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Scribed by Guoming Wang

Summary

Today we show how to construct an efficient CCA-secure public-key encryption scheme in the random oracle model using RSA.

As we discussed in the previous lecture, a cryptographic scheme defined in the random oracle model is allowed to use a random function ${H: \{ 0,1 \}^n \rightarrow \{ 0,1 \}^m}$ which is known to all the parties. In an implementation, usually a cryptographic hash function replaces the random oracle. In general, the fact that a scheme is proved secure in the random oracle model does not imply that it is secure when the random oracle is replaced by a hash function; the proof of security in the random oracle model gives, however, at least some heuristic confidence in the soundness of the design.

Scribed by Steve Hanna

Summary

Today we discuss the three ways in which definitions of security given in class differ from the way they are given in the Katz-Lindell textbook,.

Then we study the security of hybrid encryption schemes, in which a public-key scheme is used to encode the key for a private-key scheme, and the private-key scheme is used to encode the plaintext.

We also define RSA and note that in order to turn RSA into an encryption scheme we need a mechanism to introduce randomness.

Summary

Today we show how to construct an efficient CCA-secure public-key encryption scheme in the random oracle model using RSA.

As we discussed in the previous lecture, a cryptographic scheme defined in the random oracle model is allowed to use a random function ${H: \{ 0,1 \}^n \rightarrow \{ 0,1 \}^m}$ which is known to all the parties. In an implementation, usually a cryptographic hash function replaces the random oracle. In general, the fact that a scheme is proved secure in the random oracle model does not imply that it is secure when the random oracle is replaced by a hash function; the proof of security in the random oracle model gives, however, at least some heuristic confidence in the soundness of the design.

Summary

In the last lecture we described a very complex signature scheme based on one-time signatures and pseudorandom functions. Unfortunately there is no known simple and efficient signature scheme which is existentially unforgeable under a chosen message attack under general assumptions.

Today we shall see a very simple scheme based on RSA which is secure in the random oracle model. In this model, all parties have oracle access to a random function ${H : \{ 0,1 \}^n \rightarrow \{ 0,1 \}^m}$. In implementations, this random function is replaced by a cryptographic hash function. Unfortunately, the proof of security we shall see today breaks down when the random oracle is replaced by hash function, but at least the security in the random oracle model gives some heuristic confidence in the design soundness of the construction.

Via Boing Boing and Bruce Schneier, I bring you the web site of singularics corporation.

I cannot do justice to it, because every sentence on every page is very special, but here is about one of their products:

One very important result from our advances in mathematics is a new patent-pending encryption algorithm called Neutronic Encryptionâ„¢. Unlike strong encryption algorithms widely used today, Neutronic Encryption is not based directly on fixed prime points, but rather on the Neutronic forces that govern the distribution of the primes themselves. The resulting encryption is theoretically impossible to break.

And, in more detail,

Singularics has advanced the state of the art in cryptography by developing a new theoretically unbreakable public-key algorithm called Neutronic Encryptionâ„¢.

Our advances in Prime Number Theory have led to a new branch of mathematics called Neutronics. Neutronic functions make possible for the first time the ability to analyze regions of mathematics commonly thought to be undefined, such as the point where one is divided by zero. In short, we have developed a new way to analyze the undefined point at the singularity which appears throughout higher mathematics.

This new analytic technique has given us profound insight into the way that prime numbers are distributed throughout the integers. According to RSA’s website, the RSA public key encryption algorithm has an installed based of nearly one billion. Each of these instances of the prime number based RSA algorithm can now be deciphered using Neutronic analysis . Unlike RSA, Neutronic Encryption is not based on two large prime numbers but rather on the Neutronic forces that govern the distribution of the primes themselves. The encryption that results from Singularics’ Neutronic public-key algorithm is theoretically impossible to break.

And you know what else you can do with this newly discovered netronic forces of the primes, besides breaking RSA and realizing impossible-to-break encryption? Read the rest of this entry »