Abstract: Multivariate quadratic (MQ) cryptography requires the use of long public and private keys to ensure a sufficient security level, but this is not favorable to embedded systems, which have limited system resources. Recently, various approaches to MQ cryptography using reduced public keys have been studied. As a result of this, at CHES2011 (Cryptographic Hardware and Embedded Systems, 2011), a small public key MQ scheme, was proposed, and its feasible implementation on an embedded microprocessor was reported at CHES2012. However, the implementation of a small private key MQ scheme was not reported. For efficient implementation, random number generators can contribute to reduce the key size, but the cost of using a random number generator is much more complex than computing MQ on modern microprocessors. Therefore, no feasible results have been reported on embedded microprocessors. In this paper, we propose a feasible implementation on embedded microprocessors for a small private key MQ scheme using a pseudo-random number generator and hash function based on a block-cipher exploiting a hardware Advanced Encryption Standard (AES) accelerator. To speed up the performance, we apply various implementation methods, including parallel computation, on-the-fly computation, optimized logarithm representation, vinegar monomials and assembly programming. The proposed method reduces the private key size by about 99.9% and boosts signature generation and verification by 5.78% and 12.19% than previous results in CHES2012.
Keywords: public key cryptography; small private key; multivariate quadratic cryptography; embedded microprocessor; efficient software implementation; ATxmega128a1; AES accelerator; random number generator; signature generation
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Seo, H.; Kim, J.; Choi, J.; Park, T.; Liu, Z.; Kim, H. Small Private Key MQPKS on an Embedded Microprocessor. Sensors 2014, 14, 5441-5458.
Seo H, Kim J, Choi J, Park T, Liu Z, Kim H. Small Private Key MQPKS on an Embedded Microprocessor. Sensors. 2014; 14(3):5441-5458.
Seo, Hwajeong; Kim, Jihyun; Choi, Jongseok; Park, Taehwan; Liu, Zhe; Kim, Howon. 2014. "Small Private Key MQPKS on an Embedded Microprocessor." Sensors 14, no. 3: 5441-5458.