Cryptology ePrint Archive: Report 2010/550

Isogenies and Cryptography

RAZA ALI KAZMI

Abstract: This thesis explores the notion of isogenies and its applications to cryptography. Elliptic curve cryptography (ECC) is an efficient public cryptosystem with a short key size. For this reason it is suitable for implementing on memory-constraint devices such as smart cards, mobile devices, etc. However, these devices leak information about their private key through side channels (power consumption, electromagnetic radiation, timing etc) during cryptographic processing. In this thesis we have examined countermeasures against a specific side channel attack (power consumption) using isogeny, (a rational homomorphism between elliptic curves) and elliptic curve isomorphism. We found that these methods are an efficient way of securing cryptographic devices using ECC against power analysis attacks. We have also investigated the security and efficiency of implementation of a public key cryptosystem based on isogenies. We found that in order to implement the proposed cryptosystem one has to compute a root of the Hilbert polynomial HD(X) over Fp. Since there is no known efficient way of achieving this calculation, the proposed cryptosystem cannot be used in pract

Category / Keywords: public-key cryptography /

Date: received 27 Oct 2010, last revised 27 Oct 2010

Contact author: raza-ali kazmi at mail mcgill ca

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Version: 20101101:164229 (All versions of this report)

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