FPGA accelerated tate pairing based cryptosystems over binary fields

Shu, Chang; Kwon, Soonhak; Gaj, Kris

doi:10.1109/fpt.2006.270309

Cited by 30 publications

(36 citation statements)

References 18 publications

(59 reference statements)

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“…We design and implement Tate pairing using field programmable gate array (FPGA) over binary field GF(2 m ). It is more efficient for hardware implementation over binary field compared with other fields such as cubic field GF(3 m ) [47]. The main arithmetic units needed for the Tate pairing computation include addition, Galois field multiplication, Galois field squaring, and Galois field inversion.…”

Section: Tate Pairingmentioning

confidence: 99%

“…Their implementation can compute the Tate pairing over GF(2 283 ) quickly. The algorithm used for Tate pairing in [47] is different from [24,30]. In our work, we implemented the algorithms used in [30].…”

Section: Contributionmentioning

confidence: 99%

“…Shu et al used two modified Kwon's algorithms in [45,47]. They designed squaring, multiplication, inverter and exponentiation.…”

Section: Contributionmentioning

confidence: 99%

“…Therefore, the squarer is simply a set of XOR arrays to recombine the coefficients of a(x). And the gate count is proportional to the polynomial bit [47], which is 283 in our case.…”

Section: Squarer In Gf(2 283 )mentioning

confidence: 99%

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FPGA implementations of elliptic curve cryptography and Tate pairing over a binary field

Huang

Sweany

et al. 2008

Journal of Systems Architecture

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Elliptic curve cryptography (ECC) is an alternative to traditional techniques for public key cryptography. It offers smaller key size without sacrificing security level. Tate pairing is a bilinear map used in identity based cryptography schemes. In a typical elliptic curve cryptosystem, elliptic curve point multiplication is the most computationally expensive component. Similarly, Tate pairing is also quite computationally expensive. Therefore, it is more attractive to implement the ECC and Tate pairing using hardware than using software. The Cryptography is the most standard and efficient way to protect the security of web transactions. It can be used to protect the confidentiality, integrity, authentication, and non-reputation of the web transactions. There are two major categories of cryptography 1 schemes, i.e., public-key cryptography and symmetric-key cryptography. In public-key cryptography, the receiver and sender have their own private key and share a common public key. In symmetric-key cryptography, the receiver and sender must have the same private key, which makes it difficult to manage the private key. Public-key cryptography is easy for key distribution and key management. But it is not as efficient as symmetric-key cryptography [19,39]. Thus, it is interesting to use dedicated hardware for public-key cryptography to improve the performance.A well-known public-key cryptography algorithm is RSA, which was first proposed by and it is projected that its size will increase to 2048 bits after 2010. The performance issues of RSA with such a large key size will then become a dominant force, which can severely affect the performance of RSA. So, we would like to use 283-bit ECC in place of the 2048-bit RSA since it can significantly reduce the key length and still provides the same security level.Despite ECC's advantages over RSA, software based ECC implementations usually require long computation time, hence makes it difficult to be effectively utilized in real-time 2 The main contribution of our FPGA based design is the resources sharing and parallel processing optimization. The simulation results show that our implementation is significantly faster than the software implementation as well as previous FPGA implementations with the same security level [12, 27]. Tate PairingIdentity based cryptography schemes have opened a new territory for public key cryptography [8,38,42]. Using identity based cryptography schemes, a sender can derive the public key of a receiver without receiving the certificate of the receiver issued by a certificate authority (CA). The public key can be derived from the identity of the receiver such as the email or IP address. Pairing over elliptic curve can be used to construct the identity based cryptography schemes. It is a map from two points on the elliptic curve to another multiplicative group. It has special properties of bilinearity. Currently, the most commonly used pairing methods are Tate pairing [13] and Weil pairing [31]. Originally, Weil pairing was used to attack publi...

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Section: Tate Pairingmentioning

confidence: 99%

Section: Contributionmentioning

confidence: 99%

“…Shu et al used two modified Kwon's algorithms in [45,47]. They designed squaring, multiplication, inverter and exponentiation.…”

Section: Contributionmentioning

confidence: 99%

“…Therefore, the squarer is simply a set of XOR arrays to recombine the coefficients of a(x). And the gate count is proportional to the polynomial bit [47], which is 283 in our case.…”

Section: Squarer In Gf(2 283 )mentioning

confidence: 99%

See 2 more Smart Citations

FPGA implementations of elliptic curve cryptography and Tate pairing over a binary field

Huang

Sweany

et al. 2008

Journal of Systems Architecture

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“…There have been many research studies on software and hardware implementations of pairings. Indeed, pairings have implemented on FPGAs [7,12,23,20,3] and smart cards [22]. On the other hand, side channel attacks (SCAs) reveal secret data on hardware devices by monitoring side channel information such as power consumption and timing [15,16].…”

Section: Introductionmentioning

confidence: 99%

An Efficient Countermeasure against Side Channel Attacks for Pairing Computation

Shirase

Takagi

Okamoto

Information Security Practice and Experience

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Abstract. Pairing-based cryptosystems have been widely researched, and several efficient hardware implementations of pairings have also been proposed. However, side channel attacks (SCAs) are serious attacks on hardware implementations. Whelan et al. pointed out that pairings except the η T pairing might not be vulnerable against SCAs by setting the secret point to the first parameter [25]. This paper deals with SCAs for the η T pairing over F 3 n . To our knowledge, the randomized-projectivecoordinate method has the smallest overhead among all countermeasures against SCAs for the η T pairing. The cost of that overhead is 3nM , where M is the cost of a multiplication in F 3 n . In this paper, we propose another countermeasure based on random value additions (xp + λ) and (y p + λ), where P = (x p , y p ) is the input point, and λ is a random value in F3n . The countermeasure using the random value addition was relatively slow in the case of the scalar multiplication of elliptic curve cryptosystems. However, in the case of the η T pairing, we can construct an efficient countermeasure due to the form of the function g P (x, y) = y 3 p y − (x 3 p + x − 1) 2 for a point P = (x p , y p ). The overhead of our proposed scheme is just 0.5nM , which is a reduction of more than 75% compared with the randomized-projective-coordinate method.

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