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One document matched: draft-oiwa-httpauth-mutual-algo-02.ps
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%%Title: Mutual Authentication Protocol for HTTP: KAM3-based Cryptographic Algorithms
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(Copyright \(c\) 2014 IETF Trust and the persons identified as the document authors. All rights ) S
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0.0 -2.2 RM
8.36798 0 Nf
0.463378906 0 32 0 0 (c1) A
0.0 2.2 RM
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11 0 Nf
0.463378906 0 32 0 0 (, ) A
0.463378906 0 32 0 0 (K) A
1.2 0.0 RM
0.0 -2.2 RM
8.36798 0 Nf
0.463378906 0 32 0 0 (s1) A
0.0 2.2 RM
1.5 0.0 RM
11 0 Nf
0.463378906 0 32 0 0 (, and J for a specific) A
0.0 -2.2 RM
0 -483.6 M
(algorithm family. ) S
0 -507.8 M
0.693209112 0 32 0 0 (Please note that, from the view of cryptographic literatures, the original functionality of Augumented) A
0 -521 M
11 0 Nf
0.963120401 0 32 0 0 (PAKE is separated into the functions ) A
0.963120401 0 32 0 0 (K) A
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0.963120401 0 32 0 0 (c1) A
0.0 2.2 RM
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11 0 Nf
0.963120401 0 32 0 0 ( and ) A
0.963120401 0 32 0 0 (K) A
1.2 0.0 RM
0.0 -2.2 RM
8.36798 0 Nf
0.963120401 0 32 0 0 (s1) A
0.0 2.2 RM
1.5 0.0 RM
11 0 Nf
0.963120401 0 32 0 0 ( defined in this draft, and the functions ) A
0.963120401 0 32 0 0 (VK) A
1.2 0.0 RM
0.0 -2.2 RM
8.36798 0 Nf
0.963120401 0 32 0 0 (c) A
0.0 2.2 RM
1.5 0.0 RM
11 0 Nf
0.963120401 0 32 0 0 ( and ) A
0.0 -2.2 RM
0 -536.4 M
11 0 Nf
1.75435698 0 32 0 0 (VK) A
1.2 0.0 RM
0.0 -2.2 RM
8.36798 0 Nf
1.75435698 0 32 0 0 (s) A
0.0 2.2 RM
1.5 0.0 RM
11 0 Nf
1.75435698 0 32 0 0 ( defined in Section 11 of ) A
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1.75435698 0 32 0 0 ( as "default functions". For the purpose of) A
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(security analysis, please also refer to these functions. ) S
0 -562.8 M
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13 2 Nf
(1.1.) S
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( ) S
(Terminology) S
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11 0 Nf
2.37011719 0 32 0 0 (The key words "MUST", "MUST\240NOT", "REQUIRED", "SHALL", "SHALL\240NOT", "SHOULD",) A
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1.49739587 0 32 0 0 ("SHOULD\240NOT", "RECOMMENDED", "NOT\240RECOMMENDED", "MAY", and "OPTIONAL" in) A
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(this document are to be interpreted as described in ) S
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(.) S
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2.9309895 0 32 0 0 (The term "natural numbers" refers to the non-negative integers \(including zero\) throughout this ) A
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(document.) S
0 -50.6 M
0.861886144 0 32 0 0 (This document treats target \(codomain\) of hash functions to be octet strings. The notation INT\(H\(s\)\)) A
0 -63.8 M
(gives a natural-number output of hash function H applied to string ) S
(s.) S
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(2.) S
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( Authentication ) S
(Algorithms) S
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11 0 Nf
0.81640625 0 32 0 0 (This document specifies only one family of the authentication algorithm. The family consists of four) A
0 -131.2 M
2.23366475 0 32 0 0 (authentication algorithms, which only differ in their underlying mathematical groups and security) A
0 -144.4 M
(parameters. The algorithms do not add any additional parameters. The tokens for these algorithms ) S
(are) S
11 -165 M
gsave
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22 -168.6 M
2.421875 0 32 0 0 (iso-kam3-dl-2048-sha256: for the 2048-bit discrete-logarithm setting with the SHA-256 hash) A
22 -181.8 M
(function. ) S
11 -192.4 M
gsave
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22 -196 M
2.421875 0 32 0 0 (iso-kam3-dl-4096-sha512: for the 4096-bit discrete-logarithm setting with the SHA-512 hash) A
22 -209.2 M
(function. ) S
11 -219.8 M
gsave
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11.0 -219.769989 2.75 0 360 arc
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22 -223.4 M
2.0859375 0 32 0 0 (iso-kam3-ec-p256-sha256: for the 256-bit prime-field elliptic-curve setting with the SHA-256) A
22 -236.6 M
(hash function. ) S
11 -247.2 M
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22 -250.8 M
2.0859375 0 32 0 0 (iso-kam3-ec-p521-sha512: for the 521-bit prime-field elliptic-curve setting with the SHA-512) A
22 -264 M
(hash ) S
(function.) S
0 -288.2 M
1.56119788 0 32 0 0 (For discrete-logarithm settings, the underlying groups are the 2048-bit and 4096-bit MODP groups) A
0 -301.4 M
1.51412261 0 32 0 0 (defined in ) A
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1.51412261 0 32 0 0 ([RFC3526]) A
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1.51412261 0 32 0 0 (, respectively. See ) A
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1.51412261 0 32 0 0 ( for the exact specifications of the groups and) A
0 -314.6 M
0.0911458358 0 32 0 0 (associated parameters. The hash functions H are SHA-256 for the 2048-bit group and SHA-512 for the) A
0 -327.8 M
0.439778656 0 32 0 0 (4096-bit group, respectively, defined in ) A
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0.439778656 0 32 0 0 ( [FIPS.180-2.2002]. The hash iteration count) A
0 -341 M
(nIterPi is 16384. The representation of the parameters kc1, ks1, vkc, and vks is base64-fixed-number. ) S
0 -365.2 M
0.172916666 0 32 0 0 (For the elliptic-curve settings, the underlying groups are the elliptic curves over the prime fields P-256) A
0 -378.4 M
3.006392 0 32 0 0 (and P-521, respectively, specified in the appendix\240D.1.2 of ) A
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3.006392 0 32 0 0 (FIPS PUB ) A
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3.006392 0 32 0 0 ( [FIPS.186-3.2009]) A
0 -391.6 M
0.460156262 0 32 0 0 (specification. The hash functions H, which are referenced by the core document, are SHA-256 for the) A
0 -404.8 M
0.17135416 0 32 0 0 (P-256 curve and SHA-512 for the P-521 curve, respectively. The hash iteration count nIterPi is 16384.) A
0 -418 M
(The representation of the parameters kc1, ks1, vkc, and vks is hex-fixed-number. ) S
0 -442.2 M
0.408203125 0 32 0 0 (Note: This algorithm is based on the Key Agreement Mechanism 3 \(KAM3\) defined in Section 6.3 of ) A
0 -455.4 M
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0 -456.5 M
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8.17578125 0 32 0 0 (ISO/IEC ) A
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8.17578125 0 32 0 0 (11770-4) A
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8.17578125 0 32 0 0 ( [ISO.11770-4.2006] with a few modifications/improvements. However,) A
0 -468.6 M
1.37469947 0 32 0 0 (implementers should use this document as the normative reference, because the algorithm has been) A
0 -481.8 M
(changed in several minor details as well as major improvements. ) S
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(2.1.) S
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( Support Functions and ) S
(Notations) S
0 -532.6 M
11 0 Nf
(The algorithm definitions use several support functions and notations defined ) S
(below:) S
0 -556.8 M
(The integers in the specification are in decimal, or in hexadecimal when prefixed with ) S
("0x".) S
0 -581 M
3.04507208 0 32 0 0 (The functions named octet\(\), OCTETS\(\), and INT\(\) are those defined in the ) A
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3.04507208 0 32 0 0 (core ) A
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3.04507208 0 32 0 0 ( ) A
0 -594.2 M
([I-D.ietf-httpauth-mutual].) S
0 -618.4 M
2.67103791 0 32 0 0 (Note: The definition of OCTETS\(\) is different from the function GE2OS_x in the original ISO) A
0 -631.6 M
(specification, which takes the shortest representation without preceding zeros. ) S
0 -631.6 M
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11 0 Nf
2.79947925 0 32 0 0 (All of the algorithms defined in this specification use the default functions defined in the core) A
0 -26.4 M
11 0 Nf
1.15966797 0 32 0 0 (specification \(defined in Section 11 of ) A
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1.15966797 0 32 0 0 (\) for computing the values pi, ) A
1.15966797 0 32 0 0 (VK) A
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0.0 -2.2 RM
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1.15966797 0 32 0 0 (c) A
0.0 2.2 RM
1.5 0.0 RM
0.0 -2.2 RM
0 -41.8 M
11 0 Nf
(and ) S
(VK) S
1.2 0.0 RM
0.0 -2.2 RM
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(s) S
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(.) S
0.0 -2.2 RM
0 -55 M
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(2.2.) S
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( Functions for Discrete-Logarithm ) S
(Settings) S
0 -94.8 M
11 0 Nf
0.519886374 0 32 0 0 (In this section, an equation \(x / y mod z\) denotes a natural number w less than z that satisfies \(w * y\)) A
0 -108 M
(mod z = x mod z. ) S
0 -132.2 M
0.05 0 32 0 0 (For the discrete-logarithm, we refer to some of the domain parameters by using the following symbols: ) A
11 -152.8 M
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22 -156.4 M
(q: for "the prime" defining the MODP group. ) S
11 -167 M
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22 -170.6 M
(g: for "the generator" associated with the group. ) S
11 -181.2 M
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11.0 -181.17 2.75 0 360 arc
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22 -184.8 M
(r: for the order of the subgroup generated by ) S
(g.) S
0 -209 M
(The function J is defined as ) S
0 -233.2 M
(J\(pi\) = g^\(pi\) mod q. ) S
0 -257.4 M
11 0 Nf
(The value of ) S
(K) S
1.2 0.0 RM
0.0 -2.2 RM
8.36798 0 Nf
(c1) S
0.0 2.2 RM
1.5 0.0 RM
11 0 Nf
( is derived as ) S
0.0 -2.2 RM
0 -283.8 M
11 0 Nf
(K) S
1.2 0.0 RM
0.0 -2.2 RM
8.36798 0 Nf
(c1) S
0.0 2.2 RM
1.5 0.0 RM
11 0 Nf
( = ) S
(g^\(S) S
1.2 0.0 RM
0.0 -2.2 RM
8.36798 0 Nf
(c1) S
0.0 2.2 RM
1.5 0.0 RM
11 0 Nf
(\) mod q, ) S
0.0 -2.2 RM
0 -310.2 M
11 0 Nf
0.157645091 0 32 0 0 (where ) A
0.157645091 0 32 0 0 (S) A
1.2 0.0 RM
0.0 -2.2 RM
8.36798 0 Nf
0.157645091 0 32 0 0 (c1) A
0.0 2.2 RM
1.5 0.0 RM
11 0 Nf
0.157645091 0 32 0 0 ( is a random integer within range [1, r-1] and r is the size of the subgroup generated by g. In) A
0.0 -2.2 RM
0 -325.6 M
11 0 Nf
(addition, ) S
(S) S
1.2 0.0 RM
0.0 -2.2 RM
8.36798 0 Nf
(c1) S
0.0 2.2 RM
1.5 0.0 RM
11 0 Nf
( MUST be larger than log\(q\)/log\(g\) \(so that ) S
(g^\(S) S
1.2 0.0 RM
0.0 -2.2 RM
8.36798 0 Nf
(c1) S
0.0 2.2 RM
1.5 0.0 RM
11 0 Nf
(\) > q\). ) S
0.0 -2.2 RM
0 -352 M
11 0 Nf
2.4149816 0 32 0 0 (The value of ) A
2.4149816 0 32 0 0 (K) A
1.2 0.0 RM
0.0 -2.2 RM
8.36798 0 Nf
2.4149816 0 32 0 0 (c1) A
0.0 2.2 RM
1.5 0.0 RM
11 0 Nf
2.4149816 0 32 0 0 ( SHALL satisfy 1 < ) A
2.4149816 0 32 0 0 (K) A
1.2 0.0 RM
0.0 -2.2 RM
8.36798 0 Nf
2.4149816 0 32 0 0 (c1) A
0.0 2.2 RM
1.5 0.0 RM
11 0 Nf
2.4149816 0 32 0 0 ( < q-1. The server MUST check this condition upon) A
0.0 -2.2 RM
0 -367.4 M
(reception. ) S
0 -391.6 M
11 0 Nf
(Let an intermediate value ) S
(t) S
1.2 0.0 RM
0.0 -2.2 RM
8.36798 0 Nf
(1) S
0.0 2.2 RM
1.5 0.0 RM
11 0 Nf
( be ) S
0.0 -2.2 RM
0 -418 M
11 0 Nf
(t) S
1.2 0.0 RM
0.0 -2.2 RM
8.36798 0 Nf
(1) S
0.0 2.2 RM
1.5 0.0 RM
11 0 Nf
( = INT\(H\(octet\(1\) | ) S
(OCTETS\(K) S
1.2 0.0 RM
0.0 -2.2 RM
8.36798 0 Nf
(c1) S
0.0 2.2 RM
1.5 0.0 RM
11 0 Nf
(\)\)\), ) S
0.0 -2.2 RM
0 -444.4 M
11 0 Nf
(the value of ) S
(K) S
1.2 0.0 RM
0.0 -2.2 RM
8.36798 0 Nf
(s1) S
0.0 2.2 RM
1.5 0.0 RM
11 0 Nf
( is derived from J\(pi\) and ) S
(K) S
1.2 0.0 RM
0.0 -2.2 RM
8.36798 0 Nf
(c1) S
0.0 2.2 RM
1.5 0.0 RM
11 0 Nf
( as: ) S
0.0 -2.2 RM
0 -470.8 M
11 0 Nf
(K) S
1.2 0.0 RM
0.0 -2.2 RM
8.36798 0 Nf
(s1) S
0.0 2.2 RM
1.5 0.0 RM
11 0 Nf
( = \(J\(pi\) * ) S
(K) S
1.2 0.0 RM
0.0 -2.2 RM
8.36798 0 Nf
(c1) S
0.0 2.2 RM
1.5 0.0 RM
11 0 Nf
(^\(t) S
1.2 0.0 RM
0.0 -2.2 RM
8.36798 0 Nf
(1) S
0.0 2.2 RM
1.5 0.0 RM
11 0 Nf
(\)\)^\(S) S
1.2 0.0 RM
0.0 -2.2 RM
8.36798 0 Nf
(s1) S
0.0 2.2 RM
1.5 0.0 RM
11 0 Nf
(\) mod q ) S
0.0 -2.2 RM
0 -497.2 M
11 0 Nf
0.092726931 0 32 0 0 (where ) A
0.092726931 0 32 0 0 (S) A
1.2 0.0 RM
0.0 -2.2 RM
8.36798 0 Nf
0.092726931 0 32 0 0 (s1) A
0.0 2.2 RM
1.5 0.0 RM
11 0 Nf
0.092726931 0 32 0 0 ( is a random number within range [1, r-1]. The value of ) A
0.092726931 0 32 0 0 (K) A
1.2 0.0 RM
0.0 -2.2 RM
8.36798 0 Nf
0.092726931 0 32 0 0 (s1) A
0.0 2.2 RM
1.5 0.0 RM
11 0 Nf
0.092726931 0 32 0 0 ( MUST satisfy 1 < ) A
0.092726931 0 32 0 0 (K) A
1.2 0.0 RM
0.0 -2.2 RM
8.36798 0 Nf
0.092726931 0 32 0 0 (s1) A
0.0 2.2 RM
1.5 0.0 RM
11 0 Nf
0.092726931 0 32 0 0 ( < q-1. If) A
0.0 -2.2 RM
0 -512.6 M
11 0 Nf
0.291704953 0 32 0 0 (this condition is not held, the server MUST retry using another value for ) A
0.291704953 0 32 0 0 (S) A
1.2 0.0 RM
0.0 -2.2 RM
8.36798 0 Nf
0.291704953 0 32 0 0 (s1) A
0.0 2.2 RM
1.5 0.0 RM
11 0 Nf
0.291704953 0 32 0 0 (. The client MUST check) A
0.0 -2.2 RM
0 -528 M
(this condition upon reception. ) S
0 -552.2 M
11 0 Nf
(Let an intermediate value ) S
(t) S
1.2 0.0 RM
0.0 -2.2 RM
8.36798 0 Nf
(2) S
0.0 2.2 RM
1.5 0.0 RM
11 0 Nf
( be ) S
0.0 -2.2 RM
0 -578.6 M
11 0 Nf
(t) S
1.2 0.0 RM
0.0 -2.2 RM
8.36798 0 Nf
(2) S
0.0 2.2 RM
1.5 0.0 RM
11 0 Nf
( = INT\(H\(octet\(2\) | ) S
(OCTETS\(K) S
1.2 0.0 RM
0.0 -2.2 RM
8.36798 0 Nf
(c1) S
0.0 2.2 RM
1.5 0.0 RM
11 0 Nf
(\) | ) S
(OCTETS\(K) S
1.2 0.0 RM
0.0 -2.2 RM
8.36798 0 Nf
(s1) S
0.0 2.2 RM
1.5 0.0 RM
11 0 Nf
(\)\)\), ) S
0.0 -2.2 RM
0 -605 M
(the value z on the client side is derived by the following equation: ) S
0 -629.2 M
11 0 Nf
(z = ) S
(K) S
1.2 0.0 RM
0.0 -2.2 RM
8.36798 0 Nf
(s1) S
0.0 2.2 RM
1.5 0.0 RM
11 0 Nf
(^\(\(S) S
1.2 0.0 RM
0.0 -2.2 RM
8.36798 0 Nf
(c1) S
0.0 2.2 RM
1.5 0.0 RM
11 0 Nf
( + ) S
(t) S
1.2 0.0 RM
0.0 -2.2 RM
8.36798 0 Nf
(2) S
0.0 2.2 RM
1.5 0.0 RM
11 0 Nf
(\) / ) S
(\(S) S
1.2 0.0 RM
0.0 -2.2 RM
8.36798 0 Nf
(c1) S
0.0 2.2 RM
1.5 0.0 RM
11 0 Nf
( * ) S
(t) S
1.2 0.0 RM
0.0 -2.2 RM
8.36798 0 Nf
(1) S
0.0 2.2 RM
1.5 0.0 RM
11 0 Nf
( + pi\) mod r\) mod q. ) S
0.0 -2.2 RM
0 -631.4 M
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11 0 Nf
(The value z on the server side is derived by the following equation: ) S
0 -37.4 M
11 0 Nf
(z = ) S
(\(K) S
1.2 0.0 RM
0.0 -2.2 RM
8.36798 0 Nf
(c1) S
0.0 2.2 RM
1.5 0.0 RM
11 0 Nf
( * ) S
(g^\(t) S
1.2 0.0 RM
0.0 -2.2 RM
8.36798 0 Nf
(2) S
0.0 2.2 RM
1.5 0.0 RM
11 0 Nf
(\)\)^\(S) S
1.2 0.0 RM
0.0 -2.2 RM
8.36798 0 Nf
(s1) S
0.0 2.2 RM
1.5 0.0 RM
11 0 Nf
(\) mod q. ) S
0.0 -2.2 RM
0 -63.8 M
0.317522317 0 32 0 0 (\(Note: the original ISO specification contained a message pair containing verification of value z along) A
0 -77 M
2.38333344 0 32 0 0 (with the "transcript" of the protocol exchange. The functionality of this kind is contained in the) A
0 -90.2 M
11 0 Nf
(functions ) S
(VK) S
1.2 0.0 RM
0.0 -2.2 RM
8.36798 0 Nf
(c) S
0.0 2.2 RM
1.5 0.0 RM
11 0 Nf
( and ) S
(VK) S
1.2 0.0 RM
0.0 -2.2 RM
8.36798 0 Nf
(s) S
0.0 2.2 RM
1.5 0.0 RM
11 0 Nf
(.\)) S
0.0 -2.2 RM
0 -103.4 M
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(2.3.) S
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( Functions for Elliptic-Curve ) S
(Settings) S
0 -143.2 M
11 0 Nf
(For the elliptic-curve setting, we refer to some of the domain parameters by the following symbols: ) S
11 -163.8 M
gsave
0 setgray
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11.0 -163.77 2.75 0 360 arc
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22 -167.4 M
(q: for the prime used to define the group. ) S
11 -178 M
gsave
0 setgray
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11.0 -177.97 2.75 0 360 arc
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fill
grestore
22 -181.6 M
(G: for the defined point called the generator. ) S
11 -192.2 M
gsave
0 setgray
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11.0 -192.17 2.75 0 360 arc
closepath
fill
grestore
22 -195.8 M
(r: for the order of the subgroup generated by ) S
(G.) S
0 -220 M
0.547080576 0 32 0 0 (The function P\(p\) converts a curve point p into an integer representing point p, by computing x * 2 +) A
0 -233.2 M
1.34505212 0 32 0 0 (\(y mod 2\), where \(x, y\) are the coordinates of point p. P'\(z\) is the inverse of function P, that is, it) A
0 -246.4 M
2.06347656 0 32 0 0 (converts an integer z to a point p that satisfies P\(p\) = z. If such p exists, it is uniquely defined.) A
0 -259.6 M
0.799218774 0 32 0 0 (Otherwise, z does not represent a valid curve point. The operator + indicates the elliptic-curve group) A
0 -272.8 M
0.0770970359 0 32 0 0 (operation, and the operation [x] * p denotes an integer-multiplication of point p: it calculates p + p + ...) A
0 -286 M
1.2265625 0 32 0 0 (\(x times\) ... + p. See the literatures on elliptic-curve cryptography for the exact algorithms used for) A
0 -299.2 M
11 0 Nf
0.959284842 0 32 0 0 (those functions \(e.g. Section 3 of ) A
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153.6 -300.3 M
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0.959284842 0 32 0 0 ([RFC6090]) A
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0.959284842 0 32 0 0 (, which uses different notations, though.\) ) A
0.959284842 0 32 0 0 (0) A
1.2 0.0 RM
0.0 -2.2 RM
8.36798 0 Nf
0.959284842 0 32 0 0 (E) A
0.0 2.2 RM
1.5 0.0 RM
11 0 Nf
0.959284842 0 32 0 0 ( represents) A
0.0 -2.2 RM
0 -314.6 M
0.209635422 0 32 0 0 (the infinity point. The equation \(x / y mod z\) denotes a natural number w less than z that satisfies \(w *) A
0 -327.8 M
(y\) mod z = x mod z. ) S
0 -352 M
(The function J is defined as ) S
0 -376.2 M
(J\(pi\) = [pi] * G. ) S
0 -400.4 M
11 0 Nf
(The value of ) S
(K) S
1.2 0.0 RM
0.0 -2.2 RM
8.36798 0 Nf
(c1) S
0.0 2.2 RM
1.5 0.0 RM
11 0 Nf
( is derived as ) S
0.0 -2.2 RM
0 -426.8 M
11 0 Nf
(K) S
1.2 0.0 RM
0.0 -2.2 RM
8.36798 0 Nf
(c1) S
0.0 2.2 RM
1.5 0.0 RM
11 0 Nf
( = ) S
(P\(K) S
1.2 0.0 RM
0.0 -2.2 RM
8.36798 0 Nf
(c1) S
0.0 2.2 RM
1.5 0.0 RM
11 0 Nf
('\), where ) S
(K) S
1.2 0.0 RM
0.0 -2.2 RM
8.36798 0 Nf
(c1) S
0.0 2.2 RM
1.5 0.0 RM
11 0 Nf
(' = ) S
([S) S
1.2 0.0 RM
0.0 -2.2 RM
8.36798 0 Nf
(c1) S
0.0 2.2 RM
1.5 0.0 RM
11 0 Nf
(] * G, ) S
0.0 -2.2 RM
0 -453.2 M
11 0 Nf
0.393663198 0 32 0 0 (where ) A
0.393663198 0 32 0 0 (S) A
1.2 0.0 RM
0.0 -2.2 RM
8.36798 0 Nf
0.393663198 0 32 0 0 (c1) A
0.0 2.2 RM
1.5 0.0 RM
11 0 Nf
0.393663198 0 32 0 0 ( is a random number within range [1, r-1]. The value of ) A
0.393663198 0 32 0 0 (K) A
1.2 0.0 RM
0.0 -2.2 RM
8.36798 0 Nf
0.393663198 0 32 0 0 (c1) A
0.0 2.2 RM
1.5 0.0 RM
11 0 Nf
0.393663198 0 32 0 0 ( MUST represent a valid curve) A
0.0 -2.2 RM
0 -468.6 M
11 0 Nf
(point, and ) S
(K) S
1.2 0.0 RM
0.0 -2.2 RM
8.36798 0 Nf
(c1) S
0.0 2.2 RM
1.5 0.0 RM
11 0 Nf
(' SHALL\240NOT be ) S
(0) S
1.2 0.0 RM
0.0 -2.2 RM
8.36798 0 Nf
(E) S
0.0 2.2 RM
1.5 0.0 RM
11 0 Nf
(. The server MUST check this condition upon reception. ) S
0.0 -2.2 RM
0 -495 M
11 0 Nf
(Let an intermediate integer ) S
(t) S
1.2 0.0 RM
0.0 -2.2 RM
8.36798 0 Nf
(1) S
0.0 2.2 RM
1.5 0.0 RM
11 0 Nf
( be ) S
0.0 -2.2 RM
0 -521.4 M
11 0 Nf
(t) S
1.2 0.0 RM
0.0 -2.2 RM
8.36798 0 Nf
(1) S
0.0 2.2 RM
1.5 0.0 RM
11 0 Nf
( = INT\(H\(octet\(1\) | ) S
(OCTETS\(K) S
1.2 0.0 RM
0.0 -2.2 RM
8.36798 0 Nf
(c1) S
0.0 2.2 RM
1.5 0.0 RM
11 0 Nf
(\)\)\), ) S
0.0 -2.2 RM
0 -547.8 M
11 0 Nf
(the value of ) S
(K) S
1.2 0.0 RM
0.0 -2.2 RM
8.36798 0 Nf
(s1) S
0.0 2.2 RM
1.5 0.0 RM
11 0 Nf
( is derived from J\(pi\) and ) S
(K) S
1.2 0.0 RM
0.0 -2.2 RM
8.36798 0 Nf
(c1) S
0.0 2.2 RM
1.5 0.0 RM
11 0 Nf
(' = ) S
(P'\(K) S
1.2 0.0 RM
0.0 -2.2 RM
8.36798 0 Nf
(c1) S
0.0 2.2 RM
1.5 0.0 RM
11 0 Nf
(\) as: ) S
0.0 -2.2 RM
0 -574.2 M
11 0 Nf
(K) S
1.2 0.0 RM
0.0 -2.2 RM
8.36798 0 Nf
(s1) S
0.0 2.2 RM
1.5 0.0 RM
11 0 Nf
( = ) S
(P\([S) S
1.2 0.0 RM
0.0 -2.2 RM
8.36798 0 Nf
(s1) S
0.0 2.2 RM
1.5 0.0 RM
11 0 Nf
(] * \(J\(pi\) + ) S
([t) S
1.2 0.0 RM
0.0 -2.2 RM
8.36798 0 Nf
(1) S
0.0 2.2 RM
1.5 0.0 RM
11 0 Nf
(] * ) S
(K) S
1.2 0.0 RM
0.0 -2.2 RM
8.36798 0 Nf
(c1) S
0.0 2.2 RM
1.5 0.0 RM
11 0 Nf
('\)\), ) S
0.0 -2.2 RM
0 -600.6 M
11 0 Nf
0.444878459 0 32 0 0 (where ) A
0.444878459 0 32 0 0 (S) A
1.2 0.0 RM
0.0 -2.2 RM
8.36798 0 Nf
0.444878459 0 32 0 0 (s1) A
0.0 2.2 RM
1.5 0.0 RM
11 0 Nf
0.444878459 0 32 0 0 ( is a random number within range [1, r-1]. The value of ) A
0.444878459 0 32 0 0 (K) A
1.2 0.0 RM
0.0 -2.2 RM
8.36798 0 Nf
0.444878459 0 32 0 0 (s1) A
0.0 2.2 RM
1.5 0.0 RM
11 0 Nf
0.444878459 0 32 0 0 ( MUST represent a valid curve) A
0.0 -2.2 RM
0 -616 M
11 0 Nf
0.799262166 0 32 0 0 (point and satisfy [4] * ) A
0.799262166 0 32 0 0 (P'\(K) A
1.2 0.0 RM
0.0 -2.2 RM
8.36798 0 Nf
0.799262166 0 32 0 0 (s1) A
0.0 2.2 RM
1.5 0.0 RM
11 0 Nf
0.799262166 0 32 0 0 (\) <> ) A
0.799262166 0 32 0 0 (0) A
1.2 0.0 RM
0.0 -2.2 RM
8.36798 0 Nf
0.799262166 0 32 0 0 (E) A
0.0 2.2 RM
1.5 0.0 RM
11 0 Nf
0.799262166 0 32 0 0 (. If this condition is not satisfied, the server MUST retry using) A
0.0 -2.2 RM
0 -631.4 M
11 0 Nf
(another value for ) S
(S) S
1.2 0.0 RM
0.0 -2.2 RM
8.36798 0 Nf
(s1) S
0.0 2.2 RM
1.5 0.0 RM
11 0 Nf
(. The client MUST check this condition upon reception. ) S
0.0 -2.2 RM
0 -633.6 M
gsave
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219.9 -712 M
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8 8 Nf
(- 5 -) S
0 setgray
0 -8 M
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0 0 M
0.6 setlinewidth
0 -13.2 M
%%IncludeResource: font Times-Roman
11 0 Nf
(Let an intermediate integer ) S
(t) S
1.2 0.0 RM
0.0 -2.2 RM
8.36798 0 Nf
(2) S
0.0 2.2 RM
1.5 0.0 RM
11 0 Nf
( be ) S
0.0 -2.2 RM
0 -39.6 M
11 0 Nf
(t) S
1.2 0.0 RM
0.0 -2.2 RM
8.36798 0 Nf
(2) S
0.0 2.2 RM
1.5 0.0 RM
11 0 Nf
( = INT\(H\(octet\(2\) | ) S
(OCTETS\(K) S
1.2 0.0 RM
0.0 -2.2 RM
8.36798 0 Nf
(c1) S
0.0 2.2 RM
1.5 0.0 RM
11 0 Nf
(\) | ) S
(OCTETS\(K) S
1.2 0.0 RM
0.0 -2.2 RM
8.36798 0 Nf
(s1) S
0.0 2.2 RM
1.5 0.0 RM
11 0 Nf
(\)\)\), ) S
0.0 -2.2 RM
0 -66 M
(the value z on the client side is derived by the following equation: ) S
0 -90.2 M
11 0 Nf
(z = ) S
(P\([\(S) S
1.2 0.0 RM
0.0 -2.2 RM
8.36798 0 Nf
(c1) S
0.0 2.2 RM
1.5 0.0 RM
11 0 Nf
( + ) S
(t) S
1.2 0.0 RM
0.0 -2.2 RM
8.36798 0 Nf
(2) S
0.0 2.2 RM
1.5 0.0 RM
11 0 Nf
(\) / ) S
(\(S) S
1.2 0.0 RM
0.0 -2.2 RM
8.36798 0 Nf
(c1) S
0.0 2.2 RM
1.5 0.0 RM
11 0 Nf
( * ) S
(t) S
1.2 0.0 RM
0.0 -2.2 RM
8.36798 0 Nf
(1) S
0.0 2.2 RM
1.5 0.0 RM
11 0 Nf
( + pi\) mod r] * ) S
(P'\(K) S
1.2 0.0 RM
0.0 -2.2 RM
8.36798 0 Nf
(s1) S
0.0 2.2 RM
1.5 0.0 RM
11 0 Nf
(\)\). ) S
0.0 -2.2 RM
0 -116.6 M
(The value z on the server side is derived by the following equation: ) S
0 -140.8 M
11 0 Nf
(z = ) S
(P\([S) S
1.2 0.0 RM
0.0 -2.2 RM
8.36798 0 Nf
(s1) S
0.0 2.2 RM
1.5 0.0 RM
11 0 Nf
(] * ) S
(\(P'\(K) S
1.2 0.0 RM
0.0 -2.2 RM
8.36798 0 Nf
(c1) S
0.0 2.2 RM
1.5 0.0 RM
11 0 Nf
(\) + ) S
([t) S
1.2 0.0 RM
0.0 -2.2 RM
8.36798 0 Nf
(2) S
0.0 2.2 RM
1.5 0.0 RM
11 0 Nf
(] * G\)\). ) S
0.0 -2.2 RM
0 -154 M
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0 -154 M
[/View [/XYZ -4 603.0 null] /Dest /15 /DEST pdfmark
0 -173 M
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15 2 Nf
(3.) S
[/View [/XYZ -4 602.0 null] /Dest /59 /DEST pdfmark
( IANA ) S
(Considerations) S
0 -197.2 M
11 0 Nf
5.45859385 0 32 0 0 (Four tokens iso-kam3-dl-2048-sha256, iso-kam3-dl-4096-sha512, iso-kam3-ec-p256-sha256 and) A
0 -210.4 M
2.30436206 0 32 0 0 (iso-kam3-ec-p521-sha512 shall be allocated and registered according to the provision of the core) A
0 -223.6 M
(documentation when this document is promoted to an RFC. ) S
0 -247.8 M
(Note: More formal declarations will be added in the future drafts to meet the RFC 5226 requirements. ) S
0 -258.8 M
[/View [/XYZ -4 498.2 null] /Dest /16 /DEST pdfmark
0 -258.8 M
[/View [/XYZ -4 498.2 null] /Dest /17 /DEST pdfmark
0 -277.8 M
15 2 Nf
(4.) S
[/View [/XYZ -4 497.2 null] /Dest /60 /DEST pdfmark
( Security ) S
(Considerations) S
0 -302 M
11 0 Nf
4.87460947 0 32 0 0 (Refer the corresponding section of the core specification for algorithm-independent, generic) A
0 -315.2 M
(considerations. ) S
11 -335.8 M
gsave
0 setgray
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11.0 -335.77002 2.75 0 360 arc
closepath
fill
grestore
22 -339.4 M
6.48011351 0 32 0 0 (All random numbers used in these algorithms MUST be at least cryptographically) A
22 -352.6 M
(computationally secure against forward and backward guessing attacks. ) S
11 -363.2 M
gsave
0 setgray
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11.0 -363.170044 2.75 0 360 arc
closepath
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grestore
22 -366.8 M
4.10507822 0 32 0 0 (Computation times of all numerical operations on discrete-logarithm group elements and) A
22 -380 M
0.668269217 0 32 0 0 (elliptic-curve points MUST be normalized and made independent of the exact values, to prevent) A
22 -393.2 M
(timing-based side-channel ) S
(attacks.) S
0 -417.4 M
2.55859375 0 32 0 0 (The usual construction of authenticated key exchange algorithms are build from a key-exchange) A
0 -430.6 M
3.56529021 0 32 0 0 (period and a key verification period, and the latter usually involving some kind of exchange) A
0 -443.8 M
0.458072931 0 32 0 0 (transaction to be verified, to avoid security risks or vulnerabilities caused from mixing of values from) A
0 -457 M
0.850873172 0 32 0 0 (two or more key exchanges. In the design of the algorithms in this document, such a functionality is) A
0 -470.2 M
1.24041188 0 32 0 0 (defined in generalized manner in the core specification ) A
gsave
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254.2 -471.3 M
113.898438 0 RL
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1.24041188 0 32 0 0 ([I-D.ietf-httpauth-mutual]) A
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1.24041188 0 32 0 0 ( \(see definitions of ) A
0 -483.4 M
11 0 Nf
0.840332031 0 32 0 0 (VK) A
1.2 0.0 RM
0.0 -2.2 RM
8.36798 0 Nf
0.840332031 0 32 0 0 (c) A
0.0 2.2 RM
1.5 0.0 RM
11 0 Nf
0.840332031 0 32 0 0 ( and ) A
0.840332031 0 32 0 0 (VK) A
1.2 0.0 RM
0.0 -2.2 RM
8.36798 0 Nf
0.840332031 0 32 0 0 (s) A
0.0 2.2 RM
1.5 0.0 RM
11 0 Nf
0.840332031 0 32 0 0 (\). If any attempts to reuse the algorithm defined above with any other protocols exist,) A
0.0 -2.2 RM
0 -498.8 M
(care MUST be taken on that aspect. ) S
0 -509.8 M
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0 -509.8 M
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15 2 Nf
(5.) S
[/View [/XYZ -4 246.199829 null] /Dest /61 /DEST pdfmark
( Notice on intellectual ) S
(properties) S
0 -553 M
11 0 Nf
0.270432681 0 32 0 0 (The National Institute of Advanced Industrial Science and Technology \(AIST\) and Yahoo! Japan, Inc.) A
0 -566.2 M
0.311197907 0 32 0 0 (has jointly submitted a patent application on the protocol proposed in this documentation to the Patent) A
0 -579.4 M
0.125868052 0 32 0 0 (Office of Japan. The patent is intended to be open to any implementors of this protocol and its variants) A
0 -592.6 M
0.2734375 0 32 0 0 (under non-exclusive royalty-free manner. For the details of the patent application and its status, please) A
0 -605.8 M
(contact the author of this document. ) S
0 -630 M
1.08359373 0 32 0 0 (The elliptic-curve based authentication algorithms might involve several existing third-party patents.) A
0 -643.2 M
0.114889704 0 32 0 0 (The authors of the document take no position regarding the validity or scope of such patents, and other) A
0 -656.4 M
(patents as well. ) S
0 -656.4 M
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219.9 -712 M
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8 8 Nf
(- 6 -) S
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15 2 Nf
(6.) S
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( ) S
(References) S
0 -25.5 M
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0 -44 M
13 2 Nf
(6.1.) S
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( Normative ) S
(References) S
8 -71.3 M
%%IncludeResource: font Times-Roman
11 0 Nf
([FIPS.180-2.2002]) S
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(National Institute of Standards and Technology, ) S
(\233) S
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355.7 -72.4 M
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136.7 -85.6 M
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178.5 -120.5 M
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(International Organization for Standardization, \233Information technology \235) S
112.2 -326.5 M
(Security techniques \235 Key management \235 Part 4: Mechanisms based on) S
112.2 -339.8 M
(weak secrets,\234 ISO\240Standard 11770-4, ) S
(May\2402006.) S
8 -361.5 M
([RFC6090]) S
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( A. \(Informative\) Group Parameters for Discrete-Logarithm) S
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(Algorithms) S
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3.01204419 0 32 0 0 (The MODP group used for the iso-kam3-dl-2048-sha256 algorithm is defined by the following ) A
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(parameters.) S
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(The prime ) S
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( g = 2.) S
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( r = \(q - 1\) / 2 =) S
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0 -124.2 M
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0 -135 M
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0 -145.8 M
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0 -156.6 M
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0 -199.8 M
(       0AB9472D 45565534 7FFFFFFF FFFFFFFF.) S
0 -224 M
11 0 Nf
3.01204419 0 32 0 0 (The MODP group used for the iso-kam3-dl-4096-sha512 algorithm is defined by the following ) A
0 -237.2 M
(parameters.) S
0 -261.4 M
(The prime ) S
(is:) S
0 -283.2 M
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( q = 0xFFFFFFFF FFFFFFFF C90FDAA2 2168C234 C4C6628B 80DC1CD1) S
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0 -315.6 M
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0 -326.4 M
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0 -510 M
(       FFFFFFFF FFFFFFFF.) S
0 -534.2 M
11 0 Nf
(The generator ) S
(is:) S
0 -556 M
9.0 4 Nf
( g = 2.) S
0 -580.2 M
11 0 Nf
(The size of the subgroup generated by g ) S
(is:) S
0 -602 M
9.0 4 Nf
( r = \(q - 1\) / 2 =) S
0 -612.8 M
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(       FFFFFFFF FFFFFFFF.) S
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(Appendix) S
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( B. \(Informative\) Derived Numerical ) S
(Values) S
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0.24609375 0 32 0 0 (This section provides several numerical values for implementing this protocol, derived from the above) A
0 -240.2 M
(specifications. The values shown in this section are for informative purposes only. ) S
203.1 -268.5 M
11 2 Nf
(dl-2048) S
244.1 -268.5 M
11 2 Nf
(dl-4096) S
285 -268.5 M
11 2 Nf
(ec-p256) S
327.1 -268.5 M
11 2 Nf
(ec-p521) S
51.7 -288.3 M
11 0 Nf
(Size of ) S
(K) S
1.2 0.0 RM
0.0 -2.2 RM
8.36798 0 Nf
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0.0 2.2 RM
1.5 0.0 RM
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203.1 -289.4 M
(2048) S
244.1 -289.4 M
(4096) S
285 -289.4 M
(257) S
327.1 -289.4 M
(522) S
369.3 -289.4 M
(\(bits\)) S
51.7 -310.2 M
(hSize, Size of ) S
(H\(...\)) S
203.1 -310.2 M
(256) S
244.1 -310.2 M
(512) S
285 -310.2 M
(256) S
327.1 -310.2 M
(512) S
369.3 -310.2 M
(\(bits\)) S
51.7 -330 M
11 0 Nf
(length of ) S
(OCTETS\(K) S
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8.36798 0 Nf
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203.1 -331.1 M
(256) S
244.1 -331.1 M
(512) S
285 -331.1 M
(33) S
327.1 -331.1 M
(66) S
369.3 -331.1 M
(\(octets\)) S
51.7 -351.9 M
(length of kc1, ks1 param. ) S
(values.) S
203.1 -351.9 M
(344 ) S
(*) S
244.1 -351.9 M
(684 ) S
(*) S
285 -351.9 M
(66) S
327.1 -351.9 M
(132) S
369.3 -351.9 M
(\(octets\)) S
51.7 -371.7 M
(length of vkc, vks param. ) S
(values.) S
203.1 -371.7 M
(44 ) S
(*) S
244.1 -371.7 M
(88 ) S
(*) S
285 -371.7 M
(64) S
327.1 -371.7 M
(128) S
369.3 -371.7 M
(\(octets\)) S
51.7 -391.4 M
11 0 Nf
(minimum allowed ) S
(S) S
1.2 0.0 RM
0.0 -2.2 RM
8.36798 0 Nf
(c1) S
0.0 2.2 RM
1.5 0.0 RM
0.0 -2.2 RM
203.1 -392.5 M
11 0 Nf
(2048) S
244.1 -392.5 M
(4096) S
285 -392.5 M
(1) S
327.1 -392.5 M
(1) S
369.3 -392.5 M
(\240) S
0 -423.6 M
11 0 Nf
(\(The numbers marked with an * do not include any enclosing quotation ) S
(marks.\)) S
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15 2 Nf
(Appendix) S
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( C. \(Informative\) Draft Change ) S
(Log) S
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0 -483.6 M
15 2 Nf
(C.1.) S
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( Changes in HTTPAUTH revision ) S
(02) S
11 -504.1 M
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22 -507.8 M
11 0 Nf
(Added nIterPi parameter to adjust to the changes to the core draft. ) S
11 -518.3 M
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22 -522 M
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(01) S
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1.74939907 0 32 0 0 (Notation change: integer output of hash function will be notated as INT\(H\(*\)\), changed from ) A
22 -589.4 M
(H\(*\).) S
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PAFTECH AB 2003-2026
2026-04-24 13:04:24