Applying the Diffie-Hellman Key Exchange to RSA (UMAP)

One fact of particular interest regarding RSA is that it is a public-key system, meaning that two parties using RSA to exchange secret messages can make their encryption key e public without compromising the security of the system. The security of the system comes from the fact that even if an intruder knows the encryption key, he or she should not be able to determine the corresponding decryption key. To find the decryption key, the intruder would first have to find the prime factors of n, a problem which at this time is essentially impossible provided these factors are sufficiently large. However, if the intruder could somehow factor n, then he or she could determine the decryption key very easily through a straightforward application of the Euclidean algorithm. Hence, the RSA system has the limitation that in order to break the system, an intruder need only factor n. In this article, we discuss a technique that initially appears to remove this vulnerability from the RSA system. We do this by using the Diffie-Hellman key exchange to keep the encryption key secret between the originator and intended recipient of the messages.

Table of Contents:

INTRODUCTION

THE DIFFIE-HELLMAN KEY EXCHANGE

THE DISCRETE LOGARITHM PROBLEM

CONCLUSION

ACKNOWLEDGMENTS

REFERENCES

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