[pq] grad thesis DGMT: A Fully Dynamic Hash-Based Group Signature

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https://prism.ucalgary.ca/items/759f1bda-3e4f-4f4c-8ab6-4d247f216b0e
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2023-07
DGMT: A Fully Dynamic Hash-Based
Group Signature
Erfanian Azad Soltan, Aylar

Abstract

Abstract
With the rapid development of quantum technologies, quantum-safe
cryptographic schemes have found
significant attention. Shor’s quantum algorithms for breaking discrete
logarithm (DL) and integer factorization (IF) problems will bring
depredation for currently used public key algorithms, including RSA
(Rivest–Shamir–Adleman), DH (Diffie-Hellman) key agreement, DSA
(Digital Signature Algorithm) and
ECC (Elliptic Curve Cryptography), which their security depends on
solving mathematical hard problems
(IF and DL problem). Therefore, applications and protocols must evolve
to be quantum secure in the presence of quantum computers. It is
believed that symmetric encryptions and hash functions are resilient
to
attacks by a quantum adversary. Therefore, signature schemes have been
modified so that their security
relies on hash functions instead of the aforementioned mathematical
hard problems.
In this thesis, we consider post-quantum digital group signatures,
whose security depends on one-way functions. In practice, these
functions are replaced by cryptographic hash functions, which are
expected to
remain secure in the presence of quantum computers.
A group signature is a signature scheme that allows a group member to
anonymously sign messages on behalf
of the group, while anonymity can be annulled by an opening authority
or group manager. In fully dynamic
group signature schemes, new members can be added to the group after
the initialization phase and existing
members can be revoked from the group.
The primary aim of this thesis is twofold. Firstly, it aims to conduct
a comprehensive analysis of various
hash-based group signature schemes, taking into consideration their
security models, properties, and limitations. Moreover, this thesis
contributes to the development of a novel fully dynamic group
signature scheme,
named DGMT, which addresses the limitations of previous schemes, and
we prove its security (unforgeability, anonymity, and traceability),
and provide the complete implementation of the this scheme for the
first
time. Secondly, the thesis intends to review and evaluate various
revocation methods with the objective of
identifying potential ways to improve the revocation method utilized
in the proposed scheme