Cryptography Reference
In-Depth Information
across Fermat's Little Theorem and Euler's Theorem. Both theorems are based on
Lagrange's Theorem and are frequently used in cryptography. Furthermore, they
have a straighforward application in the RSA public key cryptosystem. The same
is true for quadratic residuosity, which has a direct application in probabilistic
encryption and many indirect applications in cryptographic protocols. Last but
not least, we introduced the elliptic curves that are used in ECC. While ECC
is a hot topic today, it should not be overemphasized. It is useful to speed up
implementations and bring down key sizes (of public key cryptosystems). It does
not, however, provide cryptosystems that are inherently new or different from the
cryptosystems that were known before ECC was proposed and deployed.
References
[1]
Koblitz, N.I., A Course in Number Theory and Cryptography , 2nd edition. Springer-Verlag, New
York, 1994.
[2]
Koblitz, N.I., Algebraic Aspects of Cryptography . Springer-Verlag, New York, 1998.
[3]
Rosen, K.H., Discrete Mathematics and Its Applications , 4th edition. McGraw Hill, 1998.
[4]
Johnsonbaugh, R., Discrete Mathematics , 5th edition. Prentice Hall, 2000.
[5]
Dossey, J.A., et al., Discrete Mathematics , 4th edition. Addison-Wesley, 2001.
[6]
Shoup, V., A Computational Introduction to Number Theory and Algebra . Cambridge University
Press, Cambridge, UK, 2005.
[7]
Maurer, U.M., “Fast Generation of Prime Numbers and Secure Public-Key Cryptographic Param-
eters,” Journal of Cryptology , Vol. 8, No. 3, 1995, pp. 123-155.
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