# [Focus on] Cybersecurity Research activities of the CAS^{3}C^{3} Team of
Laboratoire Jean Kuntzmann

Cybersecurity research activities of the CAS^{3}C^{3}
team (computer algebra, security, complex systems, codes, secrets,
cryptology) are focused on
- Design and analysis of symmetric cryptographic primitives and
their secure and efficient implementation.
- Proof of work certificates for outsourced cloud computing.
- Fault tolerant schemes in linear algebra.
- Secure protocols for multi-party, zero-knowledge or
industrial control systems.

### Proof of work certificates for outsourced cloud computing,
where a client can not blindly trust the answer of remote
computing parties

Efficiently and reliably delegating computations.
The idea is to design algorithms that can form a proof of
correctness of a result computed via a probabilistic algorithm or
through a potentially unreliable computing center.
The difficulty is to design proofs that are verifiable at a lower cost
(time, memory, ...) than that of recomputing the result.

Références:
hal-01829139
hal-01825779
hal-01657873
hal-01503870
hal-01466093
hal-01266041
hal-00932846

### Explicit computation of (freestart) collisions for the SHA-1
hash function

Signed non-linear differential path used in the computation of the
second block of a collision for the SHA-1 hash function.

Hash functions, of which SHA-1 is an example, are ubiquitous primitives in cryptography. It was known since 2005 that SHA-1 was vulnerable to collision attacks, yet it remained used in many industrial products. From 2014 to 2017, a series of work involving CASC team member Pierre Karpman improved the existing attacks and ultimately lead to an explicit computation of a collision for SHA-1. This had a positive impact on the withdrawal of this function from vulnerable systems.

Références:
hal-01982005
hal-01251023

### Fault tolerant schemes for linear algebra

Solving linear systems of parametric equations:
hal-01982114

Error correction in fast exact linear algebra:
Error correction in fast matrix multiplication and inverse
arXiv:1802.02270,
Factorization with errors:
hal-01997592

### Information retrievability, proofs and security

XPIR : Private Information Retrieval for Everyone
hal-01396142

Proofs of Retrievability with Low Server Storage
doi 10.1145/3319535.3363266

### high-order masking schemes for finite-field multiplication

A 3-NI multiplication gadget over F2 and any extension thereof.

Physical side-channel attacks are a significant threat for embedded
implementations of cryptosystems. An efficient countermeasure
against some of these attacks is the use of *masked*
operations, whereby one splits sensitive data into several
*shares* and uses multiparty computation secure in a
*probing model* to compute a shared result.

Team members' activities include the study of efficient algorithms to
evaluate the security of given masking schemes, and the design of
new *gadgets* for various operations.

Références:
hal-01878385

### Zero-knowledge protocols

In Conspiracy Santa, a variant of Secret Santa, a group of people
offer each other Christmas gifts, where each member of the group
receives a gift from the other members of the group. We have
invented a protocol that allows a group of people to share the
expenses for the gifts in such a way that no participant will
learn the price of his gift. Our solution does not require a
trusted third party, and can either be implemented physically (the
participants are in the same room and exchange money) or,
virtually, using a cryptocurrency.

More generally, we research on *Physical Cryptography*, the
art of designing protocols that can be ran without computers, for
instance using only pencil and paper or cards.

Conspiracy Santa:
hal-01777997

Padlock cryptography:
hal-02552281

Card-based cryptography:
hal-02150062
hal-01898048
hal-01326059

### Private Multi-party linear algebra and trust
computation

Secure multiparty computations (MPC) allows n players to compute
together the output of some function, using private inputs without
revealing them. This is useful, e.g., for a distributed evaluation
of trust where players compute a confidence level by combining
their mutual degrees of trust, but without revealing their
personal measures.

Références:
hal-01781554
hal-01497866
hal-01344750
hal-00607478

### Security architectures for industrial control systems

LocalPKI: A user-centric,
interoperable and IoT friendly, formally proven PKI. This security
infrastructure can be
used in constraint environments, for instance for IoT, but also
for Supervisory Control and Data Acquisition (SCADA) architectures.

LocalPKI:
hal-01963269
hal-01657605

Secured Industrial control systems:
hal-01564696

Last modified: Thu May 7 11:30:35 CEST 2020