• Journal of the Korea Institute of Information Security & Cryptology
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• v.26 no.3
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• pp.587-601
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• 2016

In this paper we suggest method for scalar recoding which is both secure against SPA and DPA. Suggested method is countermeasure to power analysis attack through scalar recoding using negative expression. Suggested method ensures safety of SPA by recoding the operation to apply same pattern to each digit. Also, by generating the random recoding output according to random number, safety of DPA is ensured. We also implement precomputation table and modified scalar addition algorithm for addition to protect against SPA that targets digit's sign. Since suggested method itself can ensure safety to both SPA and DPA, it is more effective and efficient. Through suggested method, compared to previous scalar recoding that ensures safety to SPA and DPA, operation efficiency is increased by 11%.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.26 no.5
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• pp.1099-1103
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• 2016

The user's secret key can be retrieved by the leakage informations of power consumption occurred during the execution of scalar multiplication for elliptic curve cryptographic algorithm which can be embedded on a security device. Recently, a carry random recoding method is proposed to prevent simple power and differential power analysis attack by recoding the secret key. In this paper, we show that this recoding method is still vulnerable to the differential power analysis attack due to the limitation of the size of carry bits, which is a different from the original claim.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2009.05a
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• pp.686-689
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• 2009

This paper describes a scalar multiplier for Elliptic curve cryptography. The scalar multiplier has 163-bits key size which supports the specifications of smart card standard. To reduce the computational complexity of scalar multiplication on finite field $GF(2^{163})$, the Non-Adjacent-Format (NAF) conversion algorithm based on complementary recoding is adopted. The scalar multiplier core synthesized with a $0.35-{\mu}m$ CMOS cell library has 32,768 gates and can operate up to 150-MHz@3.3-V. It can be used in hardware design of Elliptic curve cryptography processor for smart card security.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.13 no.10
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• pp.2154-2162
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• 2009

This paper describes a scalar multiplier for Elliptic curve cryptography for smart card security. The scaler multiplier has 163-bits key size which supports the specifications of smart card standard. To reduce the computational complexity of scala multiplication on finite field, the non-adjacent format (NAF) conversion algorithm which is based on complementary recoding is adopted. The scalar multiplier core synthesized with a 0.35-${\mu}m$ CMOS cell library has 32,768 gates and can operate up to 150-MHz@3.3-V. It can be used in hardware design of Elliptic curve cryptography processor for smartcard security.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.17 no.1
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• pp.127-132
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• 2007

This paper proposed receding methods for a radix-${\gamma}$ representation of the secret scalar which are resistant to SPA. Unlike existing receding method, these receding methods are left-to-right so they can be interleaved with a left-to-right scalar multiplication, removing the need to store both the scalar and its receding. Hence, these left-to-right methods are suitable for implementing on memory limited devices such as smart cards and sensor nodes

• Journal of the Korea Institute of Information Security & Cryptology
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• v.13 no.5
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• pp.169-177
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• 2003

We establish the security requirements and derive a generic condition of elliptic curve scalar multiplication to resist against DPA and Goubin’s attack. Also we show that if a scalar multiplication algorithm satisfies our generic condition, then both attacks are infeasible. Showing that the randomized signed scalar multiplication using Ha-Moon's receding algorithm satisfies the generic condition, we recommend the randomized signed scalar multiplication using Ha-Moon's receding algorithm to be protective against both attacks. Also we newly design a random recoding method to Prevent two attacks. Finally, in efficiency comparison, it is shown that the recommended method is a bit faster than Izu-Takagi’s method which uses Montgomery-ladder without computing y-coordinate combined with randomized projective coordinates and base point blinding or isogeny method. Moreover. Izu-Takagi’s method uses additional storage, but it is not the case of ours.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.17 no.2
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• pp.115-123
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• 2007

In cryptographic devices like a smart-card whose computing ability and memory are limited, cryptographic algorithms should be performed efficiently. Scalar multiplication is very important operation in Elliptic Curve Cryptosystems, and so must be constructed in safety against side channel attack(SCA). But several countermeasures proposed against SCA are exposed weaknesses by new un-dreamed analysis. 'Double-and-add always scalar multiplication' algorithm adding dummy operation being known to secure against SPA is exposed weakness by Doubling Attack. But Doubling Attack cannot apply to sABS receding proposed by Hedabou, that is another countermeasure against SPA. Our paper proposes new strengthened Doubling Attacks that can break sABS receding SPA-countermeasure and a detailed method of our attacks through experimental result.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.13 no.3
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• pp.35-43
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• 2003

The randomization of scalar multiplication in ECC is one of the fundamental concepts in defense methods against side-channel attacks. This paper proposes a countermeasure against simple and differential power analysis attacks through randomizing the transformed m-ary method based on a random m-ary receding algorithm. The proposed method requires an additional computational load compared to the standard m-ary method, yet the power consumption is independent of the secret key. Accordingly, since computational tracks using random window width can resist against SPA and DPA, the proposed countermeasure can improve the security for smart cards.