## CryptoDB

### ByeongHak Lee

#### Publications

**Year**

**Venue**

**Title**

2022

EUROCRYPT

Rubato: Noisy Ciphers for Approximate Homomorphic Encryption
📺
Abstract

A transciphering framework converts a symmetric ciphertext into a homomorphic ciphertext on the server-side, reducing computational and communication overload on the client-side. In Asiacrypt 2021, Cho et al. proposed the RtF framework that supports approximate computation.
In this paper, we propose a family of noisy ciphers, dubbed Rubato, with a novel design strategy of introducing noise to a symmetric cipher of a low algebraic degree. With this strategy, the multiplicative complexity of the cipher is significantly reduced, compared to existing HE-friendly ciphers, without degrading the overall security. More precisely, given a moderate block size (16 to 64), Rubato enjoys a low multiplicative depth (2 to 5) and a small number of multiplications per encrypted word (2.1 to 6.25) at the cost of slightly larger ciphertext expansion (1.26 to 1.31). The security of Rubato is supported by comprehensive analysis including symmetric and LWE cryptanalysis. Compared to HERA within the RtF framework, client-side and server-side throughput is improved by 22.9% and 32.2%, respectively, at the cost of only 1.6% larger ciphertext expansion.

2021

ASIACRYPT

Transciphering Framework for Approximate Homomorphic Encryption
📺
Abstract

Homomorphic encryption (HE) is a promising cryptographic primitive that enables computation over encrypted data, with a variety of applications including medical, genomic, and financial tasks. In Asiacrypt 2017, Cheon et al. proposed the CKKS scheme to efficiently support approximate computation over encrypted data of real numbers. HE schemes including CKKS, nevertheless, still suffer from slow encryption speed and large ciphertext expansion compared to symmetric cryptography.
In this paper, we propose a novel hybrid framework, dubbed RtF (Real-to-Finite-field) framework, that supports CKKS. The main idea behind this construction is to combine the CKKS and the FV homomorphic encryption schemes, and use a stream cipher using modular arithmetic in between. As a result, real numbers can be encrypted without significant ciphertext expansion or computational overload on the client side.
As an instantiation of the stream cipher in our framework, we propose a new HE-friendly cipher, dubbed HERA, and extensively analyze its security and efficiency. The main feature of HERA is that it uses a simple randomized key schedule.
Compared to recent HE-friendly ciphers such as FLIP and Rasta using randomized linear layers, HERA requires a smaller number of random bits. For this reason, HERA significantly outperforms existing HE-friendly ciphers on both the client and the server sides.
With the RtF transciphering framework combined with HERA at the 128-bit security level, we achieve small ciphertext expansion ratio with a range of 1.23 to 1.54, which is at least 23 times smaller than using (symmetric) CKKS-only, assuming the same precision bits and the same level of ciphertexts at the end of the framework. We also achieve
1.6 $\mu$s and 21.7 MB/s for latency and throughput on the client side, which are 9085 times and 17.8 times faster than the CKKS-only environment, respectively.

2021

ASIACRYPT

Toward a Fully Secure Authenticated Encryption Scheme From a Pseudorandom Permutation
📺
Abstract

In this paper, we propose a new block cipher-based authenticated encryption scheme, dubbed the Synthetic Counter with Masking (SCM) mode. SCM follows the NSIV paradigm proposed by Peyrin and Seurin (CRYPTO 2016), where a keyed hash function accepts a nonce N with associated data and a message, yielding an authentication tag T, and then the message is encrypted by a counter-like mode using both T and N. Here we move one step further by encrypting nonces; in the encryption part, the inputs to the block cipher are determined by T, counters, and an encrypted nonce, and all its outputs are also masked by an (additional) encrypted nonce, yielding keystream blocks.
As a result, we obtain, for the first time, a block cipher-based authenticated encryption scheme of rate 1/2 that provides n-bit security with respect to the query complexity (ignoring the influence of message length) in the nonce-respecting setting, and at the same time guarantees graceful security degradation in the faulty nonce model, when the underlying n-bit block cipher is modeled as a secure pseudorandom permutation. Seen as a slight variant of GCM-SIV, SCM is also parallelizable and inverse-free, and its performance is still comparable to GCM-SIV.

2021

TOSC

CTET+: A Beyond-Birthday-Bound Secure Tweakable Enciphering Scheme Using a Single Pseudorandom Permutation
📺
Abstract

In this work, we propose a construction of 2-round tweakable substitutionpermutation networks using a single secret S-box. This construction is based on non-linear permutation layers using independent round keys, and achieves security beyond the birthday bound in the random permutation model. When instantiated with an n-bit block cipher with ωn-bit keys, the resulting tweakable block cipher, dubbed CTET+, can be viewed as a tweakable enciphering scheme that encrypts ωκ-bit messages for any integer ω ≥ 2 using 5n + κ-bit keys and n-bit tweaks, providing 2n/3-bit security.Compared to the 2-round non-linear SPN analyzed in [CDK+18], we both minimize it by requiring a single permutation, and weaken the requirements on the middle linear layer, allowing better performance. As a result, CTET+ becomes the first tweakable enciphering scheme that provides beyond-birthday-bound security using a single permutation, while its efficiency is still comparable to existing schemes including AES-XTS, EME, XCB and TET. Furthermore, we propose a new tweakable enciphering scheme, dubbed AES6-CTET+, which is an actual instantiation of CTET+ using a reduced round AES block cipher as the underlying secret S-box. Extensivecryptanalysis of this algorithm allows us to claim 127 bits of security.Such tweakable enciphering schemes with huge block sizes become desirable in the context of disk encryption, since processing a whole sector as a single block significantly worsens the granularity for attackers when compared to, for example, AES-XTS, which treats every 16-byte block on the disk independently. Besides, as a huge amount of data is being stored and encrypted at rest under many different keys in clouds, beyond-birthday-bound security will most likely become necessary in the short term.

2020

EUROCRYPT

Tight Security Bounds for Double-block Hash-then-Sum MACs
📺
Abstract

In this work, we study the security of deterministic MAC constructions with a double-block internal state, captured by the double-block hash-then-sum (DBH) paradigm. Most DBH constructions, including PolyMAC, SUM-ECBC, PMAC-Plus, 3kf9 and LightMAC-Plus, have been proved to be pseudorandom up to 2^{2n/3} queries when they are instantiated with an n-bit block cipher, while the best known generic attacks require 2^{3n/4} queries.
We close this gap by proving the PRF-security of DBH constructions up to 2^{3n/4} queries (ignoring the maximum message length). The core of the security proof is to refine Mirror theory that systematically estimates the number of solutions to a system of equations and non-equations, and apply it to prove the security of the finalization function. Then we identify security requirements of the internal hash functions to ensure 3n/4-bit security of the resulting constructions when combined with the finalization function.
Within this framework, we prove the security of DBH whose internal hash function is given as the concatenation of a universal hash function using two independent keys. This class of constructions include PolyMAC and SUM-ECBC. Moreover, we prove the security of PMAC-Plus, 3kf9 and LightMAC-Plus up to 2^{3n/4} queries.

2020

ASIACRYPT

Improved Security Analysis for Nonce-based Enhanced Hash-then-Mask MACs
📺
Abstract

In this paper, we prove that the nonce-based enhanced hash-then-mask MAC (nEHtM) is secure up to 2^{3n/4} MAC queries and 2^n verification queries (ignoring logarithmic factors) as long as the number of faulty queries \mu is below 2^{3n/8}, significantly improving the previous bound by Dutta et al. Even when \mu goes beyond 2^{3n/8}, nEHtM enjoys graceful degradation of security.
The second result is to prove the security of PRF-based nEHtM; when nEHtM is based on an n-to-s bit random function for a fixed size s such that 1 <= s <= n, it is proved to be secure up to any number of MAC queries and 2^s verification queries, if (1) s = n and \mu < 2^{n/2} or (2) n/2 < s < 2^{n-s} and \mu < max{2^{s/2}, 2^{n-s}}, or (3) s <= n/2 and \mu < 2^{n/2}. This result leads to the security proof of truncated nEHtM that returns only s bits of the original tag since a truncated permutation can be seen as a pseudorandom function. In particular, when s <= 2n/3, the truncated nEHtM is secure up to 2^{n - s/2} MAC queries and 2^s verification queries as long as \mu < min{2^{n/2}, 2^{n-s}}. For example, when s = n/2 (resp. s = n/4), the truncated nEHtM is secure up to 2^{3n/4} (resp. 2^{7n/8}) MAC queries. So truncation might provide better provable security than the original nEHtM with respect to the number of MAC queries.

2020

TOSC

Highly Secure Nonce-based MACs from the Sum of Tweakable Block Ciphers
📺
Abstract

Tweakable block ciphers (TBCs) have proven highly useful to boost the security guarantees of authentication schemes. In 2017, Cogliati et al. proposed two MACs combining TBC and universal hash functions: a nonce-based MAC called NaT and a deterministic MAC called HaT. While both constructions provide high security, their properties are complementary: NaT is almost fully secure when nonces are respected (i.e., n-bit security, where n is the block size of the TBC, and no security degradation in terms of the number of MAC queries when nonces are unique), while its security degrades gracefully to the birthday bound (n/2 bits) when nonces are misused. HaT has n-bit security and can be used naturally as a nonce-based MAC when a message contains a nonce. However, it does not have full security even if nonces are unique.This work proposes two highly secure and efficient MACs to fill the gap: NaT2 and eHaT. Both provide (almost) full security if nonces are unique and more than n/2-bit security when nonces can repeat. Based on NaT and HaT, we aim at achieving these properties in a modular approach. Our first proposal, Nonce-as-Tweak2 (NaT2), is the sum of two NaT instances. Our second proposal, enhanced Hash-as-Tweak (eHaT), extends HaT by adding the output of an additional nonce-depending call to the TBC and prepending nonce to the message. Despite the conceptual simplicity, the security proofs are involved. For NaT2 in particular, we rely on the recent proof framework for Double-block Hash-then-Sum by Kim et al. from Eurocrypt 2020.

2019

ASIACRYPT

Indifferentiability of Truncated Random Permutations
Abstract

One of natural ways of constructing a pseudorandom function from a pseudorandom permutation is to simply truncate the output of the permutation. When n is the permutation size and m is the number of truncated bits, the resulting construction is known to be indistinguishable from a random function up to $$2^{{n+m}\over 2}$$ queries, which is tight.In this paper, we study the indifferentiability of a truncated random permutation where a fixed prefix is prepended to the inputs. We prove that this construction is (regularly) indifferentiable from a public random function up to $$\min \{2^{{n+m}\over 3}, 2^{m}, 2^\ell \}$$ queries, while it is publicly indifferentiable up to $$\min \{ \max \{2^{{n+m}\over 3}, 2^{n \over 2}\}, 2^\ell \}$$ queries, where $$\ell $$ is the size of the fixed prefix. Furthermore, the regular indifferentiability bound is proved to be tight when $$m+\ell \ll n$$.Our results significantly improve upon the previous bound of $$\min \{ 2^{m \over 2}, 2^\ell \}$$ given by Dodis et al. (FSE 2009), allowing us to construct, for instance, an $$\frac{n}{2}$$-to-$$\frac{n}{2}$$ bit random function that makes a single call to an n-bit permutation, achieving $$\frac{n}{2}$$-bit security.

2018

ASIACRYPT

Tweakable Block Ciphers Secure Beyond the Birthday Bound in the Ideal Cipher Model
Abstract

We propose a new construction of tweakable block ciphers from standard block ciphers. Our construction, dubbed $$\mathsf {XHX2}$$, is the cascade of two independent $$\mathsf {XHX}$$ block ciphers, so it makes two calls to the underlying block cipher using tweak-dependent keys. We prove the security of $$\mathsf {XHX2}$$ up to $$\min \{2^{2(n+m)/3},2^{n+m/2}\}$$ queries (ignoring logarithmic factors) in the ideal cipher model, when the block cipher operates on n-bit blocks using m-bit keys. The $$\mathsf {XHX2}$$ tweakable block cipher is the first construction that achieves beyond-birthday-bound security with respect to the input size of the underlying block cipher in the ideal cipher model.

#### Coauthors

- Jihoon Cho (1)
- Wonseok Choi (4)
- Benoît Cogliati (1)
- Jordan Ethan (1)
- Jincheol Ha (2)
- Akiko Inoue (1)
- Seongkwang Kim (3)
- Virginie Lallemand (1)
- Yeongmin Lee (2)
- Joohee Lee (1)
- Jooyoung Lee (9)
- Eik List (1)
- Kazuhiko Minematsu (1)
- Marine Minier (1)
- Dukjae Moon (1)
- Yusuke Naito (1)
- Mincheol Son (1)
- HyoJin Yoon (1)