A method for obtaining digital signatures and public-key cryptosystems

ABSTRACT

An encryption method is presented with the novel property that publicly revealing an encryption key does not thereby reveal the corresponding decryption key. This has two important consequences: Couriers or other secure means are not needed to transmit keys, since a message can be enciphered using an encryption key publicly revealed by the intended recipient. Only he can decipher the message, since only he knows the corresponding decryption key. A message can be “signed” using a privately held decryption key. Anyone can verify this signature using the corresponding publicly revealed encryption key. Signatures cannot be forged, and a signer cannot later deny the validity of his signature. This has obvious applications in “electronic mail” and “electronic funds transfer” systems. A message is encrypted by representing it as a number M, raising M to a publicly specified power e, and then taking the remainder when the result is divided by the publicly specified product, n, of two large secret prime numbers p and q. Decryption is similar; only a different, secret, power d is used, where e * d = 1(mod (p - 1) * (q - 1)). The security of the system rests in part on the difficulty of factoring the published divisor, n.

REFERENCES

• 1: Diffie, W., and Hellman, M. New directions in cryptography. IEEE Trans. Inform. Theory IT-22, 6 (Nov. 1976), 644-654.
• 2: Diffie, W., and Hellman, M. Exhaustive cryptanalysis of the NBS data encryption standard. Computer 10 (June 1977), 74-84.
• 3: Donald E. Knuth, The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms, Addison-Wesley Longman Publishing Co., Inc., Boston, MA, 1997
• 4: Levine, J., and Brawley, J.V. Some cryptographie applications of permutation polynomials. Cryptologio 1 (Jan. 1977), 76-92.
• 5: Ralph C. Merkle, Secure communications over insecure channels, Communications of the ACM, v.21 n.4, p.294-299, April 1978 [doi>10.1145/359460.359473]
• 6: Gary L. Miller, Riemann's Hypothesis and tests for primality, Proceedings of seventh annual ACM symposium on Theory of computing, p.234-239, May 05-07, 1975, Albuquerque, New Mexico, United States [doi>10.1145/800116.803773]
• 7: Niven, I., and Zuckerman, H.S. An Introduction to the Theory of Numbers. Wiley, New York, 1972.
• 8: Pohlig, S.C., and Hellman, M.E. An improved algorithm for computing logarithms over GF(p) and its cryptographic significance. To appear in IEEE Trans. Inform. Theory, 1978.
• 9: Pollard, J.M. Theorems on factorizarion and primality testing. Proc. Camb. Phil. Soc. 76 (1974), 521-528.
• 10: Potter, R.J., Electronic mail. Science 195, 4283 (March 1977), 1160-1164.
• 11: Rabin, M.O., Probabilistic algorithms. In Algorithms and Complexity, J. F. Traub, Ed., Academic Press, New York, 1976, pp. 21-40.
• 12: Solovay, R., and Strassen, V. A Fast Monte-Carlo test for primality. SIAM J. Compmg. 6 (March 1977), 84-85.
• 13: Federal Register, Vol. 40, No. 52, March 17, 1975.
• 14: Federal Register, Vol. 40, No. 149, August 1, 1975.

INDEX TERMS

Keywords:
authentication, cryptography, digital signatures, electronic funds transfer, electronic mail, factorization, message-passing, prime number, privacy, public-key cryptosystems, security