Biblio

This research aims to implement different modular exponentiation algorithms and evaluate the average complexity and compare it to the theoretical value. We use the library GMP to implement seven modular exponentiation algorithms. They are Left-to-right Square and Multiply, Right-to-left Square and Multiply, Left-to-right Signed Digit Square, and Multiply Left-to-right Square and Multiply Always Right-to-left Square and Multiply Always, Montgomery Ladder and Joye Ladder. For some exponent bit length, we choose 1024 bits and execute each algorithm on many exponent values and count the average numbers of squares and the average number of multiplications. Whenever relevant, our programs will check the consistency relations between the registers at the end of the exponentiation.

This paper proposes a method that offers much higher security for Iseki's fully homomorphic encryption (FHE), a recently proposed secure computation scheme. The key idea is re-encrypting already encrypted data. This second encryption is executed using new common keys, whereby two or more encryptions offer much stronger security.

Control-hijacking attacks include code injection attacks and code reuse attacks. In recent years, with the emergence of the defense mechanism data-execution prevention(DEP), code reuse attacks have become mainstream, such as return-oriented programming(ROP), Jump-Oriented Programming(JOP), and Counterfeit Object-oriented Programming(COOP). And a series of defensive measures have been proposed, such as DEP, address space layout randomization (ASLR), coarse-grained Control-Flow Integrity(CFI) and fine-grained CFI. In this paper, we propose a new attack called function-oriented programming(FOP) to construct malicious program behavior. FOP takes advantage of the existing function of the C program to induce attack. We propose concrete algorithms for FOP gadgets and build a tool to identify FOP gadgets. FOP can successfully bypass coarse-grained CFI, and FOP also can bypass some existing fine-grained CFI technologies, such as shadow stack technology. We show a real-world attack for proftpd1.3.0 server in the Linux x64 environment. We believe that the FOP attack will encourage people to come up with more effective defense measures.