Ronald Cramer
On recent algebraic paradigms for practical
encryption with chosen cipher-text security
After briefly reviewing public-key crypto-systems and their security,
I'll discuss some recent results on practical public-key crypto-systems that
enjoy the highest level of security for such systems. This is joint work with
Victor Shoup (Courant Institute, NYU).
A Hash Proof System (HPS) is a new cryptographic primitive that enables
generic construction of a public-key crypto-system that withstands adaptively
chosen ciphertext attacks. Concrete instance of HPS can be constructed from
groups that admit certain convenient homomorphisms. Security is derived
from the hardness of distinguishing a given sub-group from the rest of the
group.
This leads to several new practical schemes. One example is based on
the classical Quadratic Residuosity Assumption, while another is based
on Paillier's Decision Composite Residuosity Assumption. The so-called
Cramer-Shoup scheme (1998), which is based on the Decisional
Diffie/Hellman assumption and which was up to now the only practical
public-key crypto-system proven to be secure against adaptive chosen
cipher-text attack in the standard cryptographic model, is also an
instance of the construction. Time permitting we will discuss recent proposals for
identity based encryption based on pairings on elliptic curves.
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