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Algebraic Structures I (Matrices, Groups, Rings, and Fields)
Published in R. Balakrishnan, Sriraman Sridharan, Discrete Mathematics, 2019
R. Balakrishnan, Sriraman Sridharan
The normal subgroups of a groups G are those subgroups of G that are left invariant by all the inner automorphisms of G.
A Quantum Resistant Chameleon Hashing and Signature Scheme
Published in IETE Journal of Research, 2022
The first chameleon signature scheme was proposed by Krawczyk and Rabin [1] suffers from key exposure problem. In identity-based chameleon hash function proposed by Ateniese et al. [2], the collision produced by the recipient enables the signer to recover the recipient's trapdoor information that is related to that particular transaction. Their scheme does not solve the problem of key exposure completely. To address this drawback, Chen et al. [3] proposed a complete key exposure free chameleon hash function in the gap Diffie Hellman group with bilinear pairings. In [4] Ateniese et al. proposed three non-pairing based key exposure free schemes of which two schemes are based on RSA and factoring, and one based on Strong Diffie Hellman and Discrete Logarithm Problem(DLP). In [5], Wei Gao proposed a chameleon hash function based on factoring and proved its security by introducing a variant Rabin signature scheme and in [6] the authors proposed a DLP-based key exposure free chameleon hash function with Schnorr signature. In [7], Chen et al. proposed a key exposure free chameleon hash and signature scheme based on DLP, without using the gap Diffie Hellman groups. In [8], Pan et al. proposed a family of chameleon hash functions and strongly unforgeable one-time signature schemes based on DLP over inner automorphism groups. Thanalakshmi et al. [9] proposed a graph-based key exposure free chameleon signature scheme. As it is built on a collision resistant one-way hash function and a pseudo random generator, they claim that the scheme is secured against quantum computers.