Some remarks on the Herlestam-Johannesson algorithm for computing logarithms over GF(2/sup P/). [Potential threat to Pohlig-Hellman Cryptosystem]
At the 1981 IEEE Symposium on Information Theory, T. Herlestam and R. Johannesson presented a heurestic method for computing logarithms over GF(2/sup p/). They reported computing logarithms over GF(2/sup 31/) with surprisingly few iterations and claimed that the running time of their algorithm was polynomial in p. If this were true, the algorithm could be used to cryptanalyze the Pohlig-Hellman cryptosystem, currently in use by Mitre Corporation for key distribution. The Mitre system operates in GF(2/sup 127/). However, the algorithm was not implemented for GF(2/sup p/) for p > 31 because it would require multiple precision arithmetic. Consequently attempts to evaluate the possible threat to the Pohlig-Hellman cryptosystem have centered on modeling the algorithm so that some predictions could be made analytically about the number of iterations required to find logarithms over GF(2/sup p/) for p > 31.
- Research Organization:
- Sandia National Labs., Albuquerque, NM (USA)
- DOE Contract Number:
- AC04-76DP00789
- OSTI ID:
- 5074765
- Report Number(s):
- SAND-82-1908C; CONF-820852-2; ON: DE82020628
- Country of Publication:
- United States
- Language:
- English
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