6,021 research outputs found
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
Isogeny-based post-quantum key exchange protocols
The goal of this project is to understand and analyze the supersingular isogeny Diffie Hellman (SIDH), a post-quantum key exchange protocol which security lies on the isogeny-finding problem between supersingular elliptic curves. In order to do so, we first introduce the reader to cryptography focusing on key agreement protocols and motivate the rise of post-quantum cryptography as a necessity with the existence of the model of quantum computation. We review some of the known attacks on the SIDH and finally study some algorithmic aspects to understand how the protocol can be implemented
Analysis of Parallel Montgomery Multiplication in CUDA
For a given level of security, elliptic curve cryptography (ECC) offers improved efficiency over classic public key implementations. Point multiplication is the most common operation in ECC and, consequently, any significant improvement in perfor- mance will likely require accelerating point multiplication. In ECC, the Montgomery algorithm is widely used for point multiplication. The primary purpose of this project is to implement and analyze a parallel implementation of the Montgomery algorithm as it is used in ECC. Specifically, the performance of CPU-based Montgomery multiplication and a GPU-based implementation in CUDA are compared
I2PA, U-prove, and Idemix: An Evaluation of Memory Usage and Computing Time Efficiency in an IoT Context
The Internet of Things (IoT), in spite of its innumerable advantages, brings
many challenges namely issues about users' privacy preservation and constraints
about lightweight cryptography. Lightweight cryptography is of capital
importance since IoT devices are qualified to be resource-constrained. To
address these challenges, several Attribute-Based Credentials (ABC) schemes
have been designed including I2PA, U-prove, and Idemix. Even though these
schemes have very strong cryptographic bases, their performance in
resource-constrained devices is a question that deserves special attention.
This paper aims to conduct a performance evaluation of these schemes on
issuance and verification protocols regarding memory usage and computing time.
Recorded results show that both I2PA and U-prove present very interesting
results regarding memory usage and computing time while Idemix presents very
low performance with regard to computing time
Still Wrong Use of Pairings in Cryptography
Several pairing-based cryptographic protocols are recently proposed with a
wide variety of new novel applications including the ones in emerging
technologies like cloud computing, internet of things (IoT), e-health systems
and wearable technologies. There have been however a wide range of incorrect
use of these primitives. The paper of Galbraith, Paterson, and Smart (2006)
pointed out most of the issues related to the incorrect use of pairing-based
cryptography. However, we noticed that some recently proposed applications
still do not use these primitives correctly. This leads to unrealizable,
insecure or too inefficient designs of pairing-based protocols. We observed
that one reason is not being aware of the recent advancements on solving the
discrete logarithm problems in some groups. The main purpose of this article is
to give an understandable, informative, and the most up-to-date criteria for
the correct use of pairing-based cryptography. We thereby deliberately avoid
most of the technical details and rather give special emphasis on the
importance of the correct use of bilinear maps by realizing secure
cryptographic protocols. We list a collection of some recent papers having
wrong security assumptions or realizability/efficiency issues. Finally, we give
a compact and an up-to-date recipe of the correct use of pairings.Comment: 25 page
I2PA : An Efficient ABC for IoT
Internet of Things (IoT) is very attractive because of its promises. However,
it brings many challenges, mainly issues about privacy preserving and
lightweight cryptography. Many schemes have been designed so far but none of
them simultaneously takes into account these aspects. In this paper, we propose
an efficient ABC scheme for IoT devices. We use ECC without pairing, blind
signing and zero knowledge proof. Our scheme supports block signing, selective
disclosure and randomization. It provides data minimization and transactions'
unlinkability. Our construction is efficient since smaller key size can be used
and computing time can be reduced. As a result, it is a suitable solution for
IoT devices characterized by three major constraints namely low energy power,
small storage capacity and low computing power
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