Abstract

Multivariate Public Key Cryptography (MPKC) is one of the main candidates for post-quantum cryptography, especially in the area of signature schemes. In this paper, we instantiate a certificate Identity-Based Signature (IBS) scheme based on Rainbow, one of the most efficient and secure multivariate signature schemes. In addition, we revise the previous identity-based signature scheme IBUOV based on the Unbalanced Oil and Vinegar (UOV) scheme on the security and choice of parameters and obtain that our scheme is more efficient than IBUOV in terms of key sizes and signature sizes.

Highlights

  • Post-quantum cryptography is a new direction in the last two decades after the thread of polynomial quantum algorithms of Shor [1], which totally broke the currently most widely-used public key cryptosystems such as RSA [2], DSA [3], and ECC [4]

  • We present the construction of an Identity-Based Signature (IBS) scheme from a digital signature scheme

  • We instantiated an identity-based signature scheme based on a provably-secure

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Summary

Introduction

Post-quantum cryptography is a new direction in the last two decades after the thread of polynomial quantum algorithms of Shor [1], which totally broke the currently most widely-used public key cryptosystems such as RSA [2], DSA [3], and ECC [4] It has received much more attention recently after the call of NIST [5] for proposals of post-quantum cryptosystems to be standardized in the near future. Digital certificates linking public keys with identities of users are needed, and this fact leads to some drawbacks in efficiency and simplicity For this reason, the alternative framework of identity-based cryptography was introduced by Shamir [14].

Preliminaries
Multivariate Public Key Cryptography
Unbalanced Oil and Vinegar Signature Scheme
Rainbow Signature Scheme
Modified UOV Signature Scheme
Modified Rainbow Signature Scheme
Direct Attacks
The Rank Attacks
UOV Attack
Rainbow-Band-Separation Attack
Collision Attacks against the Hash Function
Construction
Parameters
Findings
Conclusions

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