF(2 n ) ought to be avoided in all cryptographic applications. On the other hand, ...
The First Ten Years of PublicKey Cryptography
, 1988
"... Publickey cryptosystems separate the capacities for encryption and decryption so that 7) many people can encrypt messages in such a way that only one person can read them, or 2) one person can encrypt messages in such a way that many people can read them. This separation allows important improvemen ..."
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Publickey cryptosystems separate the capacities for encryption and decryption so that 7) many people can encrypt messages in such a way that only one person can read them, or 2) one person can encrypt messages in such a way that many people can read them. This separation allows important improvements in the management of cryptographic keys and makes it possible to ‘sign ’ a purely digital message. Public key cryptography was discovered in the Spring of 1975 and has followed a surprising course. Although diverse systems were proposed early on, the ones that appear both practical and secure today are all very closely related and the search for new and different ones has met with little success. Despite this reliance on a limited mathematical foundation publickey cryptography is revolutionizing communication security by making possible secure communication networks with hundreds of thousands of subscribers.
Using El Gamal Cryptosystem in Message Feedback Mode for Computing Cost Reduction
, 2013
"... This paper discuses comparatively more efficient and cost effective scheme of El Gamal Cryptosystem by introducing the concept of using the established cryptosystems into message feedback mode. The idea behind this is, “an established cryptographic scheme can be used to initiate any communication, a ..."
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This paper discuses comparatively more efficient and cost effective scheme of El Gamal Cryptosystem by introducing the concept of using the established cryptosystems into message feedback mode. The idea behind this is, “an established cryptographic scheme can be used to initiate any communication, and further users may switch to some lightweight process so that the degree of secrecy is maintained by means of the public key cryptosystem and the performance is achieved by using some other lightweight process. Approach discussed in this paper is of using message itself as One Time Pad (OTP), because any automation can‟t produce any random pad than a human being, and their messages posses same property. The length of Key used in El Gamal encryption and size of OTP determines the level of secrecy offered by the proposed system. Further a discussion is made upon the other dimensions of degree of security provided in such implementation. So as a result an applied approach is presented to design a data security mechanism for which users will use message itself as a One Time Pad and El Gamal Cryptosystem to initiate the operations and subsequent steps will involve simple XOR operations for cryptographic purpose.