Cryptology ePrint Archive: Report 2019/513

New Code-Based Privacy-Preserving Cryptographic Constructions

Khoa Nguyen and Hanh Tang and Huaxiong Wang and Neng Zeng

Abstract: Code-based cryptography has a long history but did suffer from periods of slow development. The field has recently attracted a lot of attention as one of the major branches of post-quantum cryptography. However, its subfield of privacy-preserving cryptographic constructions is still rather underdeveloped, e.g., important building blocks such as zero-knowledge range proofs and set membership proofs, and even proofs of knowledge of a hash preimage, have not been known under code-based assumptions. Moreover, almost no substantial technical development has been introduced in the last several years.

This work introduces several new code-based privacy-preserving cryptographic constructions that considerably advance the state-of-the-art in code-based cryptography. Specifically, we present $3$ major contributions, each of which potentially yields various other applications. Our first contribution is a code-based statistically hiding and computationally binding commitment scheme with companion zero-knowledge (ZK) argument of knowledge of a valid opening that can be easily extended to prove that the committed bits satisfy other relations. Our second contribution is the first code-based zero-knowledge range argument for committed values, with communication cost logarithmic in the size of the range. A special feature of our range argument is that, while previous works on range proofs/arguments (in all branches of cryptography) only address ranges of non-negative integers, our protocol can handle signed fractional numbers, and hence, can potentially find a larger scope of applications. Our third contribution is the first code-based Merkle-tree accumulator supported by ZK argument of membership, which has been known to enable various interesting applications. In particular, it allows us to obtain the first code-based ring signatures and group signatures with logarithmic signature sizes.

Category / Keywords: cryptographic protocols / Code-based cryptography, zero-knowledge, range arguments, set membership arguments, ring signatures, group signatures

Date: received 17 May 2019

Contact author: khoantt at ntu edu sg

Available format(s): PDF | BibTeX Citation

Version: 20190520:130559 (All versions of this report)

Short URL: ia.cr/2019/513


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