# Sophie Germain and Safe Primes

Sophie Germain (born 1776 in Paris) was a French mathematician and who used safe primes to investigate Fermat’s Last Theorem. Sophie gained her knowledge of mathematics by studying the works of Euler, and communicated her ideas with other famous mathematics scholars including Legendre and Gauss. In fact, at the time, she faced great resistance in her studies, including from her parent who confiscated her candles and took away her clothes, in order to stall her research. Sophie also hid her gender when communicating with Gauss and used the pseudonym of M. LeBlanc. …

# The MALICIOUS framework: Tweakable Block Ciphers

Adding a backdoor has been an attack method of choice for Eve. Overall the opportunity to insert a backdoor into symmetric-key methods such as has not been successful. That changed when, in 2020, Peyrin et al [1] proposed “ The MALICIOUS Framework: Embedding Backdoors into Tweakable Block Ciphers.”

# Low Multiplicative Complexity — LowMC

Let’s take six numbers: 6, 3, 10, 5, 9 and 3. We want you to multiply pairs of numbers and then add them. For this most of us we would compute 18, 50 and 27, and then add these to get 95. The multiplication part had three operations and the add was just a single operation. If we do this for many pairs we can see the computation gets more timely for the multiplication, and the end part is perhaps still just a single addition.

When we implement cryptography we typically use two operations: AND and XOR. These can be…

# Lockdown Easing? Let’s Go For A Post-Quantum Picnic

And then there were three: CRYSTALS Dilithium, Falcon and Rainbow. These are the finalists for the NIST standard for Post Quantum Cryptography (PQC) of digital signatures. Basically, they will replace RSA and ECC in an era of quantum computers, and provide the core of trust on the Internet. Dilithium and Falcon are lattice methods, and Rainbow uses multivariate quadratic polynomials. So while lattice looks like a winner because of its speed of computation and key size, there is a competition for an alternative winner.

Two of the alternative winner finalists are SPHINCS+ and Picnic. These methods have a core advantage…

# Haraka v2 — The Short Input Hash

In cryptography, we often focus on making sure we can create a hash for any number of bytes as an input. But what happens if we have a short input that we want to hash? Using methods such as SHA-1 and SHA-2 (aka SHA-256) will often be inefficient as they tend to compress (or squeeze) the data inputs through a number of stages. The focus is thus to squeeze the data down to a standard number of bits and then add collision protection. …

# SPHINCS+: A Hash-based Quantum Robust Method

One of my great academic heroes is the mighty Daniel J Bernstein (djb). In the last 20 years, he has contributed so much to cryptography, and in building a more trusted world. He created research around ChaCha20, Salsa20, Curve 25519, twisted elliptic curves, AES timing attacks, and so much more. But one contribution that I particularly like is the SPHINCS+ signature framework [here]:

# Under Starters Orders: It’s A Three Horse Race — Dilithium, Rainbow and Falcon … But Who Will Win The Cyber Stakes?

And so we see the rise of the quantum computer, and where our cybersecurity world will change in a disruptive way. At the core of cybersecurity is trust, and at the core of digital trust is the digital signature. This magical operation proves identity, it protects integrity and it defines (near) certainty. Presently, we are probably just at the start of our journey to make every transaction trustworthy, and so we need to understand how our existing methods can be made secure into the future.

Our existing methods for digital signing include DSA (/RSA), ECDSA and EdDSA. DSA uses RSA…

# Rainbow — The PCQ Oil and Vinegar Method: Small Signatures, But Larger Keys (than Lattice)

Here’s my 6 am doodles from this morning on multivariate cryptography:

# “The Great Fire of Ransomware”: Should The Insurance Industry Take a Lead In Improving Cybersecurity?

With ransomware and data exfiltration, we have two blunt weapons that few companies can cope with, let alone put a value on the full cost of an attack. Imagine if someone managed to get all the broadband records of every citizen in the UK, or, indeed all of their emails and WhatsApp chats? With a conviction rate of less than 0.07% for a cyberattack, the rewards from ransomware attacks often vastly outways the risks involved.

With Travelex, we saw a company going from being worth billions to zero in a matter of a few months, and with people losing their…

# Venus Is Just Two Minutes Away, When Fibre is Not Glass, and Unbreakable Wi-fi!

I have an ear for picking up on things that are not quite scientifically correct. So, whenever I hear Journey singing:

`We're heading for Venus and still we stand tall 'Cause maybe they've seen us and welcome us all, yea With so many light years to go and things to be found (To be found) I'm sure that we'll all miss her so`

I correct it in my head, knowing that Venus is only two minutes by light. And when I see this advert, I have to say that fibre optic cables are made from glass and not copper:

## Prof Bill Buchanan OBE

Professor of Cryptography. Serial innovator. Believer in fairness, justice & freedom. EU Citizen. Auld Reekie native. Old World Breaker. New World Creator.

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