A Fault Attack for Scalar Multiplication in Elliptic Curve Digital Signature Algorithm
The dominant operation in cryptographic scheme of elliptic curve is the multiplication using point on an elliptic curve by an integer. This paper specifically discusses the competent algorithms for scalar multiplication a very tedious process in Elliptic
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Abstract The dominant operation in cryptographic scheme of elliptic curve is the multiplication using point on an elliptic curve by an integer. This paper specifically discusses the competent algorithms for scalar multiplication a very tedious process in Elliptic Curve Cryptography that are relevant for systems using constrained resources like smart cards. The taxonomy of the work in the open literature for these devices is not only from security perspectives, but likewise some implementation attack, such as fault attacks, must be considered. We survey different implementation approaches and algorithms with the purpose of providing a valuable reference of implementing scalar multiplication in order to retrieve information with a way to determine secret signing key. In addition, this paper provides a review of injecting different fault attacks in a system constrained environment with Elliptic Curve Cryptography. Finally, some arguments about future scope that should be undertaken are provided.
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Keywords Fault attack Scalar multiplication Elliptic curve digital signature algorithm
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Elliptic curve cryptography
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1 Introduction The necessity to provide a secure and sound approach in the direction to authorize the genuineness of digital sources and contents is now a days an emerging requirement for cutting edge computing frameworks and the fulfilling the demand by cryptographic digital signature protocols. In modern computing environment, the most creative and existing cryptosystem ready to provide a signature scheme D. Jyotiyana ⋅ V.P. Saxena (✉) Department of Computer Science and Engineering, Government Women Engineering College, Ajmer, India e-mail: [email protected] D. Jyotiyana e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2017 H.R. Vishwakarma and S. Akashe (eds.), Computing and Network Sustainability, Lecture Notes in Networks and Systems 12, DOI 10.1007/978-981-10-3935-5_29
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accomplish the need of authenticity of digital contents are signified using Elliptic Curve Digital Signature Algorithm (ECDSA), standardised by both IEEE and NIST [1] and also be recommended by NSA suite B. Elliptic Curve Cryptographic algorithms, with Discrete Logarithmic Problem (specifically ECDLP) provided the rigid security that are suitable for system with constrained resources like mobile devices or smart cards with storing the secret key confidentially in a tamper-proof device. Without destroying the information, it is considered to be hard to retrieve the key, the decryption or signing process usually done inside the card for security purpose [1]. In a situation where the signature is perform in the device might be seized via fast access to the secret token used for signing holding the secret key for example a smart card and ready to replicate it before sending back to the authentic possessor. Thus, various adversarial attacks have been developed with purpose of regulating the secret signing key. These attacking policies must depend on information with faults tha
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