Abstract
Multivariate quadratic (MQ) equations-based cryptography is one of the most promising alternatives for currently used public-key cryptographic algorithms in the post-quantum era. It is important to design practical public-key signature schemes on embedded processors and resource-constrained devices for emerging applications in Internet of Things. The MQ-signature schemes are suitable for low-cost constrained devices since they require only modest computational resources. In this paper, we propose an efficient MQ-signature scheme, SOV, using sparse polynomials with a shorter secret key and give its security analysis against known algebraic attacks. Compared to Rainbow, the secret key of SOV has reduced by a factor of 90% without increasing the public key size. In particular, SOV requires signatures of 52 bytes, while ECDSA-256 requires signatures of 64 bytes.
Highlights
It is known that if a large scale quantum computer capable of implementing Shor’s algorithm [41] is developed the discrete logarithm problem (DLP) and the integer factorization problem (IFP) are solved in polynomial time
Currently used public-key cryptographic algorithms based on the these problems such as RSA, DSA and ECDSA could be broken by the quantum computer
There are public-key cryptographic algorithms believed to remain secure against a quantum computer: lattice-based, code-based, hash-based, multivariate quadratic (MQ) equations-based and supersingular Isogeny-based
Summary
It is known that if a large scale quantum computer capable of implementing Shor’s algorithm [41] is developed the discrete logarithm problem (DLP) and the integer factorization problem (IFP) are solved in polynomial time. Gligoroski et al [27] presented a new signature scheme, MQQ-SIG, using multivariate quadratic quasigroups They succeeded in reducing the secret key and improving signing performance significantly, but required a larger public key. TTS [14], [15] and enhanced TTS (enTTS) [44], [45] used sparse polynomials to reduce the secret key and signing cost, but had lager public key than other MQ-schemes. We propose an efficient MQ-signature scheme with a shorter secret key and signatures maintaining the public key size. EnTTS based on sparse polynomials reduces the secret key size and its signing cost, but its public key is about 2 times lager than that of Rainbow.
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