On computing logarithms over GF(2p)

• In this paper we present a new, heuristic method for computing logarithms over GF(2P). When 2P-1 is a Mersenne prime <231-1 it works in very short running times on a general purpose computer. It is based on the interdependent relations f,~(t) = t-2~f(t) 2" and log f~s(t) = - 2' + 2" log f(t), where f and frs are polynomials over GF(2). Its cryptographic significance is discussed and it can be considered as an attempt to swindle MITRE Corporation which reportedly is using a public key distribution system, based on the presumed difficulty in computing logarithms over GF(2127).

Subject headings

TEKNIK OCH TEKNOLOGIER  -- Elektroteknik och elektronik (hsv//swe)

ENGINEERING AND TECHNOLOGY  -- Electrical Engineering, Electronic Engineering, Information Engineering (hsv//eng)

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art (subject category)

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