What a lovely hat

The Supersingular Isogeny Diffie-Hellman (SIDH) scheme is a public key cryptosystem that was submitted to the National Institute of Standards and Technology's competition for the standardization of post-quantum cryptography protocols. The private key in SIDH consists of an isogeny whose degree is a prime power. In July 2022, Castryck and Decru discovered an attack that completely breaks the scheme by recovering Bob's secret key, using isogenies between higher dimensional abelian varieties to...

We construct the first multi-input functional encryption (MIFE) and indistinguishability obfuscation (iO) schemes for pseudorandom functionalities, where the output of the functionality is pseudorandom for every input seen by the adversary. Our MIFE scheme relies on LWE and evasive LWE (Wee, Eurocrypt 2022 and Tsabary, Crypto 2022) for constant arity functions, and a strengthening of evasive LWE for polynomial arity. Thus, we obtain the first MIFE and iO schemes for a nontrivial...

Cryptographic group actions are a leading contender for post-quantum cryptography, and have also been used in the development of quantum cryptographic protocols. In this work, we explore quantum group actions, which consist of a group acting on a set of quantum states. We show the following results: 1. In certain settings, statistical (even query bounded) security is impossible, analogously to post-quantum classical group actions. 2. We construct quantum state group actions and prove that...

Much work has been done recently on developing password-authenticated key exchange (PAKE) mechanisms with post-quantum security. However, modern guidance recommends the use of hybrid schemes—schemes which rely on the combined hardness of a post-quantum assumption, e.g., learning with Errors (LWE), and a more traditional assumption, e.g., decisional Diffie-Hellman. To date, there is no known hybrid PAKE construction, let alone a general method for achieving such. In this paper, we present...

We present $\mathsf{Protoss}$, a new balanced PAKE protocol with optimal communication efficiency. Messages are only 160 bits long and the computational complexity is lower than all previous approaches. Our protocol is proven secure in the random oracle model and features a security proof in a strong security model with multiple parties and multiple sessions, while allowing for generous attack queries including multiple $\mathsf{Test}$-queries. Moreover, the proof is in the practically...

The Noise specification describes how to systematically construct a large family of Diffie-Hellman based key exchange protocols, including the secure transports used by WhatsApp, Lightning, and WireGuard. As the specification only makes informal security claims, earlier work has explored which formal security properties may be enjoyed by protocols in the Noise framework, yet many important questions remain open. In this work we provide the most comprehensive, systematic analysis of the...

In the (preprocessing) Decisional Diffie-Hellman (DDH) problem, we are given a cyclic group $G$ with a generator $g$ and a prime order $N$, and we want to prepare some advice of size $S$, such that we can efficiently distinguish $(g^{x},g^{y},g^{xy})$ from $(g^{x},g^{y},g^{z})$ in time $T$ for uniformly and independently chosen $x,y,z$ from $\mathbb{Z}_N$. This is a central cryptographic problem whose computational hardness underpins many widely deployed schemes, such as the Diffie–Hellman...

The use of Internet of Things (IoT) devices in embedded systems has become increasingly popular with advancing technologies. These devices become vulnerable to cyber attacks as they gain popularity. The cryptographic operations performed for the purpose of protection against cyber attacks are crucial to yield fast results in open networks and not slow down network traffic. Therefore, to enhance communication security, studies have been conducted in the literature on using asymmetric...

Oblivious transfer (OT) is a fundamental cryptographic protocol that plays a crucial role in secure multi-party computation (MPC). Most practical OT protocols by, e.g., Naor and Pinkas (SODA'01) or Chou and Orlandi (Latincrypt'15), are based on Diffie-Hellman (DH)-like assumptions and not post-quantum secure. In contrast, many other components of MPC protocols, including garbled circuits and secret sharings, are post-quantum secure. The reliance on non-post-quantum OT protocols presents a...

Transitioning from classically to quantum secure key agreement protocols may require to exchange fundamental components, for example, exchanging Diffie-Hellman-like key exchange with a key encapsulation mechanism (KEM). Accordingly, the corresponding security proof can no longer rely on the Diffie-Hellman assumption, thus invalidating the security guarantees. As a consequence, the security properties have to be re-proven under a KEM-based security notion. We initiate the study of the...

We revisit the construction of multiparty non-interactive key-exchange protocols with fine-grained security, which was recently studied in (Afshar et al., Eurocrypt 2023). Their work introduced a 4-party non-interactive key exchange with quadratic hardness, and proved it secure in Shoup's generic group model. This positive result was complemented with a proof that $n$-party non-interactive key exchange with superquadratic security cannot exist in Maurer's generic group model, for any $n\geq...

Signal recently deployed a new handshake protocol named PQXDH to protect against "harvest-now-decrypt-later" attacks of a future quantum computer. To this end, PQXDH adds a post-quantum KEM to the Diffie-Hellman combinations of the prior X3DH handshake. In this work, we give a reductionist security analysis of Signal's PQXDH handshake in a game-based security model that captures the targeted "maximum-exposure" security against both classical and quantum adversaries, allowing fine-grained...

Adaptor signatures can be viewed as a generalized form of the standard digital signature schemes where a secret randomness is hidden within a signature. Adaptor signatures are a recent cryptographic primitive and are becoming an important tool for blockchain applications such as cryptocurrencies to reduce on-chain costs, improve fungibility, and contribute to off-chain forms of payment in payment-channel networks, payment-channel hubs, and atomic swaps. However, currently used adaptor...

We propose a new key exchange protocol based on the Generalised Diffie-Hellman Key Exchange. In the latter, instead of using a group-action, we consider a semigroup action. In our proposal, the semigroup is the set of oriented knots in $\mathbb{S}^3$ with the operation of connected sum. As a semigroup action, we choose the action of the semigroup on itself through the connected sum. For the protocol to work, we need to use knot invariants, which allow us to create the shared secret key...

In this paper, we construct the first password authenticated key exchange (PAKE) scheme from isogenies with Universal Composable (UC) security in the random oracle model (ROM). We also construct the first two PAKE schemes with UC security in the quantum random oracle model (QROM), one is based on the learning with error (LWE) assumption, and the other is based on the group-action decisional Diffie- Hellman (GA-DDH) assumption in the isogeny setting. To obtain our UC-secure PAKE scheme in...

Weak forward secrecy (wFS) of authenticated key exchange (AKE) protocols is a passive variant of (full) forward secrecy (FS). A natural mechanism to upgrade from wFS to FS is the use of key confirmation messages which compute a message authentication code (MAC) over the transcript. Unfortunately, Gellert, Gjøsteen, Jacobson and Jager (GGJJ, CRYPTO 2023) show that this mechanism inherently incurs a loss proportional to the number of users, leading to an overall non-tight reduction, even if...

The iMessage PQ3 protocol is an end-to-end encrypted messaging protocol designed for exchanging data in long-lived sessions between two devices. It aims to provide classical and post-quantum confidentiality for forward secrecy and post-compromise secrecy, as well as classical authentication. Its initial authenticated key exchange is constructed from digital signatures plus elliptic curve Diffie–Hellman and post-quantum key exchanges; to derive per-message keys on an ongoing basis, it employs...

At EUROCRYPT’23, Castryck and Decru, Maino et al., and Robert present efficient attacks against supersingular isogeny Diffie-Hellman key exchange protocol (SIDH). Drawing inspiration from these attacks, Andrea Basso, Luciano Maino, and Giacomo Pope introduce FESTA, an isogeny-based trapdoor function, along with a corresponding IND-CCA secure public key encryption (PKE) protocol at ASIACRYPT’23. FESTA incorporates either a diagonal or circulant matrix into the secret key to mask torsion...

In the past three decades, an impressive body of knowledge has been built around secure and private password authentication. In particular, secure password-authenticated key exchange (PAKE) protocols require only minimal overhead over a classical Diffie-Hellman key exchange. PAKEs are also known to fulfill strong composable security guarantees that capture many password-specific concerns such as password correlations or password mistyping, to name only a few. However, to enjoy both...

The Signal protocol and its X3DH key exchange core are regularly used by billions of people in applications like WhatsApp but are unfortunately not quantum-secure. Thus, designing an efficient and post-quantum secure X3DH alternative is paramount. Notably, X3DH supports asynchronicity, as parties can immediately derive keys after uploading them to a central server, and deniability, allowing parties to plausibly deny having completed key exchange. To satisfy these constraints, existing...

In this paper, we study the design of efficient signature and public-key encryption (PKE) schemes in the presence of both leakage and tampering attacks. Firstly, we formalize the strong leakage and tamper-resilient (sLTR) security model for signature, which provides strong existential unforgeability, and deals with bounded leakage and restricted tampering attacks, as a counterpart to the sLTR security introduced by Sun et al. (ACNS 2019) for PKE. Then, we present direct constructions...

Vehicle Ad Hoc Networks (VANETs) play a pivotal role in intelligent transportation systems, offering dynamic communication between vehicles, Road Side Units (RSUs), and the internet. Given the open-access nature of VANETs and the associated threats, such as impersonation and privacy violations, ensuring the security of these communications is of utmost importance. This paper presents the Identity-based Cluster Authentication and Key Exchange (ID-CAKE) scheme, a new approach to address...

The Internet Key Exchange version 2 (IKEv2) (RFC 7296) is a component of IPsec used to authenticate two parties (the initiator and responder) to each other and to establish a set of security parameters for the communications. The security parameters include secret keys to encrypt and authenticate data as well as the negotiation of a set of cryptographic algorithms. The core documentation uses exclusively Diffie-Hellman exchanges to agree the security information. However, this is not a...

In 2012, Ding, Xie and Lin designed a key exchange protocol based on Ring-LWE problem, called the DXL key exchange protocol, which can be seen as an extended version of the Diffie-Hellman key exchange. In this protocol, Ding et al. achieved key exchange between the communicating parties according to the associativity of matrix multiplications, that is, $(x^T\cdot A)\cdot y = x^T\cdot (A\cdot y)$, where $x,y$ are column vectors and $A$ is a square matrix. However, the DXL key exchange...

This paper analyses the Secure Remote Password Protocol (SRP) in the context of provable security. SRP is an asymmetric Password-Authenticated Key Exchange (aPAKE) protocol introduced in 1998. It allows a client to establish a shared cryptographic key with a server based on a password of potentially low entropy. Although the protocol was part of several standardization efforts, and is deployed in numerous commercial applications such as Apple Homekit, 1Password or Telegram, it still lacks a...

Non-interactive key exchange (NIKE) schemes like the Diffie-Hellman key exchange are a widespread building block in several cryptographic protocols. Since the Diffie-Hellman key exchange is not post-quantum secure, it is important to investigate post-quantum alternatives. We analyze the security of the LWE-based NIKE by Ding et al. (ePrint 2012) and Peikert (PQCrypt 2014) in a multi-user setting where the same public key is used to generate shared keys with multiple other users. The...

Web3 applications based on blockchains regularly need access to randomness that is unbiased, unpredictable, and publicly verifiable. For Web3 gaming applications, this becomes a crucial selling point to attract more users by providing credibility to the "random reward" distribution feature. A verifiable random function (VRF) protocol satisfies these requirements naturally, and there is a tremendous rise in the use of VRF services. As most blockchains cannot maintain the secret keys required...

We propose a generic construction of password-based authenticated key exchange (PAKE) from key encapsulation mechanisms (KEM). Assuming that the KEM is oneway secure against plaintext-checkable attacks (OW-PCA), we prove that our PAKE protocol is \textit{tightly secure} in the Bellare-Pointcheval-Rogaway model (EUROCRYPT 2000). Our tight security proofs require ideal ciphers and random oracles. The OW-PCA security is relatively weak and can be implemented tightly with the Diffie-Hellman...

Shor's algorithm efficiently solves the discrete logarithm problem (DLP) by taking advantage of the commutativity structure of the group underlying the problem. To counter Shor's algorithm, Horan et al. propose a DLP analogue in the semidirect product semigroup $G\rtimes \mathrm{End}(G)$, given a (semi)group $G$, to construct a quantum-resistant Diffie-Hellman key exchange based on it. For general (semi)groups, the semidirect discrete logarithm problem (SDLP) can be reduced to the hidden...

The major objective of this paper is to present a theoretical model for an algorithm that has not been previously described in the literature, capable of generating a secret key through the transmission of data over a public channel. We explain how the method creates a shared secret key by attaining commutativity through the multiplication of the modular exponentiation of a minimum of two bases and an equal number of private exponents for each party involved in the exchange. In addition, we...

We construct the first tightly secure authenticated key exchange (AKE) protocol from lattices. Known tight constructions are all based on Diffie-Hellman-like assumptions. Thus, our protocol is the first construction with tight security from a post-quantum assumption. Our AKE protocol is constructed tightly from a new security notion for key encapsulation mechanisms (KEMs), called one-way security against checkable chosen-ciphertext attacks (OW- ChCCA). We show how an OW-ChCCA secure KEM...

The Supersingular Isogeny Diffie-Hellman (SIDH) protocol has been the main and most efficient isogeny-based encryption protocol, until a series of breakthroughs led to a polynomial-time key-recovery attack. While some countermeasures have been proposed, the resulting schemes are significantly slower and larger than the original SIDH. In this work, we propose a new countermeasure technique that leads to significantly more efficient and compact protocols. To do so, we introduce the...

A Key Derivation Function (KDF) generates a uniform and highly random key-stream from weakly random key material. KDFs are broadly used in various security protocols such as digital signatures and key exchange protocols. HKDF, the most deployed KDF in practice, is based on the extract-then-expand paradigm. It is presently used, among others, in the Signal Protocol for end-to-end encrypted messaging. HKDF is a generic KDF for general input sources and thus is not optimized for...

Of the many families of cryptographic schemes proposed to be post-quantum, a relatively unexplored set of examples comes from group-based cryptography. One of the more central schemes from this area is the so-called Semidirect Product Key Exchange (SDPKE), a generalisation of Diffie-Hellman Key Exchange that is plausibly post-quantum. In this report we survey the state of the literature relating to SDPKE, providing a high-level discussion of security, as well as a comprehensive overview of...

In this work, we initiate a study of $K$-NIKE protocols in the fine-grained setting, in which there is a polynomial gap between the running time of the honest parties and that of the adversary. Our goal is to show the possibility, or impossibility, of basing such protocols on weaker assumptions than those of $K$-NIKE for $K \geq 3$. Our contribution is threefold. - We show that random oracles can be used to obtain fine-grained $K$-NIKE protocols for every constant $K$. In particular,...

Despite recent breakthrough results in attacking SIDH, the CSIDH protocol remains a secure post-quantum key exchange protocol with appealing properties. However, for obtaining efficient CSIDH instantiations one has to resort to small secret keys. In this work, we provide novel methods to analyze small key CSIDH, thereby introducing the representation method ---that has been successfully applied for attacking small secret keys in code- and lattice-based schemes--- also to the isogeny-based...

Computationally sound protocol verification tools promise to deliver full-strength cryptographic proofs for security protocols. Unfortunately, current tools lack either modularity or automation. We propose a new approach based on a novel use of information flow and refinement types for sound cryptographic proofs. Our framework, Owl, allows type-based modular descriptions of security protocols, wherein disjoint subprotocols can be programmed and automatically proved secure separately....

Password Authenticated Key Exchange (PAKE) have become a key building block in many security products as they provide interesting efficiency/security trade-offs. Indeed, a PAKE allows to dispense with the heavy public key infrastructures and its efficiency and portability make it well suited for applications such as Internet of Things or e-passports. With the emerging quantum threat and the effervescent development of post-quantum public key algorithms in the last five years, one would...

Blind signatures allow a signer to issue signatures on messages chosen by the signature recipient. The main property is that the recipient's message is hidden from the signer. There are many applications, including Chaum's e-cash system and Privacy Pass, where no special distribution of the signed message is required, and the message can be random. Interestingly, existing notions do not consider this practical use case separately. In this paper, we show that constraining the recipient's...

This is the second update of this report. In this update, we partially solve Open problem 2 and completely solve Open problem 3 from the previous version. By doing this we address one modification of the Panny's attack done by Nils Langius. In the first update we introduced conditions for choosing the parameters that render the attacks (both classical and quantum algorithms attacks) proposed by Lorenz Panny in March 2023 on the first variant, inapplicable. For the classical attack, we...

The advent of quantum computers has sparked significant interest in post-quantum cryptographic schemes, as a replacement for currently used cryptographic primitives. In this context, lattice-based cryptography has emerged as the leading paradigm to build post-quantum cryptography. However, all existing viable replacements of the classical Diffie-Hellman key exchange require additional rounds of interactions, thus failing to achieve all the benefits of this protocol. Although earlier work has...

The elliptic curve family of schemes has the lowest computational latency, memory use, energy consumption, and bandwidth requirements, making it the most preferred public key method for adoption into network protocols. Being suitable for embedded devices and applicable for key exchange and authentication, ECC is assuming a prominent position in the field of IoT cryptography. The attractive properties of the relatively new curve Curve448 contribute to its inclusion in the TLS1.3 protocol and...

We introduce CorrGapCDH, the Gap Computational Diffie-Hellman problem in the multi-user setting with Corruptions. In the random oracle model, our assumption tightly implies the security of the authenticated key exchange protocols NAXOS in the eCK model and (a simplified version of) X3DH without ephemeral key reveal. We prove hardness of CorrGapCDH in the generic group model, with optimal bounds matching the one of the discrete logarithm problem. We also introduce CorrCRGapCDH, a stronger...

Authenticated key-exchange (AKE) protocols are an important class of protocols that allow two parties to establish a common session key over an insecure channel such as the Internet to then protect their communication. They are widely deployed in security protocols such as TLS, IPsec and SSH. Besides the confidentiality of the communicated data, an orthogonal but increasingly important goal is the protection of the confidentiality of the identities of the involved parties (aka privacy). For...

Elliptic Curve Hidden Number Problem (EC-HNP) was first introduced by Boneh, Halevi and Howgrave-Graham at Asiacrypt 2001. To rigorously assess the bit security of the Diffie--Hellman key exchange with elliptic curves (ECDH), the Diffie--Hellman variant of EC-HNP, regarded as an elliptic curve analogy of the Hidden Number Problem (HNP), was presented at PKC 2017. This variant can also be used for practical cryptanalysis of ECDH key exchange in the situation of side-channel attacks. In...

In the context of quantum-resistant cryptography, cryptographic group actions offer an abstraction of isogeny-based cryptography in the Commutative Supersingular Isogeny Diffie-Hellman (CSIDH) setting. In this work, we revisit the security of two previously proposed natural protocols: the Group Action Hashed ElGamal key encapsulation mechanism (GA-HEG KEM) and the Group Action Hashed Diffie-Hellman non-interactive key-exchange (GA-HDH NIKE) protocol. The latter protocol has already been...

Elliptic curves are abelian varieties of dimension one; the two-dimensional analogue are abelian surfaces. In this work we present an algorithm to compute $(2^n,2^n)$-isogenies of abelian surfaces defined over finite fields. These isogenies are the natural generalization of $2^n$-isogenies of elliptic curves. Our algorithm is designed to be used in higher-dimensional variants of isogeny-based cryptographic protocols such as G2SIDH which is a genus-$2$ version of the Supersingular Isogeny...

We present an efficient key recovery attack on the Supersingular Isogeny Diffie-Hellman protocol (SIDH). The attack is based on Kani's "reducibility criterion" for isogenies from products of elliptic curves and strongly relies on the torsion point images that Alice and Bob exchange during the protocol. If we assume knowledge of the endomorphism ring of the starting curve then the classical running time is polynomial in the input size (heuristically), apart from the factorization of a small...

SIDH is a key exchange algorithm proposed by Jao and De Feo that is conjectured to be post-quantum secure. The majority of work based on an SIDH framework uses elliptic curves in Montgomery form; this includes the original work by Jao, De Feo and Plût and the sate of the art implementation of SIKE. Elliptic curves in twisted Edwards form have also been used due to their efficient elliptic curve arithmetic, and complete Edwards curves have been used for their benefit of providing added...

We present two provably secure password-authenticated key exchange (PAKE) protocols based on a commutative group action. To date the most important instantiation of isogeny-based group actions is given by CSIDH. To model the properties more accurately, we extend the framework of cryptographic group actions (Alamati et al., ASIACRYPT 2020) by the ability of computing the quadratic twist of an elliptic curve. This property is always present in the CSIDH setting and turns out to be crucial in...

We propose a new Diffie-Hellman-like Non-Interactive Key Exchange that uses the Lattice Isomorphisms as a building block. Our proposal also relies on a group action structure, implying a similar security setup as in the Commutative Supersingular Isogeny Diffie-Hellman (CSIDH) protocol where Kuperberg's algorithm applies. We short label our scheme as LIKE. As with the original Diffie-Hellman protocol, our proposed scheme is also passively secure. We provide a proof-of-concept constant-time...

We introduce PQNoise, a post-quantum variant of the Noise framework. We demonstrate that it is possible to replace the Diffie-Hellman key-exchanges in Noise with KEMs in a secure way. A challenge is the inability to combine key pairs of KEMs, which can be resolved by certain forms of randomness-hardening for which we introduce a formal abstraction. We provide a generic recipe to turn classical Noise patterns into PQNoise patterns. We prove that the resulting PQNoise patterns achieve...

The COVID-19 pandemic has caused many countries to deploy novel digital contact tracing (DCT) systems to boost the efficiency of manual tracing of infection chains. In this paper, we systematically analyze DCT solutions and categorize them based on their design approaches and architectures. We analyze them with regard to effectiveness, security, privacy, and ethical aspects and compare prominent solutions with regard to these requirements. In particular, we discuss the shortcomings of the...

Key exchange protocols from the learning with errors (LWE) problem share many similarities with the Diffie–Hellman–Merkle (DHM) protocol, which plays a central role in securing our Internet. Therefore, there has been a long time effort in designing authenticated key exchange directly from LWE to mirror the advantages of DHM-based protocols. In this paper, we revisit signal leakage attacks and show that the severity of these attacks against LWE-based (authenticated) key exchange is still...

The Oriented Supersingular Isogeny Diffie-Hellman is a post-quantum key exchange scheme recently introduced by Colò and Kohel. It is based on the group action of an ideal class group of a quadratic imaginary order on a subset of supersingular elliptic curves, and in this sense it can be viewed as a generalization of the popular isogeny based key exchange CSIDH. From an algorithmic standpoint, however, OSIDH is quite different from CSIDH. In a sense, OSIDH uses class groups which are more...

Tamarin Prover is a formal security analysis tool that is used to analyse security properties of various authentication and key exchange protocols. It provides built-ins like Diffie-Hellman, Hashing, XOR, Symmetric and Asymmetric encryption as well as Bilinear pairings. The shortfall in Tamarin Prover is that it does not support elliptic curve point addition operation. In this paper, we present a simple IBE (Identity-Based Encryption) based key exchange protocol and tamarin model. For...

Currently, public-key compression of supersingular isogeny Diffie-Hellman (SIDH) and its variant, supersingular isogeny key encapsulation (SIKE) involve pairing computation and discrete logarithm computation. Both of them require large storage for precomputation to accelerate the performance. In this paper, we propose a novel method to compute only three discrete logarithms instead of four, in exchange for computing a lookup table efficiently. We also suggest another alternative method to...

All instances of the semidirect key exchange protocol, a generalisation of the famous Diffie-Hellman key exchange protocol, satisfy the so-called ``telescoping equality''; in some cases, this equality has been used to construct an attack. In this report we present computational evidence suggesting that an instance of the scheme called `MOBS (Matrices Over Bitstrings)' is an example of a scheme where the telescoping equality has too many solutions to be a practically viable means to conduct an attack.

In 2014, the author conceived of a quantal version of the classical cryptographic Diffie-Hellman key exchange protocol. However, the paper was declined to be published (by a not disclosed journal). No further publication attempts were made by the author. In the time afterwards, the aforementioned idea was conceived by others as well, resulting in a number of publications regarding this topic and even slight improvements. Thereby underlining the significance of the author's original idea,...

We investigate the quality of security reductions for non-interactive key exchange (NIKE) schemes. Unlike for many other cryptographic building blocks (like public-key encryption, signatures, or zero-knowledge proofs), all known NIKE security reductions to date are non-tight, i.e., lose a factor of at least the number of users in the system. In that sense, NIKE forms a particularly elusive target for tight security reductions. The main technical obstacle in achieving tightly secure NIKE...

Some key agreement schemes, such as Diffie--Hellman key agreement, reduce to Rabi--Sherman key agreement, in which Alice sends $ab$ to Charlie, Charlie sends $bc$ to Alice, they agree on key $a(bc) = (ab)c$, where multiplicative notation here indicates some specialized associative binary operation. All non-interactive key agreement schemes, where each peer independently determines a single delivery to the other, reduce to this case, because the ability to agree implies the existence of an...

We show that the soundness proof for the De Feo-Jao-Plut identification scheme (the basis for supersingular isogeny Diffie--Hellman (SIDH) signatures) contains an invalid assumption, and we provide a counterexample for this assumption---thus showing the proof of soundness is invalid. As this proof was repeated in a number of works by various authors, multiple pieces of literature are affected by this result. Due to the importance of being able to prove knowledge of an SIDH key (for example,...

We present a polynomial-time adaptive attack on the genus-2 variant of the SIDH protocol (G2SIDH) and describe an improvement to its secret selection procedure. G2SIDH is a generalisation of the Supersingular Isogeny Diffie--Hellman key exchange into the genus-2 setting which was proposed by Flynn and Ti. G2SIDH is able to achieve the same security as SIDH while using fields a third of the size. We analyze the keyspace of G2SIDH and achieve an improvement to the secret selection by using...

Expanding graphs are known due to their remarkable applications to Computer Science. We are looking for their applications to Post Quantum Cryptography. One of them is postquantum analog of Diffie-Hellman protocol in the area of intersection of Noncommutative and Multivariate Cryptographies .This graph based protocol allows correspondents to elaborate collision cubic transformations of affine space Kn defined over finite commutative ring K. Security of this protocol rests on the...

A two-party authenticated key exchange (AKE) protocol allows each of the two parties to share a common secret key over insecure channels even in the presence of active adversaries who can actively control and modify the exchanged messages. To capture the various kind of malicious behaviors of the adversaries, there have been lots of efforts to define the security models. Amongst them, the extended Canetti-Krawczyk (eCK) security model is considered as one of the strongest ones and widely...

OPAQUE [Jarecki et al., Eurocrypt 2018] is an asymmetric password authenticated key exchange (aPAKE) protocol that is being developed as an Internet standard and for use within TLS 1.3. OPAQUE combines an Oblivious PRF (OPRF) with an authenticated key exchange to provide strong security properties, including security against pre-computation attacks (called saPAKE security). However, the security of OPAQUE relies crucially on the security of the OPRF. If the latter breaks (by cryptanalysis,...

We build the first construction of a partially oblivious pseudorandom function (POPRF) that does not rely on bilinear pairings. Our construction can be viewed as combining elements of the 2HashDH OPRF of Jarecki, Kiayias, and Krawczyk with the Dodis-Yampolskiy PRF. We analyze our POPRF’s security in the random oracle model via reduction to a new one-more gap strong Diffie-Hellman inversion assumption. The most significant technical challenge is establishing confidence in the new assumption,...

With the development of side-channel attacks, a necessity arises to invent authenticated key exchange protocols in a leakage-resilient manner. Constructing authenticated key exchange protocols using existing cryptographic schemes is an effective method, as such construction can be instantiated with any appropriate scheme in a way that the formal security argument remains valid. In parallel, constructing authenticated key exchange protocols that are proven to be secure in the standard model...

The J-PAKE protocol is a Password Authenticated Key Establishment protocol whose security rests on Diffie-Hellman key establishment and Non-Interactive Zero Knowledge proofs. It has seen widespread deployment and has previously been proven secure, including forward secrecy, in a game-based model. In this paper we show that this earlier proof can be re-cast in the Universal Composability framework, thus yielding a stronger result. We also investigate the extension of such proofs to a...

The key exchange protocol that establishes initial shared secrets in the handshake of the Signal end-to-end encrypted messaging protocol has several important characteristics: (1) it runs asynchronously (without both parties needing to be simultaneously online), (2) it provides implicit mutual authentication while retaining deniability (transcripts cannot be used to prove either party participated in the protocol), and (3) it retains security even if some keys are compromised (forward...

This paper presents Multidimentional ModDiv public key exchange protocol which security is based on the hardness of an LWR problem instance consisting on finding a secret vector $\textbf{X}$ in $\mathbb{Z}_{q}^{n}$ knowing vectors $\textbf{A}$ and $\textbf{B}$ respectively in $\mathbb{Z}_{p}^{m}$ and $\mathbb{Z}_{p-q}^{m-n}$, where elements of vector $\textbf{B}$ are defined as follows : $ B(i)$ = ($\sum_{j=1}^{j=n} A(i+n-j) \times X(j)$) $ Mod(P)Div(Q)$. Mod is integer modulo, Div is...

RSA cryptography is an asymmetric communication protocol, and it is facing diverse issues. Recent research works suggest that RSA security has already broken. On the contrary, AES is the most used symmetric-key cryptography protocol, and it is also facing issues. Literature search suggests that there is an issue of cryptanalysis attacks. A shared secret key requires for AES cryptography. The most famous key exchange protocol is Diffie-Hellman; however, it has an issue of the number field...

Symmetric key cryptography is applied in almost all secure communications to protect all sensitive information from attackers, for instance, banking, and thus, it requires extra attention due to diverse applications. Moreover, it is vulnerable to various attacks, for example, cryptanalysis attacks. Cryptanalysis attacks are possible due to a single-keyed encryption system. The state-of-the-art symmetric communication protocol uses a single secret key to encrypt/decrypt the entire...

We propose the first tight security proof for the ordinary two-message signed Diffie-Hellman key exchange protocol in the random oracle model. Our proof is based on the strong computational Diffie-Hellman assumption and the multi-user security of a digital signature scheme. With our security proof, the signed DH protocol can be deployed with optimal parameters, independent of the number of users or sessions, without the need to compensate any security loss. We abstract our approach with a...

We use matrices over bit strings as platforms for Diffie-Hellman-like public key exchange protocols. When multiplying matrices like that, we use Boolean OR operation on bit strings in place of addition and Boolean AND operation in place of multiplication. As a result, (1) computations with these matrices are very efficient; (2) standard methods of attacking Diffie-Hellman-like protocols are not applicable.

The algebraic structures that are non-commutative and non-associative known as entropic groupoids that satisfy the "Palintropic" property i.e., $x^{\mathbf{A} \mathbf{B}} = (x^{\mathbf{A}})^{\mathbf{B}} = (x^{\mathbf{B}})^{\mathbf{A}} = x^{\mathbf{B} \mathbf{A}}$ were proposed by Etherington in '40s from the 20th century. Those relations are exactly the Diffie-Hellman key exchange protocol relations used with groups. The arithmetic for non-associative power indices known as Logarithmetic was...

We analyze the security of the TLS 1.3 key establishment protocol, as specified at the end of its rigorous standardization process. We define a core key-schedule and reduce its security to concrete assumptions against an adversary that controls client and server configurations and adaptively chooses some of their keys. Our model supports all key derivations featured in the standard, including its negotiated modes and algorithms that combine an optional Diffie-Hellman exchange for...

In a recent eprint, Rahman and Shpilrain proposed a Diffie-Hellman style key exchange based on a semidirect product of $n × n$-matrices over a finite field. We show that, using public information, an adversary can recover the agreed upon secret key by solving a system of $n^2$ linear equations.

Supersingular isogeny Diffie-Hellman key exchange (SIDH) is a post-quantum protocol based on the presumed hardness of computing an isogeny between two supersingular elliptic curves given some additional torsion point information. Unlike other isogeny-based protocols, SIDH has been widely believed to be immune to subexponential quantum attacks because of the non-commutative structure of the endomorphism rings of supersingular curves. We contradict this commonly believed misconception in this...

We construct the currently most efficient signature schemes with tight multi-user security against adaptive corruptions. It is the first generic construction of such schemes, based on lossy identification schemes (Abdalla etal; JoC 2016), and the first to achieve strong existential unforgeability. It also has significantly more compact signatures than the previously most efficient construction by Gjosteen and Jager (CRYPTO 2018). When instantiated based on the decisional Diffie-Hellman...

Internet of Things (IoT) promises a strong connection between digital and physical environments. Nevertheless, such framework comes with huge security vulnerabilities, due to the heterogeneous nature of devices and of the diversity of their provenance. Furthermore, the resource constraints of weaker devices, such as sensors, require a lightweight design of security protocols. In 2018, Liu et al. presented a new system with access control key updates and direct user revocation, that are...

We offer a public key exchange protocol based on a semidirect product of two cyclic (semi)groups of matrices over Z_p. One of the (semi)groups is additive, the other one multiplicative. This allows us to take advantage of both operations on matrices to diffuse information. We note that in our protocol, no power of any matrix or of any element of Z_p is ever exposed, so all standard attacks on Diffie-Hellman-like protocols are not applicable.

LWE based key-exchange protocols lie at the heart of post-quantum public-key cryptography. However, all existing protocols either lack the non-interactive nature of Diffie-Hellman key-exchange or polynomial LWE-modulus, resulting in unwanted efficiency overhead. We study the possibility of designing non-interactive LWE-based protocols with polynomial LWE-modulus. To this end, • We identify and formalize simple non-interactive and polynomial LWE-modulus variants of existing protocols, where...

An oblivious PRF, or OPRF, is a protocol between a client and a server, where the server has a key $k$ for a secure pseudorandom function $F$, and the client has an input $x$ for the function. At the end of the protocol the client learns $F(k,x)$, and nothing else, and the server learns nothing. An OPRF is verifiable if the client is convinced that the server has evaluated the PRF correctly with respect to a prior commitment to $k$. OPRFs and verifiable OPRFs have numerous applications, such...

Basic key exchange protocols built from the learning with errors (LWE) assumption are insecure if secret keys are reused in the face of active attackers. One example of this is Fluhrer’s attack on the Ding, Xie, and Lin (DXL) LWE key exchange protocol, which exploits leakage from the signal function for error correction. Protocols aiming to achieve security against active attackers generally use one of two techniques: demonstrating well-formed keyshares using re-encryption like in the...

SIDH and CSIDH are key exchange protocols based on isogenies and conjectured to be quantum-resistant. Since the protocols are similar to the classical Diffie–Hellman, they are vulnerable to the man-in-the-middle attack. A key exchange which is resistant to such an attack is called an authenticated key exchange (AKE), and many isogeny-based AKEs have been proposed. However, the parameter sizes of the existing schemes should be large since they all have relatively large security losses in...

We exploit the Diffie-Hellman-like structure of CSIDH to build a quantum-resistant authenticated key-exchange algorithm. Our security proof has optimal tightness, which means that the protocol is efficient even when instantiated with theoretically-sound security parameters. Compared to previous isogeny-based authenticated key-exchange protocols, our scheme is extremely simple, its security relies only on the underlying CSIDH-problem and it has optimal communication complexity for CSIDH-based...

Diffie-Hellman key exchange (DHKE) is a widely adopted method for exchanging cryptographic key material in realworld protocols like TLS-DH(E). Past attacks on TLS-DH(E) focused on weak parameter choices or missing parameter validation. The confidentiality of the computed DH share, the premaster secret, was never questioned; DHKE is used as a generic method to avoid the security pitfalls of TLS-RSA. We show that due to a subtle issue in the key derivation of all TLS-DH(E) cipher suites in...

We propose a generic construction of 2-pass authenticated key exchange (AKE) scheme with explicit authentication from key encapsulation mechanism (KEM) and signature (SIG) schemes. We improve the security model due to Gjosteen and Jager [Crypto2018] to a stronger one. In the strong model, if a replayed message is accepted by some user, the authentication of AKE is broken. We define a new security notion named ''IND-mCPA with adaptive reveals'' for KEM. When the underlying KEM has such a...

We analyze the handshake protocol of the Transport Layer Security (TLS) protocol, version 1.3. We address both the full TLS 1.3 handshake (the one round-trip time mode, with signatures for authentication and (elliptic curve) Diffie–Hellman ephemeral ((EC)DHE) key exchange), and the abbreviated resumption/"PSK" mode which uses a pre-shared key for authentication (with optional (EC)DHE key exchange and zero round-trip time key establishment). Our analysis in the reductionist security framework...

Symmetric password-authenticated key exchange (sPAKE) can be seen as an extension of traditional key exchange where two parties agree on a shared key if and only if they share a common secret (possibly low-entropy) password. We present the first sPAKE protocol to simultaneously achieve the following properties: - only two exponentiations per party, the same as plain unauthenticated Diffie-Hellman key agreement (and likely optimal); - optimal round complexity: a single flow (one message...

We give new, fully-quantitative and concrete bounds that justify the SIGMA and TLS 1.3 key exchange protocols not just in principle, but in practice. By this we mean that, for standardized elliptic curve group sizes, the overall protocol actually achieves the intended security level. Prior work gave reductions of both protocols' security to the underlying building blocks that were loose (in the number of users and/or sessions), so loose that they gave no guarantees for practical...

Reverse Firewalls (RFs) were introduced by Mironov and Stephens-Davidowitz to address algorithm-substitution attacks (ASAs) in which an adversary subverts the implementation of a provably-secure cryptographic primitive to make it insecure. This concept was applied by Dodis et al. in the context of secure key exchange (handshake phase), where the adversary wants to exfiltrate sensitive information by using a subverted client implementation. RFs are used as a means of "sanitizing" the...

Abstract--- This paper demonstrates fast and compact implementations of Elliptic Curve Cryptography (ECC) for efficient key agreement over Curve25519. Curve25519 has been recently adopted as a key exchange method for several applications such as connected small devices as well as cloud, and included in the National Institute of Standards and Technology (NIST) recommendations for public key cryptography. This paper presents three different performance level designs including lightweight,...

Can Alice and Bob agree on a uniformly random secret key without having any truly secret randomness to begin with? Here we consider a setting where Eve can get partial leakage on the internal state of both Alice and Bob individually before the protocol starts. They then run a protocol using their states without any additional randomness and need to agree on a shared key that looks uniform to Eve, even after observing the leakage and the protocol transcript. We focus on non-interactive (one...

Mass surveillance can be more easily achieved leveraging fear and desire of the population to feel protected while affected by devastating events. Indeed, in such scenarios, governments can adopt exceptional measures that limit civil rights, usually receiving large support from citizens. The COVID-19 pandemic is currently affecting daily life of many citizens in the world. People are forced to stay home for several weeks, unemployment rates quickly increase, uncertainty and sadness...

The optimization of the main key compression bottlenecks of the supersingular isogeny key encapsulation mechanism (SIKE) has been a target of research in the last few years. Significant improvements were introduced in the recent works of Costello et al. and Zanon et al. The combination of the techniques in previous works reduced the running time of binary torsion basis generation in decompression by a factor of 29 compared to previous work. On the other hand, generating such a basis still...

Since its proposal in Asiacrypt 2018, the commutative isogeny-based key exchange protocol (CSIDH) has spurred considerable attention to improving its performance and re-evaluating its classical and quantum security guarantees. In this paper we discuss how the optimal strategies employed by the Supersingular Isogeny Diffie-Hellman (SIDH) key agreement protocol can be naturally extended to CSIDH. Furthermore, we report a software library that achieves moderate but noticeable performance...

This paper introduces 4 way vectorization of Montgomery ladder on any Montgomery form elliptic curve. Our algorithm takes 2M^4+1S^4 (M^4: A vector of four field multiplications, S^4: A vector of four field squarings) per ladder step for variable-scalar variable-point multiplication. This paper also introduces new formulas for doing arithmetic over GF(2^255-19).

We present novel strategies and concrete algorithms for the parallel computation of the Supersingular Isogeny-based Diffie-Hellman key exchange (SIDH) protocol when executed on multi-core platforms. The most relevant design idea exploited by our approach is that of concurrently computing scalar multiplication operations along with a parallelized version of the strategies required for constructing and evaluating large smooth degree isogenies. We report experimental results showing that a...