Asynchronous Remote Key Generation (ARKG), introduced by Frymann et al. at CCS 2020, allows for the generation of unlinkable public keys by third parties, for which corresponding private keys may be later learned only by the key pair’s legitimate owner. These key pairs can then be used in common public-key cryptosystems, including signatures, PKE, KEMs, and schemes supporting delegation, such as proxy signatures. The only known instance of ARKG generates discrete-log-based keys.In this paper, we introduce new ARKG constructions for lattice-based cryptosystems. The key pairs generated using our ARKG scheme can be applied to lattice-based signatures and KEMs, which have recently been selected for standardisation in the NIST PQ process, or as alternative candidates.In particular, we address challenges associated with the noisiness of lattice hardness assumptions, which requires a new generalised definition of ARKG correctness, whilst preserving the security and privacy properties of the former instantiation. Our ARKG construction uses key encapsulation techniques by Brendel et al. (SAC 2020) coined Split KEMs. As an additional contribution, we also show that Kyber (Bos et al., EuroS&P 2018) can be used to construct a Split KEM. The security of our protocol is based on standard LWE assumptions. We also discuss its use with selected candidates from the NIST process and provide an implementation and benchmarks.Asynchronous Remote Key Generation (ARKG), introduced by Frymann et al. at CCS 2020, allows for the generation of unlinkable public keys by third parties, for which corresponding private keys may be later learned only by the key pair’s legitimate owner. These key pairs can then be used in common public-key cryptosystems, including signatures, PKE, KEMs, and schemes supporting delegation, such as proxy signatures. The only known instance of ARKG generates discrete-log-based keys.In this paper, we introduce new ARKG constructions for lattice-based cryptosystems. The key pairs generated using our ARKG scheme can be applied to lattice-based signatures and KEMs, which have recently been selected for standardisation in the NIST PQ process, or as alternative candidates.In particular, we address challenges associated with the noisiness of lattice hardness assumptions, which requires a new generalised definition of ARKG correctness, whilst preserving the security and privacy properties of the former instantiation. Our ARKG construction uses key encapsulation techniques by Brendel et al. (SAC 2020) coined Split KEMs. As an additional contribution, we also show that Kyber (Bos et al., EuroS&P 2018) can be used to construct a Split KEM. The security of our protocol is based on standard LWE assumptions. We also discuss its use with selected candidates from the NIST process and provide an implementation and benchmarks.

IEEE European Symposium on Security and PrivacyJul 1, 20237 citations

Secure Distributed Computing

Jeffrey I. Schiller

Scientific AmericanNov 1, 199442 citations

Asynchronous Distributed Key Generation for Computationally-Secure Randomness, Consensus, and Threshold Signatures.

Eleftherios Kokoris Kogias, Dahlia Malkhi, Alexander Spiegelman

In this paper, we present the first Asynchronous Distributed Key Generation (ADKG) algorithm which is also the first distributed key generation algorithm that can generate cryptographic keys with a dual (f,2f+1)-threshold (where f is the number of faulty parties). As a result, using our ADKG we remove the trusted setup assumption that the most scalable consensus algorithms make. In order to create a DKG with a dual (f,2f+1)- threshold we first answer in the affirmative the open question posed by Cachin et al. [7] on how to create an Asynchronous Verifiable Secret Sharing (AVSS) protocol with a reconstruction threshold of f+1<k łe 2f+1, which is of independent interest. Our High-threshold-AVSS (HAVSS) uses an asymmetric bivariate polynomial to encode the secret. This enables the reconstruction of the secret only if a set of k nodes contribute while allowing an honest node that did not participate in the sharing phase to recover his share with the help of f+1 honest parties. Once we have HAVSS we can use it to bootstrap scalable partially synchronous consensus protocols, but the question on how to get a DKG in asynchrony remains as we need a way to produce common randomness. The solution comes from a novelEventually Perfect Common Coin (EPCC) abstraction that enables the generation of a common coin from n concurrent HAVSS invocations. EPCC's key property is that it is eventually reliable, as it might fail to agree at most f times (even if invoked a polynomial number of times). UsingEPCC we implement anEventually Efficient Asynchronous Binary Agreement (EEABA) which is optimal when the EPCC agrees and protects safety when EPCC fails. Finally, using EEABA we construct the first ADKG which has the same overhead and expected runtime as the best partially-synchronous DKG (O(n4) words, O(f) rounds). As a corollary of our ADKG, we can also create the first Validated Asynchronous Byzantine Agreement (VABA) that does not need a trusted dealer to setup threshold signatures of degree n-f. Our VABA has an overhead of expected O(n2) words and O(1) time per instance, after an initial O(n4) words and O(f) time bootstrap via ADKG.In this paper, we present the first Asynchronous Distributed Key Generation (ADKG) algorithm which is also the first distributed key generation algorithm that can generate cryptographic keys with a dual (f,2f+1)-threshold (where f is the number of faulty parties). As a result, using our ADKG we remove the trusted setup assumption that the most scalable consensus algorithms make. In order to create a DKG with a dual (f,2f+1)- threshold we first answer in the affirmative the open question posed by Cachin et al. [7] on how to create an Asynchronous Verifiable Secret Sharing (AVSS) protocol with a reconstruction threshold of f+1<k łe 2f+1, which is of independent interest. Our High-threshold-AVSS (HAVSS) uses an asymmetric bivariate polynomial to encode the secret. This enables the reconstruction of the secret only if a set of k nodes contribute while allowing an honest node that did not participate in the sharing phase to recover his share with the help of f+1 honest parties. Once we have HAVSS we can use it to bootstrap scalable partially synchronous consensus protocols, but the question on how to get a DKG in asynchrony remains as we need a way to produce common randomness. The solution comes from a novelEventually Perfect Common Coin (EPCC) abstraction that enables the generation of a common coin from n concurrent HAVSS invocations. EPCC's key property is that it is eventually reliable, as it might fail to agree at most f times (even if invoked a polynomial number of times). UsingEPCC we implement anEventually Efficient Asynchronous Binary Agreement (EEABA) which is optimal when the EPCC agrees and protects safety when EPCC fails. Finally, using EEABA we construct the first ADKG which has the same overhead and expected runtime as the best partially-synchronous DKG (O(n4) words, O(f) rounds). As a corollary of our ADKG, we can also create the first Validated Asynchronous Byzantine Agreement (VABA) that does not need a trusted dealer to setup threshold signatures of degree n-f. Our VABA has an overhead of expected O(n2) words and O(1) time per instance, after an initial O(n4) words and O(f) time bootstrap via ADKG.

ACM SIGSAC Conference on Computer and Communications Security (CCS)Oct 30, 2020118 citations

Practical Asynchronous Distributed Key Generation

Sourav Das, Thomas Yurek, Zhuolun Xiang +3 more

Distributed Key Generation (DKG) is a technique to bootstrap threshold cryptosystems without a trusted third party and is a building block to decentralized protocols such as randomness beacons, threshold signatures, and general multiparty computation. Until recently, DKG protocols have assumed the synchronous model and thus are vulnerable when their underlying network assumptions do not hold. The recent advancements in asynchronous DKG protocols are insufficient as they either have poor efficiency or limited functionality, resulting in a lack of concrete implementations. In this paper, we present a simple and concretely efficient asynchronous DKG (ADKG) protocol. In a network of n nodes, our ADKG protocol can tolerate up to $t\lt n/3$ malicious nodes and have an expected $O(\kappa n^{3})$ communication cost, where $\kappa$ is the security parameter. Our ADKG protocol produces a field element as the secret and is thus compatible with off-the-shelf threshold cryptosystems. We implement our ADKG protocol and evaluate it using a network of up to 128 nodes in geographically distributed AWS instances. Our evaluation shows that our protocol takes as low as 3 and 9.5 seconds to terminate for 32 and 64 nodes, respectively. Also, each node sends only 0.7 Megabytes and 2.9 Megabytes of data during the two experiments, respectively.Distributed Key Generation (DKG) is a technique to bootstrap threshold cryptosystems without a trusted third party and is a building block to decentralized protocols such as randomness beacons, threshold signatures, and general multiparty computation. Until recently, DKG protocols have assumed the synchronous model and thus are vulnerable when their underlying network assumptions do not hold. The recent advancements in asynchronous DKG protocols are insufficient as they either have poor efficiency or limited functionality, resulting in a lack of concrete implementations. In this paper, we present a simple and concretely efficient asynchronous DKG (ADKG) protocol. In a network of n nodes, our ADKG protocol can tolerate up to $t\lt n/3$ malicious nodes and have an expected $O(\kappa n^{3})$ communication cost, where $\kappa$ is the security parameter. Our ADKG protocol produces a field element as the secret and is thus compatible with off-the-shelf threshold cryptosystems. We implement our ADKG protocol and evaluate it using a network of up to 128 nodes in geographically distributed AWS instances. Our evaluation shows that our protocol takes as low as 3 and 9.5 seconds to terminate for 32 and 64 nodes, respectively. Also, each node sends only 0.7 Megabytes and 2.9 Megabytes of data during the two experiments, respectively.

IEEE Symposium on Security and Privacy (S&P)May 1, 2022108 citations

Adaptively secure distributed public-key systems

Yair Frankel, PHILIP D. MACKENZIE, Moti M. Yung

Theoretical Computer ScienceSep 1, 20024 citations

t\lt n/3

malicious nodes and have an expected

O(\kappa n^{3})

communication cost, where

\kappa

is the security parameter. Our ADKG protocol produces a field element as the secret and is thus compatible with off-the-shelf threshold cryptosystems. We implement our ADKG protocol and evaluate it using a network of up to 128 nodes in geographically distributed AWS instances. Our evaluation shows that our protocol takes as low as 3 and 9.5 seconds to terminate for 32 and 64 nodes, respectively. Also, each node sends only 0.7 Megabytes and 2.9 Megabytes of data during the two experiments, respectively.