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Distributed key generation (DKG) is a cryptographic process in which multiple parties contribute to the calculation of a shared public and private key set. Unlike most public key encryption models, distributed key generation does not rely on Trusted Third Parties.[1] Instead, the participation of a threshold of honest parties determines whether a key pair can be computed successfully.[2] Distributed key generation prevents single parties from having access to a private key. The involvement of many parties requires Distributed key generation to ensure secrecy in the presence of malicious contributions to the key calculation.[1]

Key management is, well, the process of managing (cryptographic) keys, the usual meaning implies management over the whole lifetime of the key. Key distribution is a part of key management, but it also includes key generation, key escrow (for backup purposes), key deletion, key revokation, key usage and key trust management. Generating Keys for Encryption and Decryption.; 3 minutes to read +7; In this article. Creating and managing keys is an important part of the cryptographic process. Symmetric algorithms require the creation of a key and an initialization vector (IV). The key must be kept secret from anyone who should not decrypt your data.

Distributed Key Generation is commonly used to decrypt shared ciphertexts or create group digital signatures.[2]

History[edit]

Distributed key generation protocol was first specified by Torben Pedersen in 1991. This first model depended on the security of the Joint-Feldman Protocol for verifiable secret sharing during the secret sharing process.[3]

In 1999, Rosario Gennaro, Stanislaw Jarecki, Hugo Krawczyk, and Tal Rabin produced a series of security proofs demonstrating that Feldman verifiable secret sharing was vulnerable to malicious contributions to Pedersen's distributed key generator that would leak information about the shared private key.[4] The same group also proposed an updated distributed key generation scheme preventing malicious contributions from impacting the value of the private key.


Methods[edit]

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The distributed key generation protocol specified by Gennaro, Jarecki, Krawczyk, and Rabin assumes that a group of players has already been established by an honest party prior to the key generation. It also assumes the communication between parties is synchronous.[4]

  1. All parties use Pedersen's verifiable secret sharing protocol to share the results of two random polynomial functions.
  2. Every party then verifies all the shares they received. If verification fails, the recipient broadcasts a complaint for the party whose share failed. Each accused party then broadcasts their shares. Each party then has the opportunity to verify the broadcast shares or disqualify accused parties. All parties generate a common list of non-disqualified parties.
  3. Each non-disqualified party broadcasts a set of values constructed by raising a common generator to the power of each value used in one polynomial in Part 1.
  4. These broadcast values are verified by each party similarly to as in Part 2. When a verification fails, the party now broadcasts both the values received in Part 1 and the values received in Part 3. For each party with verifiable complaints, all other parties reconstruct their own value sets in order to eliminate disqualified contributions.
  5. The group computes the private key as the product of every qualified contribution (each qualified party's random polynomial evaluated at 0).[4]


Avoiding the Synchrony Assumption[edit]

In 2009, Aniket Kate and Ian Goldberg presented a Distributed key generation protocol suitable for use over the Internet.[5] Unlike earlier constructions, this protocol does not require a broadcast channel or the synchronous communication assumption, and a ready-to-use library is available.

Robustness[edit]

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In many circumstances, a robust distributed key generator is necessary. Robust generator protocols can reconstruct public keys in order to remove malicious shares even if malicious parties still remain in the qualified group during the reconstruction phase.[4] For example, robust multi-party digital signatures can tolerate a number of malicious users roughly proportionate to the length of the modulus used during key generation.[6]

Sparse Evaluated DKG[edit]

Distributed key generators can implement a sparse evaluation matrix in order to improve efficiency during verification stages. Sparse evaluation can improve run time from O(nt){displaystyle O(nt)} (where n{displaystyle n} is the number of parties and t{displaystyle t} is the threshold of malicious users) to O(log3n){displaystyle O(log^{3}n)}. Instead of robust verification, sparse evaluation requires that a small set of the parties verify a small, randomly picked set of shares. This results in a small probability that the key generation will fail in the case that a large number of malicious shares are not chosen for verification.[7]

Applications[edit]

Distributed key generation and distributed key cryptography are rarely applied over the internet because of the reliance on synchronous communication.[4]

Distributed key cryptography is useful in key escrow services where a company can meet a threshold to decrypt a ciphertext version of private key. This way a company can require multiple employees to recover a private key without giving the escrow service a plaintext copy.[1]

Distributed key generation is also useful in server-side password authentication. If password hashes are stored on a single server, a breach in the server would result in all the password hashes being available for attackers to analyze offline. Variations of distributed key generation can authenticate user passwords across multiple servers and eliminate single points of failure.[8][9]

Distributed key generation is more commonly used for group digital signatures. This acts as a form of voting, where a threshold of group members would have to participate in order for the group to digitally sign a document.[2]

References[edit]

  1. ^ abcKate, Aniket; Goldberg, Ian (2010). Distributed Private-Key Generators for Identity Based Cryptography. Security and Cryptography for Networks. Lecture Notes in Computer Science. 6280. pp. 436–453. CiteSeerX10.1.1.389.4486. doi:10.1007/978-3-642-15317-4_27. ISBN978-3-642-15316-7.
  2. ^ abcBoldyreva, Alexandra (2003). Threshold Signatures, Multisignatures and Blind Signatures Based on the Gap-Diffie-Hellman-Group Signature Scheme(PDF). Public Key Cryptography. Lecture Notes in Computer Science. 2567. pp. 31–46. doi:10.1007/3-540-36288-6_3. ISBN978-3-540-00324-3.
  3. ^Pedersen, T. P. (1992). 'Non-Interactive and Information-Theoretic Secure Verifiable Secret Sharing'. Advances in Cryptology — CRYPTO '91. Lecture Notes in Computer Science. 576. pp. 129–140. doi:10.1007/3-540-46766-1_9. ISBN978-3-540-55188-1.
  4. ^ abcdeGennaro, Rosario; Jarecki, Stanislaw; Krawczyk, Hugo; Rabin, Tal (24 May 2006). 'Secure Distributed Key Generation for Discrete-Log Based Cryptosystems'. Journal of Cryptology. 20 (1): 51–83. CiteSeerX10.1.1.134.6445. doi:10.1007/s00145-006-0347-3.
  5. ^Kate, Aniket; Goldberg, Ian (2006). 'Distributed Key Generation for the Internet'. IEEE ICDCS. doi:10.1109/ICDCS.2009.21.
  6. ^Castelluccia, Claude; Jarecki, Stanisław; Kim, Jihye; Tsudik, Gene (2006). 'Secure acknowledgment aggregation and multisignatures with limited robustness'. Computer Networks. 50 (10): 1639–1652. doi:10.1016/j.comnet.2005.09.021.
  7. ^Canny, John; Sorkin, Steve (2004). Practical Large-scale Distributed Key Generation(PDF). Advances in Cryptography - EUROCRYPT 2004. Lecture Notes in Computer Science. 3027. pp. 138–152. CiteSeerX10.1.1.69.6028. doi:10.1007/978-3-540-24676-3_9. ISBN978-3-540-21935-4.
  8. ^MacKenzie, Philip; Shrimpton, Thomas; Marcus, Jakobsson (2006). 'Threshold Password-authenticated Key Exchange'. Journal of Cryptology. 19 (1): 27–66. CiteSeerX10.1.1.101.6403. doi:10.1007/s00145-005-0232-5.
  9. ^Jarecki, Stanislaw; Kiayias, Aggelos; Krawczyk, Hugo (2014). 'Round-Optimal Password-Protected Secret Sharing and T-PAKE in the Password-Only model'(PDF). Cryptology ePrint Archive. 650. Retrieved 5 November 2014.
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Key generation is the process of generating keys in cryptography. A key is used to encrypt and decrypt whatever data is being encrypted/decrypted.

Microsoft word key generator 2019. A device or program used to generate keys is called a key generator or keygen.

Generation in cryptography[edit]

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Modern cryptographic systems include symmetric-key algorithms (such as DES and AES) and public-key algorithms (such as RSA). Symmetric-key algorithms use a single shared key; keeping data secret requires keeping this key secret. Public-key algorithms use a public key and a private key. The public key is made available to anyone (often by means of a digital certificate). A sender encrypts data with the receiver's public key; only the holder of the private key can decrypt this data.

Since public-key algorithms tend to be much slower than symmetric-key algorithms, modern systems such as TLS and SSH use a combination of the two: one party receives the other's public key, and encrypts a small piece of data (either a symmetric key or some data used to generate it). The remainder of the conversation uses a (typically faster) symmetric-key algorithm for encryption.

Computer cryptography uses integers for keys. In some cases keys are randomly generated using a random number generator (RNG) or pseudorandom number generator (PRNG). A PRNG is a computeralgorithm that produces data that appears random under analysis. PRNGs that use system entropy to seed data generally produce better results, since this makes the initial conditions of the PRNG much more difficult for an attacker to guess. Another way to generate randomness is to utilize information outside the system. veracrypt (a disk encryption software) utilizes user mouse movements to generate unique seeds, in which users are encouraged to move their mouse sporadically. In other situations, the key is derived deterministically using a passphrase and a key derivation function.

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Many modern protocols are designed to have forward secrecy, which requires generating a fresh new shared key for each session.

Classic cryptosystems invariably generate two identical keys at one end of the communication link and somehow transport one of the keys to the other end of the link.However, it simplifies key management to use Diffie–Hellman key exchange instead.

The simplest method to read encrypted data without actually decrypting it is a brute-force attack—simply attempting every number, up to the maximum length of the key. Therefore, it is important to use a sufficiently long key length; longer keys take exponentially longer to attack, rendering a brute-force attack impractical. Currently, key lengths of 128 bits (for symmetric key algorithms) and 2048 bits (for public-key algorithms) are common.

Generation in physical layer[edit]

Wireless channels[edit]

A wireless channel is characterized by its two end users. By transmitting pilot signals, these two users can estimate the channel between them and use the channel information to generate a key which is secret only to them.[1] The common secret key for a group of users can be generated based on the channel of each pair of users.[2]

Optical fiber[edit]

A key can also be generated by exploiting the phase fluctuation in a fiber link.[clarification needed]

See also[edit]

  • Distributed key generation: For some protocols, no party should be in the sole possession of the secret key. Rather, during distributed key generation, every party obtains a share of the key. A threshold of the participating parties need to cooperate to achieve a cryptographic task, such as decrypting a message.

References[edit]

  1. ^Chan Dai Truyen Thai; Jemin Lee; Tony Q. S. Quek (Feb 2016). 'Physical-Layer Secret Key Generation with Colluding Untrusted Relays'. IEEE Transactions on Wireless Communications. 15 (2): 1517–1530. doi:10.1109/TWC.2015.2491935.
  2. ^Chan Dai Truyen Thai; Jemin Lee; Tony Q. S. Quek (Dec 2015). 'Secret Group Key Generation in Physical Layer for Mesh Topology'. 2015 IEEE Global Communications Conference (GLOBECOM). San Diego. pp. 1–6. doi:10.1109/GLOCOM.2015.7417477.
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