Cryptology ePrint Archive: Report 2020/1453

New (k,l,m)-verifiable multi-secret sharing schemes based on XTR public key system

Jing Yang and Fang-Wei Fu

Abstract: Secret sharing was proposed primarily in 1979 to solve the problem of key distribution. In recent decades, researchers have proposed many improvement schemes. Among all these schemes, the verifiable multi-secret sharing (VMSS) schemes are studied sufficiently, which share multiple secrets simultaneously and perceive malicious dealer as well as participants. By pointing out that the schemes presented by Dehkordi and Mashhadi in 2008 cannot detect some vicious behaviors of the dealer, we propose two new VMSS schemes by adding validity check in the verification phase to overcome this drawback. Our new schemes are based on XTR public key system, and can realize $GF(p^{6})$ security by computations in $GF(p^{2})$ without explicit constructions of $GF(p^{6})$, where $p$ is a prime. Compared with the VMSS schemes using RSA and linear feedback shift register (LFSR) public key cryptosystems, our schemes can achieve the same security level with shorter parameters by using trace function. What's more, our schemes are much simpler to operate than those schemes based on Elliptic Curve Cryptography (ECC). In addition, our schemes are dynamic and threshold changeable, which means that it is efficient to implement our schemes according to the actual situation when participants, secrets or the threshold needs to be changed.

Category / Keywords: cryptographic protocols / verifiable multi-secret sharing, XTR public key system, trace function, shorter key parameters, fast key generation, dynamism, threshold changeable.

Date: received 17 Nov 2020

Contact author: yangjing0804 at mail nankai edu cn

Available format(s): PDF | BibTeX Citation

Note: Our schemes are computationally secure (k,l,m)-VMSS schemes which can share multiple secrets simultaneously, use the public channel, have verifiability, reuse subshadows, and are both dynamic and threshold changeable with shorter parameters.

Version: 20201119:094357 (All versions of this report)

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