Key Agreement. 15 1.2 The quantum threat . . . . . . . . . . . . . . . . . . . . . . . 16 1.3 Semigroups and rings . . . . . . . . . . . . . . . . . . . . . . . 17 1.4 Associative key agreement . . . . . . . . . . . . . . . . . . . . 19 1.5 All key agreement is essentially associative . . . . . . . . . . . 20 1.6 Ring and semigroup security . . . . . . . . . . . . . . . . . . . 20 2 Key agreement 22 2.1 Schemes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 2.2 Diffie–Xxxxxxx . . . . . . . . . . . . . . . . . . . . . . . . . . 23 2.3 Domain and Ranges . . . . . . . . . . . . . . . . . . . . . . . 24 2.4 Aside: rock, scissors, paper . . . . . . . . . . . . . . . . . . . . 25 2.5 Computation and communication . . . . . . . . . . . . . . . . 26 2.6 Practical schemes . . . . . . . . . . . . . . . . . . . . . . . . . 26 2.7 Sessions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 2.8 Subschemes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 2.9 Probabilistic schemes . . . . . . . . . . . . . . . . . . . . . . . 27 2.10 Aside: faulty schemes . . . . . . . . . . . . . . . . . . . . . . . 29 2.11 Multiplicative schemes . . . . . . . . . . . . . . . . . . . . . . 31 2.12 Aside: reflective and chiral schemes . . . . . . . . . . . . . . . 33 2.13 Associative schemes . . . . . . . . . . . . . . . . . . . . . . . . 33 2.14 Aside: non-associative scheme . . . . . . . . . . . . . . . . . . 34 2.15 Equivalent schemes . . . . . . . . . . . . . . . . . . . . . . . . 35 2.16 Aside: derived schemes . . . . . . . . . . . . . . . . . . . . . . 35 2.17 Essentially associative schemes . . . . . . . . . . . . . . . . . . 37 2.18 Xxxxxx–Xxxxxxx is essentially associative . . . . . . . . . . . . . 37 2.19 Aside: a more general Xxxxxx–Xxxxxxx realm . . . . . . . . . . 39 2.20 Key agreement is essentially associative 40
Key Agreement. The agreement of symmetric key is accomplished by public key system. As shown in Figure 4, Xxxxx encodes her public key kp into acoustic signal and transmits the signal to Bob. The encoded acoustic signal from Xxxxx should preserve the channel ACR features. Bob decodes Xxxxx’s public key after verified whether it is from Xxxxx using ACR features. The message coding should be efficient and be able to tolerate errors in the channel. Then, Bob generates a session key ks and encrypts it using Xxxxx’s public key kp. Assume the encrypted session key is Ekp (ks), Bob encodes Ekp (ks) into acoustic signal and transmits the signal to Xxxxx. Xxxxx verifies the signal source is from Bob. Then she decodes Ekp (ks) and uses her private key to obtain ks. Then the session key ks can be used by Xxxxx and Xxx for further communication. In this progress, the attackers have no opportunity for spoofing due to the identity verification by ACR, and the public key system prevents attackers from deriving the session key ks.
Key Agreement. ∈ { } Key Agreement is a scheme that allows two parties, Xxxxx and Xxx, that initially share no secret, to establish a common key. For simplicity, in this paper we restrict ourselves to one-round key agreement protocols. Hence, for us a key agreement protocol is a triple of randomized interactive algorithms (KAAlice, KABob, KAKey ). Let rAlice and rBob denote the respective random inputs of the players. In the first step each algorithm P ∈ {Xxxxx, Xxx} sends to the other one a message mP = KAP (rP ). Then, Xxxxx calculates her output KAlice = XXXxx (rAlice, mBob) and Xxx calculates his output KBob = KAKey (rBob, mAlice). We require that always KAlice = KBob. Security of (Xxxxx, Xxx) is defined in the following way: for any polynomial time adversary that can see mAlice and mBob the key KAlice should be indistinguishable from a random string of the same length. Of course, if the adversary is active, then he can cause KAlice = KBob, or KP = error (for P Xxxxx, Xxx ). ∈ An example of a key agreement protocol is the protocol of Diffie and Xxxxxxx [14]. Let G be a cyclic group, and let g be its generator. The protocol works as follows: each user P selects a random exponent rP Z|G|, calculates mP := grP and sends it to the other player. Then, each player calculates K := (mP )rP . The protocol is correct, since (grAlice )rBob = (grBob )rAlice . The protocol is secure under a so-called Decisional Xxxxxx-Xxxxxxx Assumption in (G, g). See, e.g., [19] for more on this. Authenticated Key Agreement (AKA) is a protocol between Xxxxx and Xxx that share a common key K that allows them to generate a fresh session key. It can be constructed from the Key Agreement Scheme described, by asking both users to authenticated their messages with a MAC (using the key K). In our construction we will need a stronger version of this notion, that we call a Covert-AKA. This is described below.
Key Agreement. In this report, key agreement means the idea sketched in Figure 11. Formal definitions are in Chapter 2. Key agreement is a generalization of basic Diffie–Xxxxxxx key agreement, and is usually part of a larger system such as a secure handshake as a step for key distribution in a secure communication protocol. Key agreement allows two users to agree on a key by delivering each other information. Delivery is non-interactive: each delivery can be independently 1Douglas Stebila suggested the crossing of arrows in the figure to distinguish from key encapsulation. I since learned of similar but non-crossing rhombic diagram in an article of De Feo [Feo17]. generated, starting from some initial joint information. If the key agreement is secure, then the agreed key will be a secret known only to the agreeing parties. Adversaries may see the deliveries, but security depends on the adver- saries not modifying the deliveries. In other words, key agreement, as we define it, is unauthenticated. Generally, to avoid an man-in-the-middle at- tack, some extra security techniques must be applied, to authenticate the deliveries. For example, digital signatures might be applied to the deliveries. These extra mechanisms are not part of key agreement, but a necessary part of larger system. A few schemes for key agreement are • Xxxxxx and Xxxxxxx’x original (1978) modular exponentiation based key agreement, • Xxxxxxx (1987) and Xxxxxx’x (1985) elliptic curve variant of Diffie–Xxxxxxx key agreement, • Xxxxxxx, Qu and Xxxxxxxx’x (1995) double-key variant of Diffie–Xxxxxxx key agreement, and • De Feo, Jao and Plut’s (2014) super-singular isogeny Diffie–Xxxxxxx. The few schemes above (and yet fewer variations) are widely conjectured to contribute significantly to security, at least when used correctly within a larger protocol. (Furthermore, some kinds of password-authenticated key exchange, such as SPEKE and SPAKE2, also fit this model of key agreement.) Other than these few schemes and similar ones, secure key agreement seem elusive. The key agreement schemes with well-established security are sim- ilar to those above.2 Obscurer key agreements do not have well-established security (although may well be secure nonetheless).
Key Agreement. Once the certificates are verified, a unique session-key kM = H(gUS, gS , eS, eU ) is , derived from the contributions of both parties in Step 20 of Figures 2 and 5. Thus, no single party has complete control on the selection of the session-key, which is the main goal of a key agreement protocol [28].
Key Agreement. In order to establish the group key, each member Ui1, where i = 1, . . . , n should execute the following steps • Step 1: Select the Xxxxxx-Xxxxxxx (DH) private share xi and compute the public share yi = gxi mod p. (g and p are the generator and the prime modulo used in the Xxxxxx-Xxxxxxx computation. This information is public and if the nodes do not share this, then an initial broadcast round is needed.) • Step 2: Broadcast the DH public share yi to all the members in the group. • Step 3: Receive the DH public share of all the other members in the group and compute the DH key shared with each of them selects a DH private share x1 and computes its DH public share y1 = gx1 mod p. U1 then broadcasts the DH public share y1 to all the other members in the group.
Key Agreement. The Setup algorithm is executed by the ID-PKG. This part of the key agreement proto- col is only performed once and creates both the master secrets P and Q as well as the public parameters. Setup - The Setup algorithm is executed by the ID-PKG. Input: k ∈ N Step 1: Choose an arbitrary integer R > 1 from Z .
Key Agreement. Xxxxx and Xxx, living in different places, would like to communicate pri- vately. There are two security requirements which Xxxxx and Xxx have in such a setting. First, the communication should be secret, meaning that a potential eavesdropper, commonly called “Eve”, will not get any infor- mation about their communication. Second, the communication should be authentic, which means that Eve cannot insert messages without being detected. If both these requirements are met we say that Xxxxx and Xxx can communicate securely. In this thesis, we make the basic assumption that Xxxxx and Xxx share an authentic channel, i.e., the second goal is already achieved by physical means or some underlying protocol. The term key agreement refers to the following task: given an authentic channel, Xxxxx and Xxx communicate and then agree on a bit string (called the key), about which Xxx has no information. It is not so hard to see that key agreement is equivalent to achieving secret communication from an authentic channel, and our goal from now on will be to obtain a key. / For classical communication channels, key agreement is not possible unconditionally. But if we assume that Xxx is computationally bounded, i.e., if the computing time which Xxx has at her disposal is not very large, then this changes (or rather, it is commonly believed that this changes). Pro- tocols which are belived to achieve key agreement in this case were first proposed by Merkle [Mer79] (in a limited sense) and by Diffie and Hell- man [DH76], and are widely used in practice nowadays. However, we are currently unable to prove the security of any such protocol. Such a proof would imply a non-trivial lower bound for the computation of Xxx, and to give such a lower bound is a notoriously hard problem in theoretical computer science (in particular, if Xxx needs superpolynomial computa- tion to break a protocol which runs in polynomial time, then P = NP). Consequently one makes assumptions under which such a protocol is se- cure. For example one assumes that computing discrete logarithms or factoring large numbers are intractable problems. The goal of this thesis is to make this assumption as weak as possible. A very strong result of this form would be to base a key agreement pro- tocol on an arbitrary one-way function (i.e., a function which is easy to evaluate but for which it is difficult to find a preimage of a given image). However, Xxxxxxxxxxx and Xxxxxx [IR89] showed that this is not possible using ...
Key Agreement. To establish a common shared secret key, the three parties could naively perform the two-party key exchange protocol with each other, and as a result of this first round, establish three secret keys. Then, they will need three more passes to finally establish a common key. This approach would take nine passes in total. Here, we present our approach, described in previous section, that takes only four passes.
Key Agreement. The City of Tenino will assign one Quarry House key to SSSS to be used exclusively during the hours of operation as specified in section III of this rental agreement. If an SSSS employee needs access to the Quarry House outside of lease hours, s/he must first receive permission from the City of Tenino.
