Authentication Codes. Before we can discuss privacy amplification over a non-authentic public channel, authentication codes need to be studied, since these codes can provide unconditional authenticity for a public channel. M |G| ∈ S G G S M G × S → M G First we introduce the terminology of authentication codes. A general authenti- cation code is a triple ( , , ) of finite sets and a map e : . Here is called the set of source states, which are pieces of information to be transmitted. For any specific s, s , which is called an encoding rule, the map e maps to a subset of , the set of messages, of size . An encoding rule is also called an authenti- cation key, and it is the common information shared by Xxxxx and Xxx beforehand, but Xxx has no access to it. There are two kinds of attacks. In an impersonation attack, Xxx inserts a message on the channel and impersonates the sender. In a substitution attack, Xxx replaces a correct message over the channel by a false one. The success probabilities for Xxx when trying these attacks are denoted by PI and PS, respectively. The probability of deception is defined by PD = max(PI, PS). For any authentication codes, we have the trivial inequalities PI ≥ |G| and PS ≥ |G|—1 . |M| |M|—1 ∈ X ∈ S ∈ G G S X G × S → X In the context of privacy amplification, Xxxxx randomly chooses a hash function, denoted by the random variable G, from a class of hash functions, and transfers it to Bob. As shown in Figure 3.1, the random variable G has the same length as S, the partially secret string used to generate the final secret. Since G does not necessarily need to be secret, authentication codes without secrecy are enough for privacy amplification against Xxx’s active attacks. Therefore, we take interest in authentication codes where the messages carry all information about the source states. These kinds of authentication codes are called Cartesian codes, or systematic authentication codes, in analogy to systematic codes in coding theory. A Cartesian code is a triple ( , , ) of finite sets and a map ƒ : , where for any s and g , any message is of the form m = (g, x) with x = ƒ (g, s). The value x is called the tag or authenticator of g. According to Theorem 1 in [29], one has PS ≥ PI for Cartesian codes. Authentication codes with PI = |G| are optimal against the impersonation attack, and also called I-equitable authen|Mtic|ation codes. It is easy to see that any Cartesian I-equitable authentication code satisfies PD = PS ≥ 1/|X |.
Authentication Codes. In the event any authentication code, identifier, or password is to be generated in conjunction with the use of any Philips-branded Personal TV System Box, Philips shall have the right to generate any such code, identifier, or password.
Authentication Codes. In addition to your User ID and Password, the use of advanced authentication or Out of Band Authentication (“OOBA”) is required at login. When you initially log in you are prompted for a telephone number, an automated phone call occurs that prompts entering a code that is displayed on screen when accessing the Service. A second option for authentication is to provide a phone number that can receive text messages. In that case, a text message prompt is generated with the ability to reply to the text message with the code displayed on screen. If at any time, the computer being used for access is not recognized, OOBA will be requested when logging in from that computer.
