## CryptoDB

### Kenneth G. Paterson

#### Publications

**Year**

**Venue**

**Title**

2022

EUROCRYPT

Anonymous, Robust Post-Quantum Public Key Encryption
Abstract

A core goal of the NIST PQC competition is to produce PKE schemes which, even if attacked with a large-scale quantum computer, maintain the security guarantees needed by applications. The main security focus in the NIST PQC context has been IND-CCA security, but other applications demand that PKE schemes provide 'anonymity' (Bellare et al., ASIACRYPT 2001), and 'robustness' (Abdalla et al., TCC 2010). Examples of such applications include anonymous cryptocurrencies, searchable encryption, and auction protocols. However, almost nothing is known about how to build post-quantum PKE schemes offering these security properties. In particular, the status of the NIST PQC candidates with respect to anonymity and robustness is unknown.
This paper initiates a systematic study of anonymity and robustness for post-quantum PKE schemes. Firstly, we identify implicit rejection as a crucial design choice shared by most post-quantum KEMs, show that implicit rejection renders prior results on anonymity and robustness for KEM-DEM PKEs inapplicable, and transfer prior results to the implicit-rejection setting where possible. Secondly, since they are widely used to build post-quantum PKEs, we examine how the Fujisaki-Okamoto (FO) transforms (Fujisaki and Okamoto, Journal of Cryptology 2013) confer robustness and enhance weak anonymity of a base PKE.
We then leverage our theoretical results to study the anonymity and robustness of three NIST KEM finalists---Saber, Kyber, and Classic McEliece---and one alternate, FrodoKEM. Overall, our findings for robustness are definitive: we provide positive robustness results for Saber, Kyber, and FrodoKEM, and a negative result for Classic McEliece. Our negative result stems from a striking property of KEM-DEM PKE schemes built with the Classic McEliece KEM: for any message 'm', we can construct a single hybrid ciphertext 'c' which decrypts to the chosen 'm' under any Classic McEliece private key.
Our findings for anonymity are more mixed: we identify barriers to proving anonymity for Saber, Kyber, and Classic McEliece. We also found that in the case of Saber and Kyber, these barriers lead to issues with their IND-CCA security claims. We have worked with the Saber and Kyber teams to fix these issues, but they remain unresolved. On the positive side, we were able to prove anonymity for FrodoKEM and a variant of Saber introduced by D'Anvers et al. (AFRICACRYPT 2018). Our analyses of these two schemes also identified technical gaps in their IND-CCA security claims, but we were able to fix them.

2020

JOFC

Multilinear Maps from Obfuscation
Abstract

We provide constructions of multilinear groups equipped with natural hard problems from indistinguishability obfuscation, homomorphic encryption, and NIZKs. This complements known results on the constructions of indistinguishability obfuscators from multilinear maps in the reverse direction. We provide two distinct, but closely related constructions and show that multilinear analogues of the $${\text {DDH}} $$ DDH assumption hold for them. Our first construction is symmetric and comes with a $$\kappa $$ κ -linear map $$\mathbf{e }: {{\mathbb {G}}}^\kappa \longrightarrow {\mathbb {G}}_T$$ e : G κ ⟶ G T for prime-order groups $${\mathbb {G}}$$ G and $${\mathbb {G}}_T$$ G T . To establish the hardness of the $$\kappa $$ κ -linear $${\text {DDH}} $$ DDH problem, we rely on the existence of a base group for which the $$\kappa $$ κ -strong $${\text {DDH}} $$ DDH assumption holds. Our second construction is for the asymmetric setting, where $$\mathbf{e }: {\mathbb {G}}_1 \times \cdots \times {\mathbb {G}}_{\kappa } \longrightarrow {\mathbb {G}}_T$$ e : G 1 × ⋯ × G κ ⟶ G T for a collection of $$\kappa +1$$ κ + 1 prime-order groups $${\mathbb {G}}_i$$ G i and $${\mathbb {G}}_T$$ G T , and relies only on the 1-strong $${\text {DDH}} $$ DDH assumption in its base group. In both constructions, the linearity $$\kappa $$ κ can be set to any arbitrary but a priori fixed polynomial value in the security parameter. We rely on a number of powerful tools in our constructions: probabilistic indistinguishability obfuscation, dual-mode NIZK proof systems (with perfect soundness, witness-indistinguishability, and zero knowledge), and additively homomorphic encryption for the group $$\mathbb {Z}_N^{+}$$ Z N + . At a high level, we enable “bootstrapping” multilinear assumptions from their simpler counterparts in standard cryptographic groups and show the equivalence of PIO and multilinear maps under the existence of the aforementioned primitives.

2019

TOSC

libInterMAC: Beyond Confidentiality and Integrity in Practice
📺
Abstract

Boldyreva et al. (Eurocrypt 2012) defined a fine-grained security model capturing ciphertext fragmentation attacks against symmetric encryption schemes. The model was extended by Albrecht et al. (CCS 2016) to include an integrity notion. The extended security model encompasses important security goals of SSH that go beyond confidentiality and integrity to include length hiding and denial-of-service resistance properties. Boldyreva et al. also defined and analysed the InterMAC scheme, while Albrecht et al. showed that InterMAC satisfies stronger security notions than all currently available SSH encryption schemes. In this work, we take the InterMAC scheme and make it fully ready for use in practice. This involves several steps. First, we modify the InterMAC scheme to support encryption of arbitrary length plaintexts and we replace the use of Encrypt-then-MAC in InterMAC with modern noncebased authenticated encryption. Second, we describe a reference implementation of the modified InterMAC scheme in the form of the library libInterMAC. We give a performance analysis of libInterMAC. Third, to test the practical performance of libInterMAC, we implement several InterMAC-based encryption schemes in OpenSSH and carry out a performance analysis for the use-case of file transfer using SCP. We measure the data throughput and the data overhead of using InterMAC-based schemes compared to existing schemes in OpenSSH. Our analysis shows that, for some network set-ups, using InterMAC-based schemes in OpenSSH only moderately affects performance whilst providing stronger security guarantees compared to existing schemes.

2019

PKC

Safety in Numbers: On the Need for Robust Diffie-Hellman Parameter Validation
Abstract

We consider the problem of constructing Diffie-Hellman (DH) parameters which pass standard approaches to parameter validation but for which the Discrete Logarithm Problem (DLP) is relatively easy to solve. We consider both the finite field setting and the elliptic curve setting.For finite fields, we show how to construct DH parameters (p, q, g) for the safe prime setting in which
$$p=2q+1$$
is prime, q is relatively smooth but fools random-base Miller-Rabin primality testing with some reasonable probability, and g is of order q mod p. The construction involves modifying and combining known methods for obtaining Carmichael numbers. Concretely, we provide an example with 1024-bit p which passes OpenSSL’s Diffie-Hellman validation procedure with probability
$$2^{-24}$$
(for versions of OpenSSL prior to 1.1.0i). Here, the largest factor of q has 121 bits, meaning that the DLP can be solved with about
$$2^{64}$$
effort using the Pohlig-Hellman algorithm. We go on to explain how this parameter set can be used to mount offline dictionary attacks against PAKE protocols. In the elliptic curve case, we use an algorithm of Bröker and Stevenhagen to construct an elliptic curve E over a finite field
$${\mathbb {F}}_p$$
having a specified number of points n. We are able to select n of the form
$$h\cdot q$$
such that h is a small co-factor, q is relatively smooth but fools random-base Miller-Rabin primality testing with some reasonable probability, and E has a point of order q. Concretely, we provide example curves at the 128-bit security level with
$$h=1$$
, where q passes a single random-base Miller-Rabin primality test with probability 1/4 and where the elliptic curve DLP can be solved with about
$$2^{44}$$
effort. Alternatively, we can pass the test with probability 1/8 and solve the elliptic curve DLP with about
$$2^{35.5}$$
effort. These ECDH parameter sets lead to similar attacks on PAKE protocols relying on elliptic curves.Our work shows the importance of performing proper (EC)DH parameter validation in cryptographic implementations and/or the wisdom of relying on standardised parameter sets of known provenance.

2018

TOSC

Frequency-smoothing encryption: preventing snapshot attacks on deterministically encrypted data
Abstract

Statistical analysis of ciphertexts has been recently used to carry out devastating inference attacks on deterministic encryption (Naveed, Kamara, and Wright, CCS 2015), order-preserving/revealing encryption (Grubbs et al., S&P 2017), and searchable encryption (Pouliot and Wright, CCS 2016). At the heart of these inference attacks is classical frequency analysis. In this paper, we propose and evaluate another classical technique, homophonic encoding, as a means to combat these attacks. We introduce and develop the concept of frequency-smoothing encryption (FSE) which provably prevents inference attacks in the snapshot attack model, wherein the adversary obtains a static snapshot of the encrypted data, while preserving the ability to efficiently and privately make point queries. We provide provably secure constructions for FSE schemes, and we empirically assess their security for concrete parameters by evaluating them against real data. We show that frequency analysis attacks (and optimal generalisations of them for the FSE setting) no longer succeed.

2018

TCHES

Cold Boot Attacks on Ring and Module LWE Keys Under the NTT
★
Abstract

In this work, we consider the ring- and module- variants of the LWE problem and investigate cold boot attacks on cryptographic schemes based on these problems, wherein an attacker is faced with the problem of recovering a scheme’s secret key from a noisy version of that key. The leakage resilience of cryptography based on the learning with errors (LWE) problem has been studied before, but there are only limited results considering the parameters observed in cold boot attack scenarios. There are two main encodings for storing ring- and module-LWE keys, and, as we show, the performance of cold boot attacks can be highly sensitive to the exact encoding used. The first encoding stores polynomial coefficients directly in memory. The second encoding performs a number theoretic transform (NTT) before storing the key, a commonly used method leading to more efficient implementations. We first give estimates for a cold boot attack complexity on the first encoding method based on standard algorithms; this analysis confirms that this encoding method is vulnerable to cold boot attacks only at very low bit-flip rates. We then show that, for the second encoding method, the structure introduced by using an NTT is exploitable in the cold boot setting: we develop a bespoke attack strategy that is much cheaper than our estimates for the first encoding when considering module-LWE keys. For example, at a 1% bit-flip rate (which corresponds roughly to what can be achieved in practice for cold boot attacks when applying cooling), a cold boot attack on Kyber KEM parameters has a cost of 243 operations when the second, NTT-based encoding is used for key storage, compared to 270 operations with the first encoding. On the other hand, in the case of the ring-LWE-based KEM, New Hope, the cold boot attack complexities are similar for both encoding methods.

2014

ASIACRYPT

2012

PKC

#### Program Committees

- CHES 2022
- Crypto 2018
- FSE 2016
- Crypto 2016
- Eurocrypt 2015
- PKC 2014
- Eurocrypt 2013
- Asiacrypt 2013
- Crypto 2012
- Asiacrypt 2012
- Eurocrypt 2011 (Program chair)
- Crypto 2011
- PKC 2010
- PKC 2009
- Eurocrypt 2008
- Crypto 2007
- PKC 2006
- Eurocrypt 2006
- Asiacrypt 2006

#### Coauthors

- Michel Abdalla (1)
- Sattam S. Al-Riyami (2)
- Martin R. Albrecht (6)
- Mihir Bellare (2)
- Fabrice Benhamouda (1)
- Simon R. Blackburn (1)
- Alexandra Boldyreva (2)
- Torben Brandt Hansen (1)
- Liqun Chen (1)
- Jean Paul Degabriele (3)
- Alexander W. Dent (1)
- Amit Deo (1)
- Adam Everspaugh (1)
- Pooya Farshim (4)
- Marc Fischlin (1)
- Eduarda S. V. Freire (1)
- Eduarda S.V. Freire (1)
- Steven D. Galbraith (1)
- Paul Grubbs (1)
- Felix Günther (1)
- Shuai Han (1)
- Dennis Hofheinz (4)
- Eike Kiltz (1)
- Hugo Krawczyk (1)
- Caroline Kudla (2)
- Marie-Sarah Lacharité (1)
- Enrique Larraia (2)
- Benoît Libert (3)
- Shengli Liu (1)
- Atul Luykx (1)
- Varun Maram (1)
- Giorgia Azzurra Marson (1)
- Jake Massimo (1)
- Kanta Matsuura (1)
- Bart Mennink (1)
- Chris J. Mitchell (1)
- Sean Murphy (1)
- Alain Passelègue (1)
- Bertram Poettering (2)
- Antigoni Polychroniadou (1)
- Elizabeth A. Quaglia (2)
- Thomas Ristenpart (2)
- Phillip Rogaway (1)
- Jacob C. N. Schuldt (6)
- Samuel Scott (1)
- Thomas Shrimpton (1)
- Dale L. Sibborn (2)
- Martijn Stam (3)
- Christoph Striecks (1)
- Susan Thomson (2)
- Gaven J. Watson (2)
- Hoeteck Wee (1)
- Peter R. Wild (1)
- Joanne Woodage (1)
- Arnold K. L. Yau (2)