One document matched: draft-oiwa-http-mutualauth-algo-00.ps

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(Mutual Authentication Protocol for HTTP:) S
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(This Internet-Draft is submitted in full conformance with the provisions of BCP\24078 and ) S
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(Copyright \(c\) 2011 IETF Trust and the persons identified as the document authors. All rights ) S
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1.56119788 0 32 0 0 (For discrete-logarithm settings, the underlying groups are the 2048-bit and 4096-bit MODP groups) A
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1.51412261 0 32 0 0 (defined in ) A
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1.51412261 0 32 0 0 (, respectively. See ) A
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1.51412261 0 32 0 0 (Appendix\240A) A
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1.51412261 0 32 0 0 ( for the exact specifications of the groups and) A
0 -91.2 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 -104.4 M
(4096-bit group. The representation of the fields wa, wb, oa, and ob is base64-fixed-number. ) S
0 -128.6 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 -141.8 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.186-3.2009]) A
0 -155 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
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4.87199497 0 32 0 0 (P-256 curve and SHA-512 for the P-521 curve, respectively, defined in ) A
gsave
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([FIPS.180-2.2002]. The representation of the fields wa, wb, oa, and ob is hex-fixed-number. ) S
0 -205.6 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 -218.8 M
gsave
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8.17578125 0 32 0 0 (ISO/IEC ) A
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8.17578125 0 32 0 0 ( [ISO.11770-4.2006] with a few modifications/improvements. However,) A
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1.37469947 0 32 0 0 (implementers should use this document as the normative reference, because the algorithm has been) A
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(changed in several minor details as well as major improvements. ) S
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%%IncludeResource: font Times-Bold
13 2 Nf
(2.1.) S
[/View [/XYZ -4 500.800049 null] /Dest /48 /DEST pdfmark
( Support functions and ) S
(notations) S
0 -296 M
11 0 Nf
(The algorithm definitions use several support functions and notations defined ) S
(below:) S
0 -320.2 M
(The integers in the specification are in decimal, or in hexadecimal when prefixed with ) S
("0x".) S
0 -344.4 M
4.17157459 0 32 0 0 (The two functions named octet\(\) and OCTETS\(\) are those defined in the ) A
gsave
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4.17157459 0 32 0 0 (core ) A
gsave
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4.17157459 0 32 0 0 (specification) A
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4.17157459 0 32 0 0 ( ) A
0 -357.6 M
([draft-oiwa-http-mutualauth].) S
0 -381.8 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 -395 M
(specification, which takes the shortest representation without preceding zeros. ) S
0 -419.2 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 -432.4 M
(specification for functions pi, o_A and ) S
(o_B.) S
0 -443.4 M
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0 -443.4 M
[/View [/XYZ -4 313.599945 null] /Dest /11 /DEST pdfmark
0 -459 M
13 2 Nf
(2.2.) S
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( Functions for discrete-logarithm ) S
(settings) S
0 -483.2 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 -496.4 M
(mod z = x mod z. ) S
0 -520.6 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 -541.2 M
gsave
0 setgray
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fill
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22 -544.8 M
(q: for "the prime" defining the MODP group. ) S
11 -555.4 M
gsave
0 setgray
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11.0 -555.370117 2.75 0 360 arc
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fill
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22 -559 M
(g: for "the generator" associated with the group. ) S
11 -569.6 M
gsave
0 setgray
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11.0 -569.570129 2.75 0 360 arc
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22 -573.2 M
(r: for the order of the subgroup generated by ) S
(g.) S
0 -597.4 M
(The function J is defined as ) S
0 -621.6 M
(J\(pi\) = g^\(pi\) mod q. ) S
0 -632.6 M
gsave
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(- 3 -) S
0 setgray
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grestore
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11 0 Nf
(The value of w_A is derived as ) S
0 -37.4 M
(w_A = g^\(s_A\) mod q, ) S
0 -61.6 M
0.109188989 0 32 0 0 (where s_A is a random integer within range [1, r-1] and r is the size of the subgroup generated by g. In) A
0 -74.8 M
(addition, s_A MUST be larger than log\(q\)/log\(g\) \(so that g^\(s_A\) > q\). ) S
0 -99 M
2.07927394 0 32 0 0 (The value of w_A SHALL satisfy 1 < w_A < q-1. The server MUST check this condition upon) A
0 -112.2 M
(reception. ) S
0 -136.4 M
(The value of w_B is derived from J\(pi\) and w_A as: ) S
0 -160.6 M
(w_B = \(J\(pi\) * w_A^\(H\(octet\(1\) | OCTETS\(w_A\)\)\)\)^s_B mod q, ) S
0 -184.8 M
0.286328137 0 32 0 0 (where s_B is a random number within range [1, r-1]. The value of w_B MUST satisfy 1 < w_B < q-1.) A
0 -198 M
1.31847429 0 32 0 0 (If this condition is not held, the server MUST retry using another value for s_B. The client MUST) A
0 -211.2 M
(check this condition upon reception. ) S
0 -235.4 M
(The value z on the client side is derived by the following equation: ) S
0 -259.6 M
0.037224263 0 32 0 0 (z = w_B^\(\(s_A + H\(octet\(2\) | OCTETS\(w_A\) | OCTETS\(w_B\)\)\) / \(s_A * H\(octet\(1\) | w_A\) + pi\) mod) A
0 -272.8 M
(r\) mod q. ) S
0 -297 M
(The value z on the server side is derived by the following equation: ) S
0 -321.2 M
(z = \(w_A * g^\(H\(octet\(2\) | OCTETS\(w_A\) | OCTETS\(w_B\)\)\)\)^s_B mod q. ) S
0 -332.2 M
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0 -332.2 M
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%%IncludeResource: font Times-Bold
13 2 Nf
(2.3.) S
[/View [/XYZ -4 424.8 null] /Dest /50 /DEST pdfmark
( Functions for elliptic-curve ) S
(settings) S
0 -372 M
11 0 Nf
(For the elliptic-curve setting, we refer to some of the domain parameters by the following symbols: ) S
11 -392.6 M
gsave
0 setgray
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11.0 -392.570038 2.75 0 360 arc
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fill
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22 -396.2 M
(q: for the prime used to define the group. ) S
11 -406.8 M
gsave
0 setgray
newpath
11.0 -406.77005 2.75 0 360 arc
closepath
fill
grestore
22 -410.4 M
(G: for the defined point called the generator. ) S
11 -421 M
gsave
0 setgray
newpath
11.0 -420.970062 2.75 0 360 arc
closepath
fill
grestore
22 -424.6 M
(r: for the order of the subgroup generated by ) S
(G.) S
0 -448.8 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 -462 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 -475.2 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 -488.4 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 -501.6 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 -514.8 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 -528 M
0.619290888 0 32 0 0 (those functions \(e.g. Section 3 of ) A
gsave
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0.619290888 0 32 0 0 ([RFC6090]) A
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0.619290888 0 32 0 0 (, which uses different notations, though.\) 0_E represents) A
0 -541.2 M
0.357617199 0 32 0 0 (the infinity point. The equation \(x / y mod z\) denotes an natural number w less than z that satisfies \(w) A
0 -554.4 M
(* y\) mod z = x mod z. ) S
0 -578.6 M
(The function J is defined as ) S
0 -602.8 M
(J\(pi\) = [pi] * G. ) S
0 -627 M
(The value of w_A is derived as ) S
0 -638 M
gsave
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(- 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
(w_A = P\(W_A\), where W_A = [s_A] * G, ) S
0 -37.4 M
0.178602427 0 32 0 0 (where s_A is a random number within range [1, r-1]. The value of w_A MUST represent a valid curve) A
0 -50.6 M
(point, and W_A SHALL\240NOT be 0_E. The server MUST check this condition upon reception. ) S
0 -74.8 M
(The value of w_B is derived from J\(pi\) and W_A = P'\(w_A\) as: ) S
0 -99 M
(w_B = P\(W_B\), where W_B = [s_B] * \(J\(pi\) + [H\(octet\(1\) | OCTETS\(w_A\)\)] * W_A\), ) S
0 -123.2 M
0.245876729 0 32 0 0 (where s_B is a random number within range [1, r-1]. The value of w_B MUST represent a valid curve) A
0 -136.4 M
0.403211802 0 32 0 0 (point and satisfy [4] * P'\(w_B\) <> 0_E. If this condition is not satisfied, the server MUST retry using) A
0 -149.6 M
(another value for s_B. The client MUST check this condition upon reception. ) S
0 -173.8 M
(The value z on the client side is derived by the following equation: ) S
0 -198 M
0.346354157 0 32 0 0 (z = P\([\(s_A + H\(octet\(2\) | OCTETS\(w_A\) | OCTETS\(w_B\)\)\) / \(s_A * H\(octet\(1\) | OCTETS\(w_A\)\) +) A
0 -211.2 M
(pi\) mod r] * W_B\), where W_B = P'\(w_B\). ) S
0 -235.4 M
(The value z on the server side is derived by the following equation: ) S
0 -259.6 M
(z = P\([s_B] * \(W_A + [H\(octet\(2\) | OCTETS\(w_A\) | OCTETS\(w_B\)\)] * G\)\), where W_A = P'\(w_A\). ) S
0 -270.6 M
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0 -270.6 M
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%%IncludeResource: font Times-Bold
15 2 Nf
(3.) S
[/View [/XYZ -4 485.400024 null] /Dest /51 /DEST pdfmark
( IANA ) S
(Considerations) S
0 -313.8 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 -327 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 -340.2 M
(documentation when this document is promoted to an RFC. ) S
0 -364.4 M
(Note: More formal declarations will be added in the future drafts to meet the RFC 5226 requirements. ) S
0 -375.4 M
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0 -375.4 M
[/View [/XYZ -4 381.599976 null] /Dest /17 /DEST pdfmark
0 -394.4 M
15 2 Nf
(4.) S
[/View [/XYZ -4 380.599976 null] /Dest /52 /DEST pdfmark
( Security ) S
(Considerations) S
0 -418.6 M
11 0 Nf
4.87460947 0 32 0 0 (Refer the corresponding section of the core specification for algorithm-independent, generic) A
0 -431.8 M
(considerations. ) S
11 -452.4 M
gsave
0 setgray
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22 -456 M
6.48011351 0 32 0 0 (All random numbers used in these algorithms MUST be at least cryptographically) A
22 -469.2 M
(computationally secure against forward and backward guessing attacks. ) S
11 -479.8 M
gsave
0 setgray
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11.0 -479.770081 2.75 0 360 arc
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22 -483.4 M
4.10507822 0 32 0 0 (Computation times of all numerical operations on discrete-logarithm group elements and) A
22 -496.6 M
0.668269217 0 32 0 0 (elliptic-curve points MUST be normalized and made independent of the exact values, to prevent) A
22 -509.8 M
(timing-based side-channel ) S
(attacks.) S
0 -520.8 M
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0 -520.8 M
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15 2 Nf
(5.) S
[/View [/XYZ -4 235.19989 null] /Dest /53 /DEST pdfmark
( Notice on intellectual ) S
(properties) S
0 -564 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 -577.2 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 -590.4 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 -603.6 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 -616.8 M
(contact the author of this document. ) S
0 -641 M
1.08359373 0 32 0 0 (The elliptic-curve based authentication algorithms might involve several existing third-party patents.) A
0 -654.2 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 -667.4 M
(patents as well. ) S
0 -667.4 M
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(- 5 -) S
0 setgray
0 -8 M
grestore
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(6.) S
[/View [/XYZ -4 757.0 null] /Dest /54 /DEST pdfmark
( ) S
(References) S
0 -25.5 M
[/View [/XYZ -4 731.5 null] /Dest /22 /DEST pdfmark
0 -44 M
13 2 Nf
(6.1.) S
[/View [/XYZ -4 728.6 null] /Dest /55 /DEST pdfmark
( 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
gsave
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(Secure Hash ) S
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(Standard) S
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(,\234 FIPS\240PUB 180-2, ) S
(August\2402002.) S
8 -106.2 M
([FIPS.186-3.2009]) S
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(National Institute of Standards and Technology, ) S
(\233) S
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(Digital) S
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(,\234 FIPS\240PUB 186-3, ) S
(June\2402009.) S
8 -141.2 M
([RFC2119]) S
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(Bradner, ) S
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(S.) S
(, ) S
(\233) S
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(Key words for use in RFCs to Indicate Requirement ) S
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(Levels) S
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(,\234 BCP\24014, RFC\2402119, March\2401997 ) S
(\() S
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(TXT) S
[/Rect [339.332764 -157.15 362.71167 -145.049988] /Subtype /Link /Border [0 0 0] /Action [/Subtype /URI /URI (http://www.rfc-editor.org/rfc/rfc2119.txt)] Cd /ANN pdfmark
(, ) S
gsave
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(HTML) S
[/Rect [366.21167 -157.15 399.36792 -145.049988] /Subtype /Link /Border [0 0 0] /Action [/Subtype /URI /URI (http://xml.resource.org/public/rfc/html/rfc2119.html)] Cd /ANN pdfmark
(, ) S
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(XML) S
[/Rect [402.86792 -157.15 429.30542 -145.049988] /Subtype /Link /Border [0 0 0] /Action [/Subtype /URI /URI (http://xml.resource.org/public/rfc/xml/rfc2119.xml)] Cd /ANN pdfmark
(\).) S
8 -176.2 M
([RFC3526]) S
[/View [/XYZ -4 842 null] /Dest /26 /DEST pdfmark
149.7 -176.2 M
(Kivinen, T. and M. Kojo, ) S
(\233) S
gsave
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269.1 -177.3 M
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(More Modular Exponential \(MODP\)) S
[/Rect [268.141357 -178.900009 432.328857 -166.8] /Subtype /Link /Border [0 0 0] /Action [/Subtype /URI /URI (http://tools.ietf.org/html/rfc3526)] Cd /ANN pdfmark
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(Diffie-Hellman groups for Internet Key Exchange ) S
gsave
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372.6 -190.5 M
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( A. \(Informative\) Group parameters for discrete-logarithm) S
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(parameters.) S
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( B. \(Informative\) Derived numerical ) S
(values) S
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(specifications. The values shown in this section are for informative purposes only. ) S
195.8 -268.5 M
11 2 Nf
(dl-2048) S
236.7 -268.5 M
11 2 Nf
(dl-4096) S
277.7 -268.5 M
11 2 Nf
(ec-p256) S
319.8 -268.5 M
11 2 Nf
(ec-p521) S
59 -288.3 M
11 0 Nf
(Size of w_A ) S
(etc.) S
195.8 -288.3 M
(2048) S
236.7 -288.3 M
(4096) S
277.7 -288.3 M
(257) S
319.8 -288.3 M
(522) S
361.9 -288.3 M
(\(bits\)) S
59 -308 M
(Size of ) S
(H\(...\)) S
195.8 -308 M
(256) S
236.7 -308 M
(512) S
277.7 -308 M
(256) S
319.8 -308 M
(512) S
361.9 -308 M
(\(bits\)) S
59 -327.8 M
(length of OCTETS\(w_A\) ) S
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195.8 -327.8 M
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236.7 -327.8 M
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277.7 -327.8 M
(33) S
319.8 -327.8 M
(66) S
361.9 -327.8 M
(\(octets\)) S
59 -347.5 M
(length of wa, wb field ) S
(values.) S
195.8 -347.5 M
(346 ) S
(*) S
236.7 -347.5 M
(686 ) S
(*) S
277.7 -347.5 M
(66) S
319.8 -347.5 M
(132) S
361.9 -347.5 M
(\(octets\)) S
59 -367.3 M
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(values.) S
195.8 -367.3 M
(46 ) S
(*) S
236.7 -367.3 M
(90 ) S
(*) S
277.7 -367.3 M
(64) S
319.8 -367.3 M
(128) S
361.9 -367.3 M
(\(octets\)) S
59 -387 M
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(s_A) S
195.8 -387 M
(2048) S
236.7 -387 M
(4096) S
277.7 -387 M
(1) S
319.8 -387 M
(1) S
361.9 -387 M
(\240) 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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(00) S
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