الفهرس | Only 14 pages are availabe for public view |
Abstract Elliptic Curve Cryptography (ECC) is one of the prominent public key methodologies because of its small key size and high security compared to other methods. Secure applications on limited environments like smart cards present implementation challenges due to the platform’s limited memory, bandwidth and computational capacity. The characteristics of ECC techniques make them suitable to overcome these challenges. This thesis investigates and improves different aspects of elliptic curve cryptography. It proposes using elliptic curves over Gaussian integers to speed up the cryptographic computations. It also introduces an elliptic curve based signcryption algorithm that provides encrypted message authentication with forward secrecy. The algorithm enables firewalls to authenticate encrypted messages without having to decrypt them. Next, the thesis moves to introducing kleptographic attacks on elliptic curves. An algorithm is presented to add a secretly embedded trapdoor with universal protection into the elliptic curve discrete logarithm problem and extends this to an attack on elliptic curve key exchange. The algorithm enables the attacker to covertly extract the shared key, which implies allowing the attacker to forge signatures and to decrypt all the communications that involve this key. The research extends this attack to elliptic curve encryption to enable the attacker to extract the secret messages without knowing the secret key. The attack is also found possible on elliptic curve signatures where it can leak the key just to the attacker. Finally an algorithm is proposed to use the Elliptic Curve Digital Signature Algorithm (ECDSA) for encrypting subliminal messages without having to use an encryption mechanism. |