### Giuseppe Persiano

Dipartimento di Informatica e Applicazioni

Università di Salerno

Italy

## Zero Knowledge and the Construction of Secure Encryption Schemes

#### Abstract

In this series of lectures we will introduce the concept of Zero Knowledge. A zero-knowledge proof system is a proof system by which a prover can convince a verifier of the veridicity of statement without revealing any additional knowledge.

We will then turn our attention to the Common Reference String model in which prover and verifier have access to the same randomly chosen string. Using this very minimal infrastructure, it is possible to give Non-Interactive Zero Knowledge proofs for all NP languages.

Finally, we will show how NIZK can be used to construct encryption schemes secure against very strong attacks (adaptive chosen ciphertext attacks).

#### Course materials

- G. Persiano. Zero knowledge and the construction of secure encryption schemes. Lecture slides [pdf].
- A. de Santis, G. di Crescenzo, R. Ostrovsky, G. Persiano,
A. Sahai. Robust non-interactive zero knowledge. In J. Kilian, ed.,
*Advances in Cryptology, CRYPTO 2001*, v. 2139 of*Lect. Notes in Comput. Sci.*, pp. 566-598. Springer, 2001. - A. de Santis, G. Persiano. Zero-knowledge proofs of knowledge
without interaction. In
*Proc. of 33rd IEEE Ann. Symp. on Foundations of Comput. Sci., FOCS '92*, pp. 427-436. IEEE CS Press, 1992. - U. Feige, D. Lapidot, A. Shamir. Multiple non-interactive zero
knowledge proofs under general assumptions.
*SIAM J. on Computing*, v. 29, n. 1, pp. 1-28, 1999. - Y. Lindell. A simpler construction of CCA2-secure public-key
encryption under general assumptions. In E. Biham, ed.,
*Advances in Cryptology, EUROCRYPT 2003*, v. 2656 of*Lect. Notes in Comput. Sci*, pp. 241-254. Springer, 2003. - M. Naor, M. Yung. Public-key cryptosystems provably secure against
chosen ciphertext attacks. In
*Proc. of 22nd Ann. ACM Symp. on Theory of Computing, STOC 1990*, pp. 427-437. ACM Press, 1990.

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