Summary
A simple method is given for finding strong, random, large primes of a given number of bits, for use in conjunction with the RSA Public Key Cryptosystem. A strong prime p is a prime satisfying: * p = 1 mod r * p = s−1 mod s * r = 1 mod t, where r,s and t are all large, random primes of a given number of bits. It is shown that the problem of finding strong, random, large primes is only 19% harder than finding random, large primes.
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References
W Diffie and M.E. Hellman, “New Directions in Cryptography”, IEEE Trans. Inform. Theory, vol. IT-22, No.6, 1976, 644–54.
R.L. Rivest, A. Shamir and L. Adleman, “A Method for obtaining Digital Signatures and Public Key Cryptosystems”, Comms ACM, 21,2, 121–126, 1978.
D.E. Knuth, “The Art of Computer Programming Volume 2, Seminumerical Algorithms”, 2nd Ed., Addison-Wesley, 1982.
D.M. Burton, “Elementary number theory”, Allyn and Bacon, 1980
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© 1985 Springer-Verlag Berlin Heidelberg
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Gordon, J. (1985). Strong Primes are Easy to Find. In: Beth, T., Cot, N., Ingemarsson, I. (eds) Advances in Cryptology. EUROCRYPT 1984. Lecture Notes in Computer Science, vol 209. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-39757-4_19
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DOI: https://doi.org/10.1007/3-540-39757-4_19
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