List of Publications of Giuseppe Persiano

Giuseppe Persiano

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  1. I. Caragiannis, A. Ferreira, C. Kaklamanis, S. Perennes, P. Persiano, and H. Rivano. Approximate Constrained Bipartite Edge Coloring. . Discrete Applied Mathematics, 2003.

    Abstract: We study the following Constrained Bipartite Edge Coloring problem: We are given a bipartite graph G(U,V,E) of maximun degree l with n vertices, in which some of the edges have been legally colored with c colors. We wish to complete the coloring of the G minimizing the total number of colors used. The problem has been proved to be NP-hard even for bipartite graphs of maximum degree three [Fiala, 2000]. Two special cases have been previously considered and tight bounds were proved by decomposing the bipartite graph into matchings which are colored into pairs using detailed potential and averaging arguments. These techniques led to 3/2-approximation algorithms for both problems. In this paper we present a randomized (1.37+o(1))-approximation algorithm for the general problem in the case where max{l,c}=omega(ln n). Our techniques are motivated by recent works on the Circular Arc Coloring problem and are essentially different and simpler than the existing ones.

  2. P. Persiano and I. Visconti. An Anonymous Credential System and a Privacy-Aware PKI. . In R. Safavi-Naini and J. Seberry, editors, Information Security and Privacy, 8th Australasian Conference, ACISP 2003, volume 2727 of Lecture Notes in Computer Science. Springer Verlag, 2003 pages 27--38.

  3. P. Persiano and I. Visconti. A secure and private system for subscription-based remote services. . ACM Trans. Inf. Syst. Secur., 2003. 6(4):472--500. ISSN 1094-9224.
    Available at http://doi.acm.org/10.1145/950191.950193.

  4. V. Auletta, I. Caragiannis, C. Kaklamanis, and P. Persiano. Randomized path coloring on binary trees. . Theoretical Computer Science, 2002. 289:355--399.

    Abstract: Motivated by the problem of WDM routing in all--optical networks, we study the following NP--hard problem. We are given a directed binary tree T and a set R of directed paths on T. We wish to assign colors to paths of R, in such way that no two paths that share a directed arc of T are assigned the same color, and the total number of colors used is minimized. Our results are expressed in terms of the depth of the tree and of the maximum load l of R, i.e. the maximum number of paths that go through a directed arc of T. So far, only deterministic greedy algorithms have been presented for the problem. The best known algorithm colors any set R of maximum load l using at most 5l/3 colors. Alternatively, we say that this algorithm has performance ratio 5/3. It is also known that no deterministic greedy algorithm can achieve a performance ratio better than 5/3. In this paper we define the class of greedy algorithms that use randomization. We study their limitations and prove that, with high probability, randomized greedy algorithms cannot achieve a performance ratio better than 3/2 when applied to binary trees of depth \Omega(l), and 1.293-o(1) when applied to binary trees of constant depth. Exploiting inherent properties of randomized greedy algorithms, we obtain the first randomized algorithm for the problem that uses at most 7l/5+o(l) colors for coloring any set of paths of maximum load l on binary trees of depth o(l^{1/3}), with high probability. We also present an existential upper bound of 7l/5+o(l) that holds on any binary tree. For the analysis of our bounds we use tail inequalities for random variables following hypergeometrical probability distributions that might be of their own interest.

  5. I. Caragiannis, C. Kaklamanis, and P. Persiano. Edge coloring of bipartite graphs with constraints. . Theoretical Computer Science, 2002. 270:361--399.
    Available at http://dx.doi.org/10.1016/S0304-3975(00)00400-X.

    Abstract: A classical result from graph theory states that the edges of an l-regular bipartite graph can be colored using exactly l colors so that edges that share an endpoint are assigned different colors. In this paper, we study two constrained versions of the bipartite edge coloring problem.

    • Some of the adges adjacent to a specific pair of opposite vertices of an l-regular bipartite graph are already colored with S colors that appear only on one edge (single colors) and D colors that appear on two edges (double colors). We show that the rest of the edges can be colored using at most max{min{l+D,3/2l},l+(S+D)/l} total colors. We also show that this bound is tight by constructing instances in which max{min{l+D,3/2l},l+(S+D)/l} colors are indeed necessary.
    • Some of the edges of an l-regular bipartite graph are already colored with S colors that appear only on one edge. We show that the rest of the edges can be colored using at most max{l+S/2,S} total colors. We also show that this bound is tight by constructing instances in which max{l+S/2,S} total colors are necessary.

  6. A. De Santis, G. Di Crescenzo, and G. Persiano. Randomness-Optimal Characterization of Two NP Proof Systems. . In J. D. P. Rolim and S. Vadhan, editors, Randomization and Approximation Techniques in Computer Science -- 6th International Workhop RANDOM 2002, volume 2483 of Lecture Notes in Computer Science. Springer Verlag, 2002 .

  7. C. Galdi and P. Persiano. Private Computation with Shared Randomness over Broadcast Channel. . In K. Kim, editor, Information Security and Cryptology - ICISC 2001: 4th International Conference, volume 2288 of Lecture Notes in Computer Science. Springer Verlag, 2002 pages 244--253.

  8. V. Auletta, I. Caragiannis, L. Gargano, C. Kaklamanis, and P. Persiano. Sparse and limited wavelength conversion in all-optical tree networks. . Theoretical Computer Science, 2001. 266:887--934.

  9. V. Auletta and G. Persiano. Optimal Pebble Motion on a Tree. . Information and Computation, 2001. 165:42--68.

  10. I. Caragiannis, A. Ferreira, C. Kaklamanis, S. Perennes, P. Persiano, and H. Rivano. Approximate Constrained Bipartite Edge Coloring. . In A. Brandst\"{a}dt and V. B. Le, editors, Graph Theoretic Concepts in Computer Science, volume 2204 of Lecture Notes in Computer Science. Springer Verlag, July 2001 pages 21--31.

  11. G. Cattaneo, L. Catuogno, A. Del Sorbo, and G. Persiano. The Design and Implementation of a Transparent Cryptographic FileSystem for Unix. . In Usenix Technical Conference, Freenix Track. June 2001 pages 199--212.

  12. A. De Santis, G. Di Crescenzo, R. Ostrovsky, G. Persiano, and A. Sahai. Robust Non-Interactive Zero Knowledge. . In J. Kilian, editor, Advances in Cryptology -- CRYPTO 2001, volume 2139 of Lecture Notes in Computer Science. Springer Verlag, 2001 pages 566--598.

  13. T. Erlebach, K. Jansen, C. Kaklamanis, and G. Persiano. Directed Tree Networks. . In C. Floudas and P. Pardalos, editors, Encyclopedia of Optimization, volume 1. Kluwer Academic Publisher, 2001 pages 444--453.

  14. C. Galdi, C. Kaklamanis, M. Montangero, and P. Persiano. Optimal and Approximate Station Placement in Networks (with Applications to Multicasting and Space Efficient Traversal). . In A. Ferreira and H. Reichel, editors, Proceedings of Symposium on Theoretical Aspects of Computer Science (STACS 2001), volume 2010 of Springer Verlag. Springer Verlag, February 2001 pages 271--281.

    Abstract: In this paper we study the k-station placement problem (k-SP problem, in short) on graphs. This problem has application to efficient multicasting in circuit-switched networks and to space efficient traversals. We show that the problem is NP-complete even for 3-stage graphs and give an approximation algorithm with logarithmic approximation ratio. Moreover we show that the problem can be solved in polynomial time for trees.

  15. V. Auletta, I. Caragiannis, C. Kaklamanis, and G. Persiano. Randomized Path Coloring in Binary Trees. . In K. Jansen and S. Khuller, editors, Approximation Algorithms for Combinatorial Optimization (APPROX 2000), volume 1913 of Lecture Notes in Computer Science. Springer Verlag, July 2000 pages 60--71.

  16. I. Caragiannis, C. Kaklamanis, and P. Persiano. Symmetric Communication in All-Optical Tree Networks. . Parallel Processing Letters, 2000. 10(4):305--313.

    Abstract: We address the problem of allocating optical bandwidth to a set of communication requests in a tree--shaped all--optical network that utilizes Wavelength Division Multiplexing (WDM) technology. In this paper, we focus on a special case of the problem considering patterns of requests that are symmetric, i.e. for any transmitter--receiver pair of nodes (u,v) there also exists its symmetric (v,u) . Our motivation lies in the fact that many services that are expected to be supported by high performance optical networks in the future, require bidirectional reservation of bandwidth. We prove that the problem of optimizing the number of wavelengths used is NP--hard even when the underlying network is a binary tree. We also present two interesting lower bounds.

  17. A. De Santis, G. Di Crescenzo, and G. Persiano. Necessary and Sufficient Assumptions for Non-Interactive Zero-Knowledge Proofs of Knowledge for all NP Relations. . In U. Montanari, J. Rolim, and E. Welzl, editors, Automata, Languages and Programming, Proceedings of the 27th International Colloquium on Automata, Languages, and Programming (ICALP 00), volume 1853 of Lecture Notes in Computer Science. Springer Verlag, 2000 pages 451--462.

  18. C. Kaklamanis, D. Krizanc, M. Montangero, and P. Persiano. Efficient Automatic Simulation of Parallel Computation on Networks of Workstations. . In J. Rolim and al., editors, ICALP Workshops 2000. Carleton Scientific, July 2000 pages 191--202.

    Abstract: Andrews et al. introduced a number of techniques for automatically hiding latency when performing simulations of networks with unit delay links on networks with arbitrary unequal delay links. In their work, they assume that processors of the host network are identical in computational power to those of the guest network being simulated. They further assume that the links of the host are able to pipeline messages, i.e., they are able to deliver P packets in time O(P+ d) where d is the delay on the link. In this paper we examine the effect of eliminating one or both of these assumptions. In particular, we provide an efficient simulation of a linear array of homogenous processors with unit delay links on a linear array of hetrogenous processors with arbitrary delay links and we show that the slowdown achieved by our simulation is optimal. We also consider the case of simulating a clique of homogenous processors with unit delay links on a clique of hetrogenous processors with arbitrary delay reducing the slowdown from the obvious bound of the maximum delay link to the average of the link delays. For the case of the linear array we consider both links with and without pipelining. For the clique simulation the links are not assumed to support pipelining. Combining our result on clique simulation with well-known techniques for simulating shared memory PRAMs on distributed memory machines provides an effective automatic compilation of a PRAM algorithm on a NOW.

  19. G. Persiano and I. Visconti. User Privacy Issues Regarding Certificates and the TLS Protocol (The Design and Implementation of the SPSL Protocol). . In Proceedings of the 7th ACM Conference on Computer and Communications Security. June 2000 pages 53--63.

  20. V. Auletta, A. Monti, D. Parente, and G. Persiano. A Linear Time Algorithm for the Feasibility of Pebble Motion on Trees. . Algorithmica, 1999. 23(3):223--245.

    Abstract: We consider the following pebble motion problem. We are given a tree T with n vertices and two arrangements R and S of k Is arrangement S reachable from R? We present an algorithm that, on input two arrangements of k pebbles on a tree with n vertices, decides in time O(n) whether the two arrangements are reachable from one another. We also give an algorithm that, on input two reachable configurations, returns a sequence of moves that transforms one configuration into the other. The pebble motion problem on trees has various applications including memory management in distributed systems, robot motion planning, and deflection routing.

  21. C. Blundo, A. De Santis, G. Persiano, and U. Vaccaro. The Randomness Complexity of Private Computation. . Computational Complexity, 1999. 8:145--168.

  22. C. Blundo, C. Galdi, and G. Persiano. Randomness Recycling in Constant-Round Private Computations. . In P. Jayanti, editor, Distributed Computing -- Proceedings of the 13th International Symposium (DISC 99), volume 1693 of Lecture Notes in Computer Science. Springer Verlag, 1999 pages 138--150.

  23. I. Caragiannis, C. Kaklamanis, and G. Persiano. Edge Coloring of Bipartite Graphs with Constraints. . In M. Kutylowski, L. Pacholski, and T. Wierzbicki, editors, Proceedings of the 24th Symposium on Mathematical Foundations of Computer Science (MFCS 99), volume 1672 of Lecture Notes in Computer Science. Springer Verlag, August 1999 pages 771--779.

  24. A. De Santis, G. Di Crescenzo, O. Goldreich, and G. Persiano. The Graph Clustering Problem Has a Perfect Zero-Knowledge Interactive Proof. . Information Processing Letters, 1999. 69:201--206.

  25. A. De Santis, G. Di Crescenzo, and G. Persiano. Non-interactive Zero-Knowledge: A Low-Randomness Characterization of NP. . In J. Wiedermann, P. vanEmde Boas, and M. Nielsen, editors, Automata, Languages and Programming, Proceedings of the 26th International Colloquium on Automata, Languages, and Programming (ICALP 99), volume 1664 of Lecture Notes in Computer Science. Springer Verlag, 1999 pages 271--280.

  26. T. Erlebach, K. Jansen, C. Kaklamanis, M. Mihail, and P. Persiano. Constrained Bipartite Edge Coloring with Applications to Wavelength Routing.. Theoretical Computer Science, 1999. 221:119--137.
    Available at doi:10.1016/S0304-3975(99)00029-8.

    Abstract: We present a polynomial-time greedy algorithm that assigns proper wavelengths to a set of requests of maximum load L per directed fiber link on a directed fiber tree using at most 5/3L wavelengths. This improves previous results of Raghavan and Upfal (STOC 1994), Mihail et al. (FOCS 1995), Kaklamanis and Persiano (ESA 96), Kumar and Schwabe (SODA, 1997). We also prove that no greedy algorithm can in general use less than 5/3L wavelengths for a set of requests of load L in a directed fiber tree, and thus our algorithm is optimal in the class of greedy algorithms.

  27. V. Auletta, I. Caragiannis, C. Kaklamanis, and G. Persiano. Efficient Wavelength Routing in Trees with Low-Degree Converters. . In P.-J. Wan, D.-Z. Du, and P. Pardalos, editors, Multichannel Optical Networks: Theory and Practice, DIMACS Series in Discrete Mathematics and Theoretical Computer Science. American Mathematical Society, March 1998 pages 1--14.

  28. V. Auletta, I. Caragiannis, C. Kaklamanis, and G. Persiano. On the complexity of wavelength converters. . In L. Brim, J. Gruska, and J. Zlatuska, editors, Mathematical Foundations of Computer Science, 23rd International Symposium, MFCS '98, volume 1450 of Lecture Notes in Computer Science. Springer Verlag, August 1998 pages 771--791.

  29. V. Auletta, D. Parente, and G. Persiano. Placing Resource on a Growing Line. . Journal of Algorithms, 1998. 26:87--110.

  30. A. De Santis, G. Di Crescenzo, and G. Persiano. A Communication Efficient Anonymous Group Identification Scheme. . In Proceedings of the Fifth ACM Conference on Computer and Communications Security. 1998 pages 73--82.

  31. A. De Santis, G. Di Crescenzo, G. Persiano, and M. Yung. Image Density is Complete for Non-Interactive-SZK. . In K. G. Larsen, S. Skyum, and G. Winskel, editors, Proceedings of the 25th International Colloquium on Automata, Languages, and Programming (ICALP 98), volume 1443 of Lecture Notes in Computer Science. Springer Verlag, 1998 pages 784--795.

  32. A. De Santis, S. Micali, and G. Persiano. Removing Interaction from Zero-Knowledge Proofs. . In R. Capocelli, editor, Proceedings of Workshop on Sequences. Springer Verlag, 1998 .

  33. T. Erlebach, K. Jansen, C. Kaklamanis, and G. Persiano. An Optimal Greedy Algorithm for Wavelength Allocation in Directed Tree Networks. . In D.-Z. Du and P. Pardalos, editors, Proceedings of the DIMACS workshop on Network Design: Connectivity and Facilities Location, DIMACS Series in Discrete Mathematics and Theoretical Computer Science. American Mathematical Society, 1998 page manca pages.

  34. V. Auletta, I. Caragiannis, C. Kaklamanis, and G. Persiano. Bandwidth Allocation Algorithms on Tree-Shaped All-Optical Networks with Wavelength Converters. . In Proceedings of the 4th International Colloquium on Structural Information and Communication Complexity (SIROCCO 97). Carleton Scientific, 1997 .

  35. V. Auletta, D. Parente, and G. Persiano. Dynamic and Static Algorithms for Optimal Placement of Resources in a Tree. . Theoretical Computer Science, 1997. 165(2):441--461.

  36. I. Caragiannis, C. Kaklamanis, and G. Persiano. Bounds on Optical Bandwidth Allocation of Directed Fiber Tree Topologies. . In Proceedings of Workshop on Optics in Computer Science WOCS 97. 1997 .

  37. A. De Santis, G. Di Crescenzo, and G. Persiano. Randomness-Efficient Non-Interactive Zero Knowledge. . In P. Degano, R. Gorrieri, and A. Marchetti-Spaccamela, editors, Automata, Languages and Programming, Proceedings of the 24th International Colloquium on Automata, Languages, and Programming (ICALP 97), volume 1256 of Lecture Notes in Computer Science. Springer Verlag, 1997 pages 716--726.

  38. T. Erlebach, K. Jansen, C. Kaklamanis, and G. Persiano. Constrained Bipartite Edge Coloring with Applications to Wavelength Routing. . In P. Degano, R. Gorrieri, and A. Marchetti-Spaccamela, editors, Automata, Languages and Programming, Proceedings of the 24th International Colloquium on Automata, Languages, and Programming (ICALP 97), volume 1256 of Lecture Notes in Computer Science. Springer Verlag, July 1997 pages 493--504.

  39. V. Auletta, A. Monti, D. Parente, and G. Persiano. A Linear Time Algorithm for the Feasibility of Pebble Motion on Trees. . In R. Karlsson and A. Lingas, editors, Proceedings of the Fifth Scandinavian Workshop on Algorithm Theory (SWAT'96), volume 1097 of Lecture Notes in Computer Science. Springer Verlag, June 1996 pages 259--270.

  40. R. De Prisco, G. Parlati, and G. Persiano. A Note on the Expected Path Length of Trees with Known Fringe. . Information Processing Letters, 1996. 59(6):309--315.

  41. A. De Santis and G. Persiano. The Power of Preprocessing in Zero-Knoweldge Proofs of Knowledge. . Journal of Cryptology, 1996. 9(3):129--148.
    Available at h% ttp://link.springer.de/link/service/journals/00145/tocs/00903.html.

  42. V. Auletta, I. Caragiannis, C. Kaklamanis, and G. Persiano. Dynamic and Static Algorithms for Optimal Placement of Resources in a Tree. . In Z. Fulop and F. Gecseg, editors, Automata, Languages and Programming, Proceedings of the 22nd International Colloquium on Automata, Languages, and Programming (ICALP '95), volume 944 of Lecture Notes in Computer Science. Springer Verlag, July 1995 pages 232--243.

  43. V. Auletta, D. Parente, and G. Persiano. Optimal Planning of Robot Motion on a Tree with Obstacles. . In J. Diaz and M. Serna, editors, Algorithms--ESA '96, Proceedings of the 4th Annual European Symposium on Algorithms, volume 1136 of Lecture Notes in Computer Science. Springer Verlag, July 1995 pages 529--545.

  44. C. Blundo, A. De Santis, G. Persiano, and U. Vaccaro. The Randomness Complexity of Private Computation. . In Z. Fulop and F. Gecseg, editors, Automata, Languages and Programming, Proceedings of the 22nd International Colloquium on Automata, Languages, and Programming ICALP '95, volume 944 of Lecture Notes in Computer Science. Springer Verlag, 1995 pages 171--182.

  45. R. De Prisco, G. Parlati, and G. Persiano. Minimal Path Length of Trees with Known Fringe. . Theoretical Computer Science, 1995. 143(1):175--188.

  46. R. De Prisco and G. Persiano. Characteristic Inequalities for Binary Trees. . Information Processing Letters, 1995. 53(4):201--207.

  47. A. De Santis, G. Di Crescenzo, and G. Persiano. Public-Key Cryptography and Zero-Knowledge Arguments. . Information and Computation, 1995. 121:23--40.

  48. C. Kaklamanis and G. Persiano. Efficient Wavelength Routing on Directed Fiber Trees. . In J. Diaz and M. Serna, editors, Algorithms--ESA '96, Proceedings of the 4th Annual European Symposium on Algorithms, volume 1136 of Lecture Notes in Computer Science. Springer Verlag, July 1995 pages 473--444.

  49. R. M. Capocelli, A. De Santis, and G. Persiano. Binary prefix codes ending with `1'. . IEEE Transactions on Information Theory, 1994. 40(4):1296--1302.

  50. A. De Santis, G. Di Crescenzo, and G. Persiano. The Knowledge Complexity of Quadratic Residuosity Languages. . Theoretical Computer Science, 1994. 132:291--317.

  51. A. De Santis, G. Di Crescenzo, G. Persiano, and M. Yung. On Monotone Formula Closure of SZK. . In Proceedings of the 35th Symposium on Foundations of Computer Science 1994, (FOCS '94). 1994 pages 454--465.

  52. A. De Santis, T. Okamoto, and G. Persiano. Zero-Knowledge Proofs of Computational Power in the Shared String Model. . In J. Pieprczyk, editor, Advances in Cryptology - ASIACRYPT '94, volume 917 of Lecture Notes in Computer Science. Springer Verlag, 1994 .

  53. G. Di Crescenzo and G. Persiano. Round-Optimal Perfect Zero-Knowledge Proofs. . Information Processing Letters, 1994. 50:93--99.

  54. C. Kaklamanis and G. Persiano. Branch-and-bound and backtrack search on mesh-connected arrays of processors. . Mathematical System Theory, 1994. 27:471--489.

  55. G. Persiano. An Optimal Algorithm for the Dining Philosophers Problem. . Parallel Processing Letters, 1994. 4(1):181--187.

  56. C. Buyukkoc and G. Persiano. An Efficient Parallel Implementation for the EM Technique in PET Imaging and a Generalization. . Elektrik, February 1993. 1(1):41--50.

  57. A. De Santis, G. Di Crescenzo, and G. Persiano. Secret Sharing and Perfect Zero Knowledge. . In D. Stinson, editor, Advances in Cryptology - CRYPTO 93, volume 773 of Lecture Notes in Computer Science. Springer Verlag, 1993 pages 73--84.

  58. A. De Santis and G. Persiano. Communication Efficient Zero-Knowledge Proofs of Knowledge (With Applications to Electronic Cash). . In A. Finkel and M. Jantzen, editors, Proceedings of the 9th Annual Symposium on Theoretical Aspects of Computer Science, STACS 92, volume 577 of Lecture Notes in Computer Science. Springer Verlag, 1992 pages 449--460.

  59. A. De Santis and G. Persiano. Tight Upper and Lower Bound on the Path Length of Binary Trees. . SIAM Journal on Computing, 1992. 23(1):12--23.

  60. A. De Santis and G. Persiano. Zero-Knowledge Proofs of Knowledge without Interaction. . In Proceedings of the 33rd Symposium on Foundations of Computer Science 1992, (FOCS '92). 1992 pages 427--437.

  61. A. De Santis, M. Yung, and G. Persiano. One-Messagge Statistical Zero-Knowledge Proofs with Space-Bounded Verifier. . In W. Kuich, editor, Automata, Languages and Programming, Proceedings of the 24th International Colloquium on Automata, Languages and Programming (ICALP '92), volume 623 of Lecture Notes in Computer Science. Springer Verlag, 1992 pages 28--40.

  62. C. Kaklamanis and G. Persiano. Branch-and-bound and backtrack search on mesh-connected arrays of processors. . In Proceedings of the 4th Annual ACM Symposium on Parallel Algorithms and Architectures (SPAA '92). ACM, 1992 pages 118--126.

  63. M. Blum, A. De Santis, S. Micali, and G. Persiano. Non Interactive Zero Knowledge. . SIAM Journal on Computing, 1991. 20:1084--1118.

  64. A. De Santis and G. Persiano. An Optimal Algorithm for the Costruction of Optimal Prefix Codes with given Fringe. . In J. Reif and J. Storer, editors, Proceedings of the 1991 IEEE Data Compression Conference, volume 944. IEEE Press, April 1991 pages 297--307.

  65. A. De Santis and G. Persiano. Tight Bounds on the Path Length of Binary Trees. . In C. Choffrut and M. Jantzen, editors, Proceedings of the 8th Annual Symposium on Theoretical Aspects of Computer Science (STACS 91), volume 480 of Lecture Notes in Computer Science. Springer Verlag, 1991 pages 478--487.

  66. C. Buyukkoc and G. Persiano. An Efficient Parallel Implementation for the EM Technique in PET Imaging and a Generalization. . In Proceedings of SPIE Conference on Statistical Image Processing. 1990 .

  67. A. De Santis and G. Persiano. Public-randomness in Public-key Cryptosystems. . In I.B.Damgard, editor, Advances in Cryptology - EUROCRYPT 90, volume 473 of Lecture Notes in Computer Science. Springer Verlag, 1990 pages 46--62.

  68. A. De Santis, S. Micali, and G. Persiano. Non-Interactive Zero-Knowledge Proof-Systems with Preprocessing. . In Advances in Cryptology -- CRYPTO 88, volume 403 of Lecture Notes in Computer Science. Springer Verlag, 1988 .

  69. A. De Santis, S. Micali, and G. Persiano. Non-Interactive Zero-Knowledge Proof-Systems. . In Advances in Cryptology -- CRYPTO 87, volume 293 of Lecture Notes in Computer Science. Springer Verlag, 1987 .