All reports by Author Shai Halevi:

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TR97-018
| 8th May 1997
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Oded Goldreich, Shai Halevi#### Eliminating Decryption Errors in the Ajtai-Dwork Cryptosystem.

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TR96-056
| 12th November 1996
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Oded Goldreich, Shai Halevi#### Public-Key Cryptosystems from Lattice Reduction Problems

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TR96-042
| 26th July 1996
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Oded Goldreich, Shai Halevi#### Collision-Free Hashing from Lattice Problems

Oded Goldreich, Shai Halevi

Following Ajtai's lead, Ajtai and Dwork have recently introduced a

public-key encryption scheme which is secure under the assumption

that a certain computational problem on lattices is hard on the

worst-case. Their encryption method may cause decryption errors,

though with small probability (i.e., inversely proportional to the

more >>>

Oded Goldreich, Shai Halevi

We present a new proposal for a trapdoor one-way function,

from which we derive public-key encryption and digital

signatures. The security of the new construction is based

on the conjectured computational difficulty of lattice-reduction

problems, providing a possible alternative to existing

more >>>

Oded Goldreich, Shai Halevi

Recently Ajtai described a construction of one-way functions whose

security is equivalent to the difficulty of some well known approximation

problems in lattices. We show that essentially the same

construction can also be used to obtain collision-free hashing.