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This Master’s thesis deals with attacks on cryptographic systems based on elliptic curves with a special focus on kleptography, a field that explores the insertion of secret backdoors into cryptographic systems to leak information without being detected. Three types of attacks are analyzed in detail: SETUP, Baby-Step Giant-Step and Pohlig-Hellman. The SETUP kleptographic attack compromises the elliptic curve Diffie-Hellman key exchange, allowing an attacker to recover the recipient’s private key. On the other hand, the BabyStep Giant-Step and Pohlig-Hellman methods focus on solving the discrete logarithm problem in elliptic curves through advanced search and factorization techniques. The results show the high effectiveness of the SETUP attack on various elliptic curves and its possible detection through execution time analysis, while the other two attacks are promising if the correct parameters are chosen, but unfeasible for modern elliptic curves and robust parameters.
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Toledo Delgado, Pedro Antonio
[1]
Torres Díaz, Néstor
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