Abstract
Nowadays, power analysis attacks are becoming more and more sophisticated. Through power analysis attacks, an attacker can obtain sensitive data stored in smart cards or other embedded devices more efficiently than with any other kind of physical attacks. Among power analysis, simple power analysis (SPA) is probably the most effective against elliptic curve cryptosystem, because an attacker can easily distinguish between point addition and point doubling in a single execution of scalar multiplication. To make elliptic curve scalar multiplication secure against SPA attacks, many methods have been proposed using special point representations. In this paper, a simple but efficient SPA-resistant multiscalar multiplication is proposed. The method is to convert the scalar into a nonadjacent form (NAF) representation at first and then constitute it in a new signed digit representation. This new representation is undertaken at a small precomputation cost, as each representation needs just one doubling and 1/2 additions for each bit. In addition, when combined with randomization techniques, the proposed method can also guard against differential power analysis (DPA) attack.
Highlights
Since being proposed independently by Koblitz [1] and Miller [2] in the mid 1980s, elliptic curve cryptosystem (ECC) has been widely applied in public key cryptography, especially in pairing cryptosystems [3, 4]. This is due to ECC using a much shorter key size than other traditional public key cryptosystems such as RSA to provide a corresponding level of security
The security of ECC is based on the hardness of the discrete logarithm problem (DLP) on an elliptic curve called elliptic curve discrete logarithm problem (ECDLP) [6]
In the case of scalar multiplication, it may be possible for an attacker to distinguish which parts of the operation were performed by a point doubling, and which parts were performed by a point addition, he has no knowledge about the private keys
Summary
Power analysis attacks are becoming more and more sophisticated. Through power analysis attacks, an attacker can obtain sensitive data stored in smart cards or other embedded devices more efficiently than with any other kind of physical attacks. Simple power analysis (SPA) is probably the most effective against elliptic curve cryptosystem, because an attacker can distinguish between point addition and point doubling in a single execution of scalar multiplication. A simple but efficient SPA-resistant multiscalar multiplication is proposed. The method is to convert the scalar into a nonadjacent form (NAF) representation at first and constitute it in a new signed digit representation. This new representation is undertaken at a small precomputation cost, as each representation needs just one doubling and 1/2 additions for each bit. When combined with randomization techniques, the proposed method can guard against differential power analysis (DPA) attack
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