# On the Existence of Three Round Zero Knowledge Proofs

### Abstract

We study the round complexity of zero-knowledge (ZK) proof systems. While five round ZK proofs for $\mathsf{NP}$ are known from standard assumptions [Goldreich-Kahan, J. Cryptology’96], Katz [TCC’08] proved that four rounds are insufficient for this task w.r.t. black-box simulation.
In this work, we study the feasibility of ZK proofs using non-black-box simulation.Our main result is that three round private-coin ZK proofs for $\mathsf{NP}$ do not exist (even w.r.t. non-black-box simulation), under certain assumptions on program obfuscation. We closely follow recent work by Kalai et al. [Crypto’17] who ruled out constant round public-coin ZK proofs under the same assumptions.

Type
Publication
37th Annual International Conference on the Theory and Applications of Cryptographic Techniques (EUROCRYPT 2018)
Date
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7096796035766602, "perplexity": 4250.012903491054}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-13/segments/1552912204300.90/warc/CC-MAIN-20190325194225-20190325220225-00215.warc.gz"}