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Diffie-Hellman groups are a widely used component in cryptographic protocols in which a shared secret is needed. These protocols are typically proven to be secure under the assumption they are impleme...
This paper addresses fast scalar multiplication for elliptic curves over finite fields. In the first part of the paper, we obtain several efficiently computable formulas for basic elliptic curves arit...
Efficient scalar multiplication algorithms require a single finite field inversion at the end to convert from projective to affine coordinates. This inversion consumes a significant proportion of the ...
This work provides a systematic analysis of primality testing under adversarial conditions, where the numbers being tested for primality are not generated randomly, but instead provided by a possibly ...
Private linear key agreement (PLKA) enables a group of users to agree upon a common session key in a broadcast encryption (BE) scenario, while traitor tracing (TT) system allows a tracer to identify c...
In contrast to related work which encrypts and acts on each bit of the input separately, our protocol compares multiple input bits simultaneously within a single ciphertext. Compared to the related pr...
Among all existing identity-based encryption (IBE) schemes in the bilinear group, Wat-IBE proposed by Waters [CRYPTO, 2009] and JR-IBE proposed by Jutla and Roy [AsiaCrypt, 2013] are quite special. A ...
Generic non-interactive zero-knowledge (NIZK) proofs can be used to prove such properties. However, generic NIZK proofs are not practical at all. For some very specific properties, specialized proofs ...
Attrapadung (Eurocrypt 2014) proposed a generic framework called pair encoding to simplify the design and proof of security of CPA-secure predicate encryption (PE) instantiated in composite order grou...
In recent years several papers have appeared investigating the classical discrete logarithm problem for elliptic curves by means of the multivariate polynomial approach based on the celebrated summati...
The discrete logarithm problem over prime fields: the safe prime case. The Smart attack, non-canonical lifts and logarithmic derivatives.
This paper reports on the number field sieve computation of a 768-bit prime field discrete logarithm, describes the different parameter optimizations and resulting algorithmic changes compared to the ...
A Ciphertext-Policy Attribute-Based Encryption (CP-ABE) allows users to specify the access policies without having to know the identities of users. In this paper, we contribute by proposing an ABE sch...
The Discrete Logarithm Problem over Prime Fields can be transformed to a Linear Multivariable Chinese Remainder Theorem.

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