Abstract
An identity-based non-interactive public key distribution system is presented that is based on a novel trapdoor one-way function allowing a trusted authority to compute the discrete logarithms modulo a publicly known composite number m while this is infeasible for an adversary not knowing the factorization of m. Without interaction with a key distribution center or with the recipient of a given message, a user can generate a mutual secure cipher key based solely on the recipient's identity and his own secret key, and subsequently send the message, encrypted with the generated cipher used in a conventional cipher, over an insecure channel to the recipient. In contrast to previously proposed identity-based systems, no public keys, certificates for public keys or other information need to be exchanged and thus the system is suitable for certain applications that do not allow for interaction. The paper solves an open problem proposed by Shamir in 1984.
Similar content being viewed by others
References
D. Atkins, M. Graff, A. K. Lenstra, and P. C. Leyland, The magic words are squeamish ossifrage, Advances in Cryptology-Asiacrypt' 94, Lecture Notes in Computer Science, Springer-Verlag, Berlin, 917 (1994). pp. 263–277.
E. Bach, Discrete logarithms and factoring, Technical Report UCB/CSD84/186, Computer Science Division, University of California, Berkeley (1984).
D. Coppersmith, A. M. Odlyzko and R. Schroeppel, Discrete Logarithms in GF.(p), Algorithmica, Vol. 1(1986) pp. 1–15.
W. Diffie and M. E. Hellman, New directions in cryptography, IEEE Transactions on Information Theory, Vol. IT-22 (1976) pp. 664–654.
B. Dixon and A. K. Lenstra, Massively parallel elliptic curve factoring, Advances in Cryptology- EUROCRYPT' 92, Lecture Notes in Computer Science, Springer-Verlag, Berlin, 658 (1993) pp. 183–193.
T. ElGamal, A public key cryptosystem and a signature scheme based on discrete logarithms, IEEE Trans-actions on Information Theory, Vol. IT-31 (1985) pp. 469–472.
M. Girault, Self-certified public keys, Advances in Cryptology-EUROCRYPT' 91, Lecture Notes in Com-puter Science, Springer-Verlag, Berlin, 547 (1991) pp. 490–497.
C. G. G¨ unther, An identity-based key-exchange protocol, Advances in Cryptology-EUROCRYPT' 89, Lecture Notes in Computer Science, Springer Verlag, Berlin, 434 (1990) pp. 29–37.
K. Koyama and K. Ohta, Identity-based conference key distribution systems, Advances in Cryptology- CRYPTO' 87, Lecture Notes in Computer Science, Springer Verlag, Berlin, 293 (1988) pp. 175–184.
A. K. Lenstra, Personal communication (1991).
A. K. Lenstra and M. S. Manasse, Factoring with two large primes, Advances in Cryptology-EUROCRYPT' 90, Lecture Notes in Computer Science, Springer Verlag, Berlin, 473 (1991) pp. 69–80.
H. W. Lenstra, Factoring integers with elliptic curves, Annals of Mathematics, Vol. 126 (1987) pp. 649–673.
A. K. Lenstra, H. W. Lenstra, M. S. Manasse, and J. M. Pollard, The number field sieve, Proc. 22nd ACM Symposium on Theory of Computing, (1990) pp. 564–572.
A. K. Lenstra and M. S. Manasse, Factoring with electronicpppn mail, Advances in Cryptology- EUROCRYPT' 89, Lecture Notes in Computer Science, Springer Verlag, Berlin, 434 (1990) pp. 355–371.
T. Matsumoto and H. Imai, On the key predistribution system: a practical solution to the key distribution problem, Advances in Cryptology-CRYPTO' 87, Lecture Notes in Computer Science, Springer Verlag, Berlin, 293 (1988) pp. 185–193.
U. M. Maurer, Fast generation of prime numbers and secure public-key cryptographic parameters, Journal of Cryptology, Vol. 8, No. 3 (1995) pp. 123–155.
U. M. Maurer and Y. Yacobi, A remark on a non-interactive public-key distribution system, Advances in Cryptology-EUROCRYPT' 92, Lecture Notes in Computer Science, Springer-Verlag, Berlin, 658 (1992) pp. 458–460.
K. S. McCurley, A key distribution system equivalent to factoring, Journal of Cryptology, Vol. 1, No. 2 (1988) pp. 95–106.
G. L. Miller, Riemann's hypothesis and tests for primality, Journal of Computer and System Sciences, Vol. 13 (1976) pp. 300–317.
Y. Murakami and M. Kasahara, An ID-based key distribution system, Proc. of ISEC90, (1990) pp. 33–40 (in Japanese).
A. M. Odlyzko, Personal communications (1991).
T. Okamoto and K. Ohta, How to utilize the randomness of zero-knowledge proofs, Advances in Cryptology-CRYPTO' 90, Lecture Notes in Computer Science, Springer-Verlag, Berlin, 537 (1991) pp. 456–475.
E. Okamoto and K. Tanaka, Key distribution based on identification information, IEEE Journal on Selected Areas in Communications, Vol. 7, No. 4 (1989) pp. 481–485.
S. C. Pohlig and M. E. Hellman, An improved algorithm for computing logarithms over GF.p/ and its cryptographic significance, IEEE Transactions on Information Theory, Vol. IT-24 (1978) pp. 106–110.
J. M. Pollard, Theorems on factorization and primality testing, Proc. Cambridge Philos. Society, Vol. 76 (1974) pp. 521–528.
R. L. Rivest, A. Shamir, and L. Adleman, A method for obtaining digital signatures and public-key cryp-tosystems, Communications of the ACM, Vol. 21 (1978) pp. 120–126.
R. J. Schoof, Elliptic curves over finite fields and the computation of square roots mod p, Mathematics of Computation, Vol. 44 (1985) pp. 483–494.
A. Shamir, Identity-based cryptosystems and signature schemes, Advances in Cryptology-CRYPTO' 84, Lecture Notes in Computer Science, Springer Verlag, Berlin, 196 (1985) pp. 47–53.
H. N. Shapiro, Introduction to the Theory of Numbers, Wiley, New York (1983).
Z. Shmuely, Composite Diffie-Hellman public-key generating systems are hard to break, TR 356, CS Dept., Technion, Israel (1985).
S. Tsujii and T. Itoh, An ID-based cryptosystem based on the discrete logarithm problem, IEEE Journal on Selected Areas in Communications, Vol. 7, No. 4 (1989) pp. 467–473.
Y. Yacobi, A key distribution “paradox,” Advances in Cryptology-CRYPTO' 90, Lecture Notes in Com-puter Science, Springer-Verlag, Berlin, 537 (1991) pp. 268–273.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Maurer, U.M., Yacobi, Y. A Non-interactive Public-Key Distribution System. Designs, Codes and Cryptography 9, 305–316 (1996). https://doi.org/10.1023/A:1027332606155
Issue Date:
DOI: https://doi.org/10.1023/A:1027332606155