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On Noncommutative Cryptography and homomorphism of stable cubical multivariate transformation groups of infinite dimensional affine spaces
Multivariate Cryptography stable transformation groups and semigroups decomposition problem of nonlinear multivariate map into given generators
2019/6/3
Noncommutative cryptography is based on applications of algebraic structures like noncommutative groups, semigroups and non-commutative rings. Its inter-section with Multivariate cryptography contains...
Further Lower Bounds for Structure-Preserving Signatures in Asymmetric Bilinear Groups
public-key cryptography Structure-Preserving Signatures
2019/1/2
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...
Pre- and post-quantum Diffie--Hellman from groups, actions, and isogenies
key exchange elliptic-curve cryptography isogenies
2018/11/13
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-...
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
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...
Efficient and Constant-Rounds Secure Comparison through Dynamic Groups and Asymmetric Computations
cryptographic protocols secure comparison
2018/3/6
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
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...
Public-Key Encryption Resistant to Parameter Subversion and its Realization from Efficiently-Embeddable Groups
Public-key encryption subversion mass surveillance
2018/1/11
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...
ABE with Tag Made Easy: Concise Framework and New Instantiations in Prime-order Groups
Attribute-based encryption Predicate encoding Prime-order bilinear group
2017/9/13
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 ...
Coppersmith's lattices and ``focus groups'': an attack on small-exponent RSA
lattice techniques RSA cryptanalysis
2017/9/1
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...
New Techniques for Structural Batch Verification in Bilinear Groups with Applications to Groth-Sahai Proofs
Batch verification bilinear maps Groth-Sahai proofs
2017/8/29
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 ...
With one it is easy, with many it gets complicated: Understanding Channel Security for Groups
secure messaging group communication confidentiality
2017/8/21
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 ...
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...
CCA-secure Predicate Encryption from Pair Encoding in Prime Order Groups: Generic and Efficient
Predicate Encryption CCA Security Pair Encoding Scheme
2017/7/6
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...
Towards a Classification of Non-interactive Computational Assumptions in Cyclic Groups
Non-Interactive Assumptions Computational Assumptions Target Assumptions
2017/4/24
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...