6,015 research outputs found
An Elliptic Curve-based Signcryption Scheme with Forward Secrecy
An elliptic curve-based signcryption scheme is introduced in this paper that
effectively combines the functionalities of digital signature and encryption,
and decreases the computational costs and communication overheads in comparison
with the traditional signature-then-encryption schemes. It simultaneously
provides the attributes of message confidentiality, authentication, integrity,
unforgeability, non-repudiation, public verifiability, and forward secrecy of
message confidentiality. Since it is based on elliptic curves and can use any
fast and secure symmetric algorithm for encrypting messages, it has great
advantages to be used for security establishments in store-and-forward
applications and when dealing with resource-constrained devices.Comment: 13 Pages, 5 Figures, 2 Table
An Improved Public Key Cryptography Based on the Elliiptic Curve
Elliptic curve cryptography offers two major benefits over RSA: more security
per bit, and a suitable key size for hardware and modern communication. Thus, this
results to smaller size of public key certificates, lower power requirements and
smaller hardware processors.
Three major approaches are used in this dissertation to enhance the elliptic curve
cryptsystems: reducing the number of the elliptic curve group arithmetic operations,
speeding up the underlying finite field operations and reducing the size of the
transited parameters. A new addition formula in the projective coordinate is
introduced, where the analysis for this formula shows that the number of
multiplications over the finite field is reduced to nine general field element
multiplications. Thus this reduction will speed up the computation of adding two
points on the elliptic curve by 11 percent. Moreover, the new formula can be used
more efficiently when it is combined with the suggested sparse elements algorithms. To speed up the underlying finite field operations, several new algorithms are
introduced namely: selecting random sparse elements algorithm, finding sparse base
points, sparse multiplication over polynomial basis, and sparse multiplication over
normal basis. The complexity analysis shows that whenever the sparse techniques
are used, the improvement rises to 33 percent compared to the standard projective
coordinate formula and improvement of 38 percent compared to affine coordinate. A
new algorithm to compress and decompress the sparse elements algorithms are
introduced to reduce the size of the transited parameters.
The enhancements are applied on three protocols and two applications. The
protocols are Diffie-Hellman, ELGamal and elliptic curve digital signature. In these
protocols the speed of encrypting, decrypting and signing the message are increased
by 23 to 38 percent. Meanwhile, the size of the public keys are reduced by 37 to 48
percent. The improved algorithms are applied to the on-line and off-line electronic
payments systems, which lead to probably the best solution to reduce the objects
size and enhance the performance in both systems
Quantum attacks on Bitcoin, and how to protect against them
The key cryptographic protocols used to secure the internet and financial
transactions of today are all susceptible to attack by the development of a
sufficiently large quantum computer. One particular area at risk are
cryptocurrencies, a market currently worth over 150 billion USD. We investigate
the risk of Bitcoin, and other cryptocurrencies, to attacks by quantum
computers. We find that the proof-of-work used by Bitcoin is relatively
resistant to substantial speedup by quantum computers in the next 10 years,
mainly because specialized ASIC miners are extremely fast compared to the
estimated clock speed of near-term quantum computers. On the other hand, the
elliptic curve signature scheme used by Bitcoin is much more at risk, and could
be completely broken by a quantum computer as early as 2027, by the most
optimistic estimates. We analyze an alternative proof-of-work called Momentum,
based on finding collisions in a hash function, that is even more resistant to
speedup by a quantum computer. We also review the available post-quantum
signature schemes to see which one would best meet the security and efficiency
requirements of blockchain applications.Comment: 21 pages, 6 figures. For a rough update on the progress of Quantum
devices and prognostications on time from now to break Digital signatures,
see https://www.quantumcryptopocalypse.com/quantum-moores-law
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