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Noncommutative cryptography is based on applications of algebraic structures like noncommutative groups, semigroups and non-commutative rings. Its inter-section with Multivariate cryptography contains...
Structure-Preserving Signatures (SPSs) are a useful tool for the design of modular cryptographic protocols. Recent series of works have shown that by limiting the message space of those schemes to the...
Diffie--Hellman key exchange is at the foundations of public-key cryptography, but conventional group-based Diffie--Hellman is vulnerable to Shor's quantum algorithm. A range of ``post-quantum Diffie-...
Optimal Succinct Arguments via Hidden Order Groups     zero knowledge  RSA       font style='font-size:12px;'> 2018/8/2
An argument of knowledge allows a prover to convince a verifier of the validity of certain statements. We construct succinct arguments of knowledge with an optimal communication complexity of O(λ) bit...
Constrained PRFs for NC1 in Traditional Groups     pseudo-randomness  constrained PRF  pairing free group       font style='font-size:12px;'> 2018/3/7
We propose new constrained pseudorandom functions (CPRFs) in traditional groups. Traditional groups mean cyclic and multiplicative groups of prime order that were widely used in the 1980s and 1990s (s...
Within recent years, secure comparison protocols have been proposed using binary decomposition and properties of algebraic fields. These have been repeatedly optimized and increased in efficiency, but...
Interactively Secure Groups from Obfuscation     indistinguishability obfuscation  Uber assumption       font style='font-size:12px;'> 2018/1/12
We construct a mathematical group in which an interactive variant of the very general Uber assumption holds. Our construction uses probabilistic indistinguishability obfuscation, fully homomorphic enc...
We initiate the study of public-key encryption (PKE) schemes and key-encapsulation mechanisms (KEMs) that retain security even when public parameters (primes, curves) they use may be untrusted and sub...
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 ...
We present a principled technique for reducing the matrix size in some applications of Coppersmith's lattice method for finding roots of modular polynomial equations. It relies on an analysis of the a...
Bilinear groups form the algebraic setting for a multitude of important cryptographic protocols including anonymous credentials, e-cash, e-voting, e-coupon, and loyalty systems. It is typical of such ...
Secure messaging systems such as TextSecure and Signal aim, among others, at providing authenticated and confidential channels between two or more communicating users. The general understanding seems ...
Impossibility of Secure Multi-Party Products in Non-Abelian Groups     foundations  mpc       font style='font-size:12px;'> 2017/7/19
Suppose nn parties have respective inputs x1,…,xn∈Gx1,…,xn∈G, where GG is a finite group. The parties would like to privately compute x1x2⋯xnx1x2⋯xn (where multiplication refers to the gro...
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...
Our analysis identifies two families of intractability assumptions, the qq-Generalized Diffie-Hellman Exponent assumptions and the qq-Simple Fractional assumptions that imply all other target assumpti...

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