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%%Title: Mutual Authentication Protocol for HTTP: KAM3-based Cryptographic Algorithms
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3.4908855 0 32 0 0 ( [I-D.ietf-httpauth-mutual]. The algorithms are based on so-called "Augmented) A
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1.15507817 0 32 0 0 (Password-based Authenticated Key Exchange" \(Augmented PAKE\) techniques. In particular, it uses) A
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1.75435698 0 32 0 0 ( as "default functions". For the purpose of) A
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(1.1.) S
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( ) S
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(.) S
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(document.) S
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( Cryptographic Overview ) S
(\(Non-normative\)) S
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(notations are used, and all group operations \(mod q and mod r\) are omitted. ) S
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( Authentication ) S
(Algorithms) S
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0.81640625 0 32 0 0 (This document specifies only one family of the authentication algorithm. The family consists of four) A
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2.23366475 0 32 0 0 (authentication algorithms, which only differ in their underlying mathematical groups and security) A
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(parameters. The algorithms do not add any additional parameters. The tokens for these algorithms ) S
(are) S
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2.421875 0 32 0 0 (iso-kam3-dl-2048-sha256: for the 2048-bit discrete-logarithm setting with the SHA-256 hash) A
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(function. ) S
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(hash function. ) S
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(function.) S
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0.439778656 0 32 0 0 ( [FIPS.180-2.2002]. The hash iteration count) A
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(nIterPi is 16384. The representation of the parameters kc1, ks1, vkc, and vks is base64-fixed-number. ) S
0 -209.8 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 -223 M
3.006392 0 32 0 0 (and P-521, respectively, specified in the appendix\240D.1.2 of ) A
gsave
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285.2 -224.1 M
54.9034081 0 RL
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3.006392 0 32 0 0 (FIPS PUB ) A
gsave
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340.1 -224.1 M
25.6601562 0 RL
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3.006392 0 32 0 0 (186-4) A
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3.006392 0 32 0 0 ( [FIPS.186-4.2013]) A
0 -236.2 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 -249.4 M
0.219970703 0 32 0 0 (P-256 curve and SHA-512 for the P-521 curve, respectively. Cofactors of these curves are 1. The hash) A
0 -262.6 M
2.67630219 0 32 0 0 (iteration count nIterPi is 16384. The representation of the parameters kc1, ks1, vkc, and vks is) A
0 -275.8 M
(hex-fixed-number. ) S
0 -300 M
0.763281226 0 32 0 0 ([[Editorial Note: remove before submission] We should take a care on recent hot discussion topic on) A
0 -313.2 M
(the choice of elliptic curves for cryptography.]] ) S
0 -337.4 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 -350.6 M
gsave
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0 -351.7 M
49.4101562 0 RL
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8.17578125 0 32 0 0 (ISO/IEC ) A
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49.4 -351.7 M
36.6601562 0 RL
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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 -363.8 M
1.37469947 0 32 0 0 (implementers should use this document as the normative reference, because the algorithm has been) A
0 -377 M
(changed in several minor details as well as major improvements. ) S
0 -388 M
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13 2 Nf
(3.1.) S
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( Support Functions and ) S
(Notations) S
0 -427.8 M
11 0 Nf
(The algorithm definitions use several support functions and notations defined ) S
(below:) S
0 -452 M
(The integers in the specification are in decimal, or in hexadecimal when prefixed with ) S
("0x".) S
0 -476.2 M
3.04507208 0 32 0 0 (The functions named octet\(\), OCTETS\(\), and INT\(\) are those defined in the ) A
gsave
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373.1 -477.3 M
24.7208538 0 RL
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3.04507208 0 32 0 0 (core ) A
gsave
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397.8 -477.3 M
56.1875 0 RL
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grestore
3.04507208 0 32 0 0 (specification) A
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3.04507208 0 32 0 0 ( ) A
0 -489.4 M
([I-D.ietf-httpauth-mutual].) S
0 -513.6 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 -526.8 M
(specification, which takes the shortest representation without preceding zeros. ) S
0 -551 M
2.79947925 0 32 0 0 (All of the algorithms defined in this specification use the default functions defined in the core) A
0 -564.2 M
11 0 Nf
1.15966797 0 32 0 0 (specification \(defined in Section 11 of ) A
gsave
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178 -565.3 M
113.898438 0 RL
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1.15966797 0 32 0 0 ([I-D.ietf-httpauth-mutual]) A
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1.15966797 0 32 0 0 (\) for computing the values pi, ) A
1.15966797 0 32 0 0 (VK) A
1.2 0.0 RM
0.0 -2.2 RM
8.36798 0 Nf
1.15966797 0 32 0 0 (c) A
0.0 2.2 RM
1.5 0.0 RM
0.0 -2.2 RM
0 -579.6 M
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 -592.8 M
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13 2 Nf
(3.2.) S
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( Functions for Discrete-Logarithm ) S
(Settings) S
0 -632.6 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 -645.8 M
(mod z = x mod z. ) S
0 -645.8 M
gsave
0 setgray
219.9 -712 M
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8 8 Nf
(- 4 -) S
0 setgray
0 -8 M
grestore
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0.6 setlinewidth
0 -13.2 M
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11 0 Nf
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 -33.8 M
gsave
0 setgray
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11.0 -33.77 2.75 0 360 arc
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grestore
22 -37.4 M
(q: for "the prime" defining the MODP group. ) S
11 -48 M
gsave
0 setgray
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11.0 -47.97 2.75 0 360 arc
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grestore
22 -51.6 M
(g: for "the generator" associated with the group. ) S
11 -62.2 M
gsave
0 setgray
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11.0 -62.170002 2.75 0 360 arc
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grestore
22 -65.8 M
(r: for the order of the subgroup generated by ) S
(g.) S
0 -90 M
(The function J is defined as ) S
0 -114.2 M
(J\(pi\) = g^\(pi\) mod q. ) S
0 -138.4 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 -164.8 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 -191.2 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 -206.6 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 -233 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 -248.4 M
(reception. ) S
0 -272.6 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 -299 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 -325.4 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 -351.8 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 -378.2 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 -393.6 M
0.0837402344 0 32 0 0 (this condition is not held, the server MUST reject the exchange. The client MUST check this condition) A
0 -406.8 M
(upon reception. ) S
0 -431 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 -457.4 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 -483.8 M
(the value z on the client side is derived by the following equation: ) S
0 -508 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 -534.4 M
(The value z on the server side is derived by the following equation: ) S
0 -558.6 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 -585 M
0.317522317 0 32 0 0 (\(Note: the original ISO specification contained a message pair containing verification of value z along) A
0 -598.2 M
2.38333344 0 32 0 0 (with the "transcript" of the protocol exchange. The functionality of this kind is contained in the) A
0 -611.4 M
11 0 Nf
(functions ) S
(VK) S
1.2 0.0 RM
0.0 -2.2 RM
8.36798 0 Nf
(c) S
0.0 2.2 RM
1.5 0.0 RM
11 0 Nf
( and ) S
(VK) S
1.2 0.0 RM
0.0 -2.2 RM
8.36798 0 Nf
(s) S
0.0 2.2 RM
1.5 0.0 RM
11 0 Nf
(.\)) S
0.0 -2.2 RM
0 -624.6 M
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0 -624.6 M
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0 -624.6 M
gsave
0 setgray
219.9 -712 M
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8 8 Nf
(- 5 -) S
0 setgray
0 -8 M
grestore
pgsave restore N
%%Page: 6 6
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%%BeginPageSetup
/pgsave save D
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0 0 M
0.6 setlinewidth
0 -15.6 M
%%IncludeResource: font Times-Bold
13 2 Nf
(3.3.) S
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( Functions for Elliptic-Curve ) S
(Settings) S
0 -39.8 M
%%IncludeResource: font Times-Roman
11 0 Nf
(For the elliptic-curve setting, we refer to some of the domain parameters by the following symbols: ) S
11 -60.4 M
gsave
0 setgray
newpath
11.0 -60.3700027 2.75 0 360 arc
closepath
fill
grestore
22 -64 M
(q: for the prime used to define the group. ) S
11 -74.6 M
gsave
0 setgray
newpath
11.0 -74.57 2.75 0 360 arc
closepath
fill
grestore
22 -78.2 M
(G: for the defined point called the generator. ) S
11 -88.8 M
gsave
0 setgray
newpath
11.0 -88.77 2.75 0 360 arc
closepath
fill
grestore
22 -92.4 M
(h: for the cofactor of the group. ) S
11 -103 M
gsave
0 setgray
newpath
11.0 -102.969994 2.75 0 360 arc
closepath
fill
grestore
22 -106.6 M
(r: for the order of the subgroup generated by ) S
(G.) S
0 -130.8 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 -144 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 -157.2 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 -170.4 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 -183.6 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 -196.8 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 -210 M
11 0 Nf
0.959284842 0 32 0 0 (those functions \(e.g. Section 3 of ) A
gsave
newpath
153.6 -211.1 M
50.1054688 0 RL
stroke
grestore
0.959284842 0 32 0 0 ([RFC6090]) A
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0.959284842 0 32 0 0 (, which uses different notations, though.\) ) 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 -225.4 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 \(w *) A
0 -238.6 M
(y\) mod z = x mod z. ) S
0 -262.8 M
(The function J is defined as ) S
0 -287 M
(J\(pi\) = [pi] * G. ) S
0 -311.2 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 -337.6 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 -364 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 -379.4 M
11 0 Nf
(point, and [h] * ) 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 -405.8 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 -432.2 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 -458.6 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 -485 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 -511.4 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 -526.8 M
11 0 Nf
1.17339408 0 32 0 0 (point and satisfy [h] * ) A
1.17339408 0 32 0 0 (P'\(K) A
1.2 0.0 RM
0.0 -2.2 RM
8.36798 0 Nf
1.17339408 0 32 0 0 (s1) A
0.0 2.2 RM
1.5 0.0 RM
11 0 Nf
1.17339408 0 32 0 0 (\) <> ) A
1.17339408 0 32 0 0 (0) A
1.2 0.0 RM
0.0 -2.2 RM
8.36798 0 Nf
1.17339408 0 32 0 0 (E) A
0.0 2.2 RM
1.5 0.0 RM
11 0 Nf
1.17339408 0 32 0 0 (. If this condition is not satisfied, the server MUST reject the) A
0.0 -2.2 RM
0 -542.2 M
(exchange. The client MUST check this condition upon reception. ) S
0 -566.4 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
(2) S
0.0 2.2 RM
1.5 0.0 RM
11 0 Nf
( be ) S
0.0 -2.2 RM
0 -592.8 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 -619.2 M
(the value z on the client side is derived by the following equation: ) S
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11 0 Nf
(z = ) S
(P\([\(S) S
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0.0 -2.2 RM
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(c1) S
0.0 2.2 RM
1.5 0.0 RM
11 0 Nf
( + ) S
(t) S
1.2 0.0 RM
0.0 -2.2 RM
8.36798 0 Nf
(2) S
0.0 2.2 RM
1.5 0.0 RM
11 0 Nf
(\) / ) 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 -39.6 M
(The value z on the server side is derived by the following equation: ) S
0 -63.8 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
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(4.) S
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( IANA ) S
(Considerations) S
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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
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2.30436206 0 32 0 0 (iso-kam3-ec-p521-sha512 shall be allocated and registered according to the provision of the core) A
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(documentation when this document is promoted to an RFC. ) S
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(Note: More formal declarations will be added in the future drafts to meet the RFC 5226 requirements. ) S
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15 2 Nf
(5.) S
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( Security ) S
(Considerations) S
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4.87460947 0 32 0 0 (Refer the corresponding section of the core specification for algorithm-independent, generic) A
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(considerations, too. ) S
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0 -264.8 M
13 2 Nf
(5.1.) S
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( General Implementation ) S
(Considerations) S
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11 0 Nf
0.99202472 0 32 0 0 (During the exchange, the value ) A
0.99202472 0 32 0 0 (VK) A
1.2 0.0 RM
0.0 -2.2 RM
8.36798 0 Nf
0.99202472 0 32 0 0 (s) A
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0.99202472 0 32 0 0 (, defined in ) A
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0.99202472 0 32 0 0 (, MUST only be sent) A
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22 -304.4 M
11 0 Nf
1.9076823 0 32 0 0 (when the server has received a correct \(expected\) value of ) A
1.9076823 0 32 0 0 (VK) A
1.2 0.0 RM
0.0 -2.2 RM
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1.9076823 0 32 0 0 (c) A
0.0 2.2 RM
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1.9076823 0 32 0 0 (. This is a requirement from) A
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22 -319.8 M
(underlying cryptography stated in ) S
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([ISO.11770-4.2006]) S
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(. ) S
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gsave
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11.0 -330.370026 2.75 0 360 arc
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22 -334 M
6.48011351 0 32 0 0 (All random numbers used in these algorithms MUST be at least cryptographically) A
22 -347.2 M
(computationally secure against forward and backward guessing attacks. ) S
11 -357.8 M
gsave
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22 -361.4 M
4.10507822 0 32 0 0 (Computation times of all numerical operations on discrete-logarithm group elements and) A
22 -374.6 M
0.668269217 0 32 0 0 (elliptic-curve points MUST be normalized and made independent of the exact values, to prevent) A
22 -387.8 M
(timing-based side-channel ) S
(attacks.) S
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0 -398.8 M
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(5.2.) S
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( Cryptographic Assumptions and ) S
(Considerations) S
0 -438.6 M
11 0 Nf
0.113970585 0 32 0 0 (The notices on this subsection is mostly for those who analyze the security of this algorithm, and those) A
0 -451.8 M
(who might want to make a derived work of this algorithm specification. ) S
11 -472.4 M
gsave
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22 -476 M
11 0 Nf
1.02434897 0 32 0 0 (Handling of invalid ) A
1.02434897 0 32 0 0 (K) A
1.2 0.0 RM
0.0 -2.2 RM
8.36798 0 Nf
1.02434897 0 32 0 0 (s1) A
0.0 2.2 RM
1.5 0.0 RM
11 0 Nf
1.02434897 0 32 0 0 ( value in the exchange \(now: to reject the exchange\) has been changed) A
0.0 -2.2 RM
22 -491.4 M
11 0 Nf
0.47408855 0 32 0 0 (from original ISO specification \(original: to retry with another random ) A
0.47408855 0 32 0 0 (S) A
1.2 0.0 RM
0.0 -2.2 RM
8.36798 0 Nf
0.47408855 0 32 0 0 (s1) A
0.0 2.2 RM
1.5 0.0 RM
11 0 Nf
0.47408855 0 32 0 0 ( value\). This is due to) A
0.0 -2.2 RM
22 -506.8 M
0.761197925 0 32 0 0 (an observation that this condition is less likely from the random error caused by unlucky choice) A
22 -520 M
11 0 Nf
2.4708426 0 32 0 0 (of ) A
2.4708426 0 32 0 0 (S) A
1.2 0.0 RM
0.0 -2.2 RM
8.36798 0 Nf
2.4708426 0 32 0 0 (s1) A
0.0 2.2 RM
1.5 0.0 RM
11 0 Nf
2.4708426 0 32 0 0 (, but more likely from the systematic failure from invalid J\(pi\) value, even implying) A
0.0 -2.2 RM
22 -535.4 M
(possible denial-of-service attacks. ) S
11 -546 M
gsave
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22 -549.6 M
0.725260437 0 32 0 0 (The usual construction of authenticated key exchange algorithms are build from a key-exchange) A
22 -562.8 M
1.99386156 0 32 0 0 (period and a key verification period, and the latter usually involving some kind of exchange) A
22 -576 M
0.642578125 0 32 0 0 (transaction to be verified, to avoid security risks or vulnerabilities caused from mixing of values) A
22 -589.2 M
2.33569336 0 32 0 0 (from two or more key exchanges. In the design of the algorithms in this document, such a) A
22 -602.4 M
0.4765625 0 32 0 0 (functionality is defined in generalized manner in the core specification ) A
gsave
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340.1 -603.5 M
113.898438 0 RL
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0.4765625 0 32 0 0 ([I-D.ietf-httpauth-mutual]) A
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22 -615.6 M
11 0 Nf
0.286865234 0 32 0 0 (\(see definitions of ) A
0.286865234 0 32 0 0 (VK) A
1.2 0.0 RM
0.0 -2.2 RM
8.36798 0 Nf
0.286865234 0 32 0 0 (c) A
0.0 2.2 RM
1.5 0.0 RM
11 0 Nf
0.286865234 0 32 0 0 ( and ) A
0.286865234 0 32 0 0 (VK) A
1.2 0.0 RM
0.0 -2.2 RM
8.36798 0 Nf
0.286865234 0 32 0 0 (s) A
0.0 2.2 RM
1.5 0.0 RM
11 0 Nf
0.286865234 0 32 0 0 (\). If any attempts to reuse the algorithm defined above with any) A
0.0 -2.2 RM
22 -631 M
(other protocols exist, care MUST be taken on that aspect. ) S
11 -641.6 M
gsave
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22 -645.2 M
2.045573 0 32 0 0 (The domain parameters chosen and specified in this draft has a few assumptions. In the DL) A
22 -658.4 M
1.65011156 0 32 0 0 (setting, q has to be safe prime \([\(q - 1\) / 2] must also be prime\), and r should be the largest) A
22 -671.6 M
1.70136714 0 32 0 0 (possible value [\(q - 1\) / 2]. In the EC setting, r has to be prime. Defining a variation of this) A
22 -671.6 M
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219.9 -712 M
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8 8 Nf
(- 7 -) S
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44 -8 M
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22 -13.2 M
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11 0 Nf
(algorithm using a different domain parameter SHOULD care about these conditions. ) S
0 -24.2 M
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0 -24.2 M
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15 2 Nf
(6.) S
[/View [/XYZ -4 731.8 null] /Dest /76 /DEST pdfmark
( Notice on intellectual ) S
(properties) S
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0.270432681 0 32 0 0 (The National Institute of Advanced Industrial Science and Technology \(AIST\) and Yahoo! Japan, Inc.) A
0 -80.6 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 -93.8 M
0.16015625 0 32 0 0 (Office of Japan. The patent is intended to be open to any implementers of this protocol and its variants) A
0 -107 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 -120.2 M
(contact the author of this document. ) S
0 -144.4 M
1.08359373 0 32 0 0 (The elliptic-curve based authentication algorithms might involve several existing third-party patents.) A
0 -157.6 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
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(patents as well. ) S
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15 2 Nf
(7.) S
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( ) S
(References) S
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(7.1.) S
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( Normative ) S
(References) S
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([FIPS.180-2.2002]) S
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(National Institute of Standards and Technology, ) S
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(,\234 FIPS\240PUB 180-2, ) S
(August\2402002.) S
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([FIPS.186-4.2013]) S
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(National Institute of Standards and Technology, ) S
(\233) S
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(July\2402013.) S
8 -313 M
0.989464402 0.989464402 scale

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1.01064777 1.01064777 scale

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(Oiwa, Y., Watanabe, H., Takagi, H., Maeda, K., Hayashi, T., and Y.) S
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(Ioku, ) S
(\233) S
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(Mutual Authentication Protocol for ) S
gsave
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325.5 -338.3 M
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(HTTP) S
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(,\234) S
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(draft-ietf-httpauth-mutual-04 \(work in progress\), ) S
(February\2402015.) S
8 -372.1 M
([RFC2119]) S
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(\() S
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(\).) S
8 -407.1 M
([RFC3526]) S
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136.7 -407.1 M
(Kivinen, T. and M. Kojo, ) S
(\233) S
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(7.2.) S
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( Informative ) S
(References) S
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112.2 -496.1 M
(International Organization for Standardization, \233Information technology \235) S
112.2 -509.4 M
(Security techniques \235 Key management \235 Part 4: Mechanisms based on) S
112.2 -522.6 M
(weak secrets,\234 ISO\240Standard 11770-4, ) S
(May\2402006.) S
8 -544.3 M
([RFC6090]) S
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112.2 -544.3 M
(McGrew, D., Igoe, K., and M. Salter, ) S
(\233) S
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(Cryptography ) S
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(Algorithms) S
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(Appendix) S
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( A. \(Informative\) Group Parameters for Discrete-Logarithm) S
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(Based ) S
(Algorithms) S
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11 0 Nf
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
0 -651.6 M
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0 -132.2 M
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0 -143 M
(       15728E5A 8AACAA68 FFFFFFFF FFFFFFFF.) S
0 -167.2 M
11 0 Nf
(The generator ) S
(is:) S
0 -189 M
9.0 4 Nf
( g = 2.) S
0 -213.2 M
11 0 Nf
(The size of the subgroup generated by g ) S
(is:) S
0 -235 M
9.0 4 Nf
( r = \(q - 1\) / 2 =) S
0 -245.8 M
(     0x7FFFFFFF FFFFFFFF E487ED51 10B4611A 62633145 C06E0E68) S
0 -256.6 M
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0 -267.4 M
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0 -278.2 M
(       F242DABB 312F3F63 7A262174 D31BF6B5 85FFAE5B 7A035BF6) S
0 -289 M
(       F71C35FD AD44CFD2 D74F9208 BE258FF3 24943328 F6722D9E) S
0 -299.8 M
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0 -310.6 M
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0 -321.4 M
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0 -332.2 M
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0 -343 M
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0 -353.8 M
(       0AB9472D 45565534 7FFFFFFF FFFFFFFF.) S
0 -378 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 -391.2 M
(parameters.) S
0 -415.4 M
(The prime ) S
(is:) S
0 -437.2 M
9.0 4 Nf
( q = 0xFFFFFFFF FFFFFFFF C90FDAA2 2168C234 C4C6628B 80DC1CD1) S
0 -448 M
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0 -491.2 M
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0 -502 M
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0 -512.8 M
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0 -523.6 M
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0 -556 M
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0 -653.2 M
(       93B4EA98 8D8FDDC1 86FFB7DC 90A6C08F 4DF435C9 34063199) S
0 -664 M
(       FFFFFFFF FFFFFFFF.) S
0 -673 M
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(The generator ) S
(is:) S
0 -35 M
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9.0 4 Nf
( g = 2.) S
0 -59.2 M
11 0 Nf
(The size of the subgroup generated by g ) S
(is:) S
0 -81 M
9.0 4 Nf
( r = \(q - 1\) / 2 =) S
0 -91.8 M
(     0x7FFFFFFF FFFFFFFF E487ED51 10B4611A 62633145 C06E0E68) S
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0 -124.2 M
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0 -135 M
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0 -286.2 M
(       143E2CA3 A735E02E CCD94B27 D04861D1 119DD0C3 28ADF3F6) S
0 -297 M
(       8FB094B8 67716BD7 DC0DEEBB 10B8240E 68034893 EAD82D54) S
0 -307.8 M
(       C9DA754C 46C7EEE0 C37FDBEE 48536047 A6FA1AE4 9A0318CC) S
0 -318.6 M
(       FFFFFFFF FFFFFFFF.) S
0 -327.6 M
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15 2 Nf
(Appendix) S
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( B. \(Informative\) Derived Numerical ) S
(Values) S
0 -372.8 M
11 0 Nf
0.24609375 0 32 0 0 (This section provides several numerical values for implementing this protocol, derived from the above) A
0 -386 M
(specifications. The values shown in this section are for informative purposes only. ) S
203.1 -414.3 M
11 2 Nf
(dl-2048) S
244.1 -414.3 M
11 2 Nf
(dl-4096) S
285 -414.3 M
11 2 Nf
(ec-p256) S
327.1 -414.3 M
11 2 Nf
(ec-p521) S
51.7 -434.1 M
11 0 Nf
(Size 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
( ) S
(etc.) S
0.0 -2.2 RM
203.1 -435.1 M
(2048) S
244.1 -435.1 M
(4096) S
285 -435.1 M
(257) S
327.1 -435.1 M
(522) S
369.3 -435.1 M
(\(bits\)) S
51.7 -456 M
(hSize, Size of ) S
(H\(...\)) S
203.1 -456 M
(256) S
244.1 -456 M
(512) S
285 -456 M
(256) S
327.1 -456 M
(512) S
369.3 -456 M
(\(bits\)) S
51.7 -475.8 M
11 0 Nf
(length of ) 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
(etc.) S
0.0 -2.2 RM
203.1 -476.9 M
(256) S
244.1 -476.9 M
(512) S
285 -476.9 M
(33) S
327.1 -476.9 M
(66) S
369.3 -476.9 M
(\(octets\)) S
51.7 -497.7 M
(length of kc1, ks1 param. ) S
(values.) S
203.1 -497.7 M
(344 ) S
(*) S
244.1 -497.7 M
(684 ) S
(*) S
285 -497.7 M
(66) S
327.1 -497.7 M
(132) S
369.3 -497.7 M
(\(octets\)) S
51.7 -517.4 M
(length of vkc, vks param. ) S
(values.) S
203.1 -517.4 M
(44 ) S
(*) S
244.1 -517.4 M
(88 ) S
(*) S
285 -517.4 M
(64) S
327.1 -517.4 M
(128) S
369.3 -517.4 M
(\(octets\)) S
51.7 -537.2 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 -538.3 M
11 0 Nf
(2048) S
244.1 -538.3 M
(4096) S
285 -538.3 M
(1) S
327.1 -538.3 M
(1) S
369.3 -538.3 M
(\240) S
0 -569.4 M
11 0 Nf
(\(The numbers marked with an * do not include any enclosing quotation ) S
(marks.\)) S
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0 -599.4 M
15 2 Nf
(Appendix) S
[/View [/XYZ -4 175.649963 null] /Dest /82 /DEST pdfmark
( C. \(Informative\) Draft Change ) S
(Log) S
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(C.1.) S
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( Changes in HTTPAUTH-WG revision ) S
(02) S
11 -38.6 M
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(No technical changes: references ) S
(updated.) S
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0 -72.2 M
15 2 Nf
(C.2.) S
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( Changes in HTTPAUTH-WG revision ) S
(01) S
11 -92.8 M
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22 -96.4 M
11 0 Nf
(Changed behavior on failed generation 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
(. ) S
0.0 -2.2 RM
11 -109.2 M
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22 -112.8 M
(Security considerations ) S
(updated.) S
0 -123.8 M
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0 -123.8 M
[/View [/XYZ -4 633.2 null] /Dest /48 /DEST pdfmark
0 -142.8 M
15 2 Nf
(C.3.) S
[/View [/XYZ -4 632.2 null] /Dest /85 /DEST pdfmark
( Changes in HTTPAUTH-WG revision ) S
(00) S
11 -163.4 M
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22 -167 M
11 0 Nf
(Added a note on the choice of elliptic ) S
(curves.) S
0 -178 M
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0 -178 M
[/View [/XYZ -4 579.0 null] /Dest /50 /DEST pdfmark
0 -197 M
15 2 Nf
(C.4.) S
[/View [/XYZ -4 578.0 null] /Dest /86 /DEST pdfmark
( Changes in HTTPAUTH revision ) S
(02) S
11 -217.6 M
gsave
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22 -221.2 M
11 0 Nf
(Added nIterPi parameter to adjust to the changes to the core draft. ) S
11 -231.8 M
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22 -235.4 M
(Added a note on the verification of exchange ) S
(transaction.) S
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0 -246.4 M
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15 2 Nf
(C.5.) S
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( Changes in HTTPAUTH revision ) S
(01) S
11 -286 M
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22 -289.6 M
11 0 Nf
1.74939907 0 32 0 0 (Notation change: integer output of hash function will be notated as INT\(H\(*\)\), changed from ) A
22 -302.8 M
(H\(*\).) S
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15 2 Nf
(C.6.) S
[/View [/XYZ -4 442.2 null] /Dest /88 /DEST pdfmark
( Changes in revision ) S
(02) S
11 -353.4 M
gsave
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22 -357 M
11 0 Nf
0.992968738 0 32 0 0 (Implementation hints in appendix changed \(number of characters for base64-fixed-number does) A
22 -370.2 M
(not contain ) S
(double-quotes\).) S
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15 2 Nf
(C.7.) S
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( Changes in revision ) S
(01) S
11 -420.8 M
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PAFTECH AB 2003-2026
2026-04-24 11:19:31