Mastodawn

Nigel Smart Nov 29, 2024

@nadim
How can you say Curve25519 does not need a hash function to work properly.

Any usage of ECC to encrypt data uses hash functions since you need to apply a KDF to the output Diffie-Hellman key in order to use it. In fact if you dont you get attacks (see some early papers which discussed MQV vs HMQV for this).

The NTT in elliptic curves is a bit like using projective coordinates in ECC. It is an optimization of the underlying math and nothing more. If you dont want the optimization you can ignore it.

Nigel Smart Oct 9, 2024

eprint Oct 9, 2024

#eprint Secret Sharing with Publicly Verifiable Deletion by Jonathan Katz, Ben Sela (https://ia.cr/2024/1596)

Secret Sharing with Publicly Verifiable Deletion

Certified deletion, an inherently quantum capability, allows a party holding a quantum state to prove that they have deleted the information contained in that state. Bartusek and Raizes (Crypto 2024) recently studied certified deletion in the context of secret sharing schemes, and showed constructions with privately verifiable proofs of deletion that can be verified only by the dealer who generated the shares. We give two constructions of secret sharing schemes with publicly verifiable certified deletion. Our first construction is based on the post-quantum security of the LWE problem, and each share requires a number of qubits that is linear in the size of an underlying classical secret sharing scheme for the same set of authorized parties. Our second construction is based on a more general assumption—the existence of post quantum one-way functions— but requires an asymptotically larger number of qubits relative to the share size of the underlying classical scheme.

IACR Cryptology ePrint Archive

Nigel Smart Oct 9, 2024

eprint Oct 8, 2024

#eprint Fully Homomorphic Encryption for Cyclotomic Prime Moduli by Robin Geelen, Frederik Vercauteren (https://ia.cr/2024/1587)

Fully Homomorphic Encryption for Cyclotomic Prime Moduli

This paper presents a Generalized BFV (GBFV) fully homomorphic encryption scheme that encrypts plaintext spaces of the form $\mathbb{Z}[x]/(\Phi_m(x), t(x))$ with $\Phi_m(x)$ the $m$-th cyclotomic polynomial and $t(x)$ an arbitrary polynomial. GBFV encompasses both BFV where $t(x) = p$ is a constant, and the CLPX scheme (CT-RSA 2018) where $m = 2^k$ and $t(x) = x - b$ is a linear polynomial. The latter can encrypt a single huge integer modulo $\Phi_m(b)$, has much lower noise growth than BFV, but it is not known to be efficiently bootstrappable. We show that by a clever choice of $m$ and higher degree polynomial $t(x)$, our scheme combines the SIMD capabilities of BFV with the low noise growth of CLPX, whilst still being efficiently bootstrappable. Moreover, we present parameter families that natively accommodate packed plaintext spaces defined by a large cyclotomic prime, such as the Fermat prime $\Phi_2(2^{16}) = 2^{16} + 1$ and the Goldilocks prime $\Phi_6(2^{32}) = 2^{64} - 2^{32} + 1$. These primes are often used in homomorphic encryption applications and zero-knowledge proof systems. Due to the lower noise growth, GBFV can evaluate much deeper circuits compared to native BFV in the same ring dimension. As a result, we can evaluate either larger circuits or work with smaller ring dimensions. In particular, we can natively bootstrap GBFV at 128-bit security already at ring dimension $n = 2^{14}$, which was impossible before. We implemented the GBFV scheme on top of the SEAL library and achieve a latency of only 2 seconds to bootstrap a ciphertext encrypting up to 8192 elements modulo $2^{16} + 1$.

IACR Cryptology ePrint Archive

Nigel Smart Oct 9, 2024

eprint Oct 4, 2024

#eprint Bit t-SNI Secure Multiplication Gadget for Inner Product Masking by John Gaspoz, Siemen Dhooghe (https://ia.cr/2024/1546)

Bit t-SNI Secure Multiplication Gadget for Inner Product Masking

Masking is a sound countermeasure to protect against differential power analysis. Since the work by Balasch et al. in ASIACRYPT 2012, inner product masking has been explored as an alternative to the well known Boolean masking. In CARDIS 2017, Poussier et al. showed that inner product masking achieves higher-order security versus Boolean masking, for the same shared size, in the bit-probing model. Wang et al. in TCHES 2020 verified the inner product masking's security order amplification in practice and proposed new gadgets for inner product masking. Finally, Wu et al. in TCHES 2022 showed that this security amplification comes from the bit-probing model, but that Wang al.'s gadgets are not higher-order bit-probing secure reducing the computation's practical security. The authors concluded their work with the open question of providing an inner product multiplication gadget which maintains the masking's bit-probing security, and conjectured that such gadget maintains the practical security order amplification of the masking during its computation. In this paper, we answer positively to Wu et al.'s open problems. We are the first to present a multiplication gadget for inner product masking which is proven secure in the bit-level probing model using the t-Strong Non-Interference (SNI) property. Moreover, we provide practical evidence that the gadget indeed maintains the security amplification of its masking. This is done via an evaluation of an assembly implementation of the gadget on an ARM Cortex-M4 core. We used this implementation to take leakage measurements and show no leakage happens for orders below the gadget's bit-probing security level either for its univariate or multivariate analysis.

IACR Cryptology ePrint Archive

Nigel Smart Oct 9, 2024

eprint Oct 4, 2024

#eprint STARK-based Signatures from the RPO Permutation by Shahla Atapoor, Cyprien Delpech de Saint Guilhem, Al Kindi (https://ia.cr/2024/1553)

STARK-based Signatures from the RPO Permutation

This work describes a digital signature scheme constructed from a zero-knowledge proof of knowledge of a pre-image of the Rescue Prime Optimized (RPO) permutation. The proof of knowledge is constructed with the DEEP-ALI interactive oracle proof combined with the Ben-Sasson--Chiesa--Spooner (BCS) transformation in the random oracle model. The EUF-CMA security of the resulting signature scheme is established from the UC-friendly security properties of the BCS transformation and the pre-image hardness of the RPO permutation. The implementation of the scheme computes signatures in 13 ms and verifies them in 1 ms on a single core when the BCS transform is implemented with the Blake3 hash function. (The multi-threaded implementation signs in 9.2 ms and also verifies in 1 ms.) These speeds are obtained with parameters achieving 122 bits of average-case security for $ 2^{122} $-bounded adversaries with access to at most $ 2^{64} $ signatures.

IACR Cryptology ePrint Archive

Nigel Smart Oct 9, 2024

eprint Sep 30, 2024

#eprint FINALLY: A Multi-Key FHE Scheme Based on NTRU and LWE by Jeongeun Park, Barry Van Leeuwen, Oliver Zajonc (https://ia.cr/2024/1505)

FINALLY: A Multi-Key FHE Scheme Based on NTRU and LWE

Multi-key fully homomorphic encryption (MKFHE), a generalization of fully homomorphic encryption (FHE), enables a computation over encrypted data under multiple keys. The first MKFHE schemes were based on the NTRU primitive, however these early NTRU based FHE schemes were found to be insecure due to the problem of over-stretched parameters. Recently, in the case of standard (non-multi key) FHE a secure version, called FINAL, of NTRU has been found. In this work we extend FINAL to an MKFHE scheme, this allows us to benefit from some of the performance advantages provided by NTRU based primitives. Thus, our scheme provides competitive performance against current state-of-the-art multi-key TFHE, in particular reducing the computational complexity from quadratic to linear in the number of keys.

IACR Cryptology ePrint Archive

Nigel Smart Aug 28, 2024

FHE.org Aug 28, 2024

New resource added to http://FHE.org/resources:

"Human In Picture (HIP) using Concrete ML" by Memento Research

https://fhe.org/resources/#00140

Know of an FHE resource that should be listed on the http://FHE.org website? Let us know!

#FHE #homomorphicencryption

Fully Homomorphic Encryption

We are a community of researchers and developers interested in advancing homomorphic encryption and other secure computation techniques.

Fully Homomorphic Encryption

Nigel Smart Aug 20, 2024

Yogthos Aug 19, 2024

Nigel Smart Feb 8, 2024

I wrote an introductory article about "Preventing the Quantum Crypto-Apocalypse with Linear Algebra with Errors" for the newsletter of the London Mathematical Society.

See page 25 of...

https://www.lms.ac.uk/sites/default/files/inline-files/NLMS_510_for_web.pdf

Nigel Smart Feb 1, 2024

FHE.org Jan 26, 2024

Register for the next Meetup on Feb 8th 4PM CEST — we'll have Jeongeun Park, a cryptographer currently working at COSIC, KU Leuven as a postdoctoral researcher presenting Towards Practical Transciphering for FHE with Setup Independent of the Plaintext Space.

https://www.meetup.com/fhe-org/events/298732824/

Towards Practical Transciphering for FHE w/ Setup Independent of Plaintext Space, Thu, Feb 8, 2024, 4:00 PM | Meetup

**Abstract** Fully Homomorphic Encryption (FHE) is a powerful tool to achieve non-interactive privacy preserving protocols with optimal computation/communication complexit

Meetup

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