High‐throughput Dickson basis multiplier with a trinomial for lightweight cryptosystems

Abstract

In this study, the authors propose a high-throughput systolic Dickson basis multiplier over GF(2 m). Use of the Dickson basis seems promising when no Gaussian normal basis exists for the field, and it can easily carry out both squaring and multiplication operations. Many squaring operations and multiplications are needed when computing the digital signatures of elliptic curve digital signature algorithm. The proposed systolic Dickson basis multiplier can concurrently compute a great number of multiplications with a high-throughput rate, thereby substantially increasing the speed of computation for digital signatures.

Low‐complexity unidirectional systolic Dickson basis multiplier for lightweight cryptosystems

“…1) are sequentially applied to the proposed multiplier for computing CT1, CT2, and CT3 step by Fig. 1 in [10]. The cell areas of a two-input XOR gate, a two-input AND gate, and a 1-bit latch are 1.596, 1.064, and 4.522 μm 2 , respectively.…”

“…Conclusions: This study has proposed a unidirectional systolic Dickson basis multiplier with low space and time complexities. The proposed one can save about 25% space complexity and 39% time complexity while comparing with the bidirectional one in [10] for NIST suggested five fields. The proposed unidirectional systolic structure can be easily redesigned to one with error detection capability and then can resist sidechannel attacks.…”

“…Chiou et al [10] developed a systolic array Dickson basis multiplier with high‐throughput. The systolic array of Chiou's multiplier [10] is a bidirectional systolic array. The bidirectional structure of systolic multiplier is hardly applied for designing multipliers with error‐detection capability resilient to side‐channel attacks on elliptic curve cryptosystems [11].…”

“…For example, no ONB exists for field size 283 which is suggested by National Institute of Standards and Technology (NIST) for elliptic curve digital signature algorithm [7]. An alternative solution to the problem on ONB and GNB is that one can employ a Dickson basis [8][9][10] for efficient design of finite field multipliers. The space complexity of Dickson basis multiplier has the same as that of an ONB one.…”

“…Hasan and Negre [9] used light-weight Dickson polynomials such as Dickson binomials and trinomials to design Dickson basis multipliers. Chiou et al [10] developed a systolic array Dickson basis multiplier with high-throughput. The systolic array of Chiou's multiplier [10] is a bidirectional systolic array.…”