A Verifiable Fully Homomorphic Encryption Scheme for Cloud Computing Security

Performing smart computations in a context of cloud computing and big data is highly appreciated today. Fully homomorphic encryption (FHE) is a smart category of encryption schemes that allows working with the data in its encrypted form. It permits us to preserve confidentiality of our sensible data and to benefit from cloud computing powers. Currently, it has been demonstrated by many existing schemes that the theory is feasible but the efficiency needs to be dramatically improved in order to make it usable for real applications. One subtle difficulty is how to efficiently handle the noise. This paper aims to introduce an efficient and verifiable FHE based on a new mathematic structure that is noise free

Cryptography: Mathematical Advancements on Cyber Security

The origin of cryptography, the study of encoding and decoding messages, dates back to ancient times around 1900 BC. The ancient Egyptians enlisted the use of basic encryption techniques to conceal personal information. Eventually, the realm of cryptography grew to include the concealment of more important information, and cryptography quickly became the backbone of cyber security. Many companies today use encryption to protect online data, and the government even uses encryption to conceal confidential information. Mathematics played a huge role in advancing the methods of cryptography. By looking at the math behind the most basic methods to the newest methods of cryptography, one can learn how cryptography has advanced and will continue to advance

Barrel Shifter Physical Unclonable Function Based Encryption

Physical Unclonable Functions (PUFs) are circuits designed to extract physical randomness from the underlying circuit. This randomness depends on the manufacturing process. It differs for each device enabling chip-level authentication and key generation applications. We present a protocol utilizing a PUF for secure data transmission. Parties each have a PUF used for encryption and decryption; this is facilitated by constraining the PUF to be commutative. This framework is evaluated with a primitive permutation network - a barrel shifter. Physical randomness is derived from the delay of different shift paths. Barrel shifter (BS) PUF captures the delay of different shift paths. This delay is entangled with message bits before they are sent across an insecure channel. BS-PUF is implemented using transmission gates; their characteristics ensure same-chip reproducibility, a necessary property of PUFs. Post-layout simulations of a common centroid layout 8-level barrel shifter in 0.13 {\mu}m technology assess uniqueness, stability and randomness properties. BS-PUFs pass all selected NIST statistical randomness tests. Stability similar to Ring Oscillator (RO) PUFs under environment variation is shown. Logistic regression of 100,000 plaintext-ciphertext pairs (PCPs) failed to successfully model BS- PUF behavior

Higher dimensional 3-adic CM construction

We find equations for the higher dimensional analogue of the modular curve X_0(3) using Mumford's algebraic formalism of algebraic theta functions. As a consequence, we derive a method for the construction of genus 2 hyperelliptic curves over small degree number fields whose Jacobian has complex multiplication and good ordinary reduction at the prime 3. We prove the existence of a quasi-quadratic time algorithm for computing a canonical lift in characteristic 3 based on these equations, with a detailed description of our method in genus 1 and 2.Comment: 23 pages; major revie

Formal Analysis of CRT-RSA Vigilant's Countermeasure Against the BellCoRe Attack: A Pledge for Formal Methods in the Field of Implementation Security

In our paper at PROOFS 2013, we formally studied a few known countermeasures to protect CRT-RSA against the BellCoRe fault injection attack. However, we left Vigilant's countermeasure and its alleged repaired version by Coron et al. as future work, because the arithmetical framework of our tool was not sufficiently powerful. In this paper we bridge this gap and then use the same methodology to formally study both versions of the countermeasure. We obtain surprising results, which we believe demonstrate the importance of formal analysis in the field of implementation security. Indeed, the original version of Vigilant's countermeasure is actually broken, but not as much as Coron et al. thought it was. As a consequence, the repaired version they proposed can be simplified. It can actually be simplified even further as two of the nine modular verifications happen to be unnecessary. Fortunately, we could formally prove the simplified repaired version to be resistant to the BellCoRe attack, which was considered a "challenging issue" by the authors of the countermeasure themselves.Comment: arXiv admin note: substantial text overlap with arXiv:1401.817