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rfc:rfc1824

Network Working Group H. Danisch Request for Comments: 1824 E.I.S.S./IAKS Category: Informational August 1995

               The Exponential Security System TESS:
              An Identity-Based Cryptographic Protocol
                   for Authenticated Key-Exchange
                      (E.I.S.S.-Report 1995/4)

Status of this Memo

 This memo provides information for the Internet community.  This memo
 does not specify an Internet standard of any kind.  Distribution of
 this memo is unlimited.

Abstract

 This informational RFC describes the basic mechanisms  and  functions
 of  an identity based system for the secure authenticated exchange of
 cryptographic keys, the generation of signatures, and  the  authentic
 distribution of public keys.

Table of Contents

 1.  Introduction and preliminary remarks . . . . . . . . . . . . .  2
     1.1.  Definition of terms/Terminology  . . . . . . . . . . . .  2
     1.2.  Required mechanisms  . . . . . . . . . . . . . . . . . .  4
 2.  Setup  . . . . . . . . . . . . . . . . . . . . . . . . . . . .  5
     2.1.  SKIA Setup . . . . . . . . . . . . . . . . . . . . . . .  5
     2.2.  User Setup . . . . . . . . . . . . . . . . . . . . . . .  5
 3.  Authentication . . . . . . . . . . . . . . . . . . . . . . . .  7
     3.1.  Zero Knowledge Authentication  . . . . . . . . . . . . .  7
     3.2.  Unilateral Authentication  . . . . . . . . . . . . . . .  8
     3.3.  Mutual Authentication  . . . . . . . . . . . . . . . . .  9
     3.4.  Message Signing  . . . . . . . . . . . . . . . . . . . . 10
 4.  Enhancements . . . . . . . . . . . . . . . . . . . . . . . . . 10
     4.1.  Non-Escrowed Key Generation  . . . . . . . . . . . . . . 11
     4.2.  Hardware Protected Key . . . . . . . . . . . . . . . . . 11
     4.3.  Key Regeneration . . . . . . . . . . . . . . . . . . . . 12
     4.4.  r ^ r  . . . . . . . . . . . . . . . . . . . . . . . . . 13
     4.5.  Implicit Key Exchange  . . . . . . . . . . . . . . . . . 13
     4.6.  Law Enforcement  . . . . . . . . . . . . . . . . . . . . 13
     4.7.  Usage of other Algebraic Groups  . . . . . . . . . . . . 14
           4.7.1  DSA subgroup SKIA Setup . . . . . . . . . . . . . 14
           4.7.2  Escrowed DSA subgroup User Setup  . . . . . . . . 14
           4.7.3  Non-Escrowed DSA subgroup User Setup  . . . . . . 15
           4.7.4  DSA subgroup Authentication . . . . . . . . . . . 15

Danisch Informational [Page 1] RFC 1824 TESS August 1995

 5.  Multiple SKIAs . . . . . . . . . . . . . . . . . . . . . . . . 15
     5.1.  Unstructured SKIAs . . . . . . . . . . . . . . . . . . . 15
     5.2.  Hierarchical SKIAs . . . . . . . . . . . . . . . . . . . 16
     5.3.  Example: A DNS-based public key structure  . . . . . . . 18
 Security Considerations  . . . . . . . . . . . . . . . . . . . . . 19
 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
 Author's Address . . . . . . . . . . . . . . . . . . . . . . . . . 21

1. Introduction and preliminary remarks

 This RFC describes The Exponential Security System TESS [1].  TESS is
 a toolbox set system of different but cooperating cryptographic
 mechanisms and functions based on the primitive of discrete
 exponentiation. TESS is based on asymmetric cryptographical protocols
 and a structure of self-certified public keys.
 The most important mechanisms TESS is based on are the ElGamal
 signature [2, 3] and the KATHY protocols (KeY exchange with embedded
 AuTHentication), which were simultaneously discovered by Guenther [4]
 and Bauspiess and Knobloch [5, 6, 7].
 This RFC explains how to create and use the secret and public keys of
 TESS and shows a method for the secure distribution of the public
 keys.
 It is expected that the reader is familiar with the basics of
 cryptography, the Discrete Logarithm Problem, and the ElGamal
 signature mechanism.
 Due to the ASCII representation of this RFC the following style is
 choosen for mathematical purposes:
  1. a ^ b means the exponentiation of a to the power of b, which is

always used within a modulo context.

  1. a[b] means a with an index or subscription of b.
  1. a = b means equality or congruency within a modulo context.

1.1. Definition of terms/Terminology

 Key pair
    A key pair is a set of a public and a secret key which belong
    together.  There are two distinct kinds of key pairs, the SKIA key
    pair and the User key pair. (As will be shown in the section about
    hierarchical SKIAs, the two kinds of keys are not really distinct.
    They are the same thing seen from a different point of view.)

Danisch Informational [Page 2] RFC 1824 TESS August 1995

 User
    Any principal (human or machine) who owns, holds and uses a User
    key pair and can be uniquely identified by any description (see
    the Identity Descriptor below).
    In this RFC example users are referred to as A, B, C or Alice and
    Bob.
 SKIA
    SKIA is an acronym for "Secure Key Issuing Authority". The SKIA is
    a trusted local authority which generates the public and secret
    part of a User key pair. It is the SKIA's duty to verify whether
    the identity encoded in the key pair (see below) belongs to the
    key holder.  It has to check passports, identity cards, driving
    licenses etc. to investigate the real world identity of the key
    owner.  Since every key has an implicite signature of the SKIA it
    came from, the SKIA is responsible for the correctness of the
    encoded identity.
    Since the SKIA has to check the real identity of users, it is
    usually able to work within a small physical range only (like a
    campus or a city).  Therefore, not all users of a wide area or
    world wide area network can get their keys from the same SKIA with
    reasonable expense.  There is the need for multiple SKIAs which
    can work locally. This implies the need of a web of trust levels
    and trust forwards.  Communication partners with keys from the
    same SKIA know the public data of their SKIA because it is part of
    their own key.  Partners with keys from different SKIAs have to
    make use of the web to learn about the origin, the trust level,
    and the public key of the SKIA which issued the other key.
 Id[A] Identity Descriptor
    The Identity Descriptor is a part of the public User key. It is a
    somehow structured bitstring describing the key owner in a certain
    way. This description of the key owner should be precise enough to
    fully identify the owner of a User key. The description depends on
    the nature of the owner. For a human this could be the name, the
    address, the phone number, date of birth, size of the feet, color
    of the eyes, or anything else. For a machine this could be the
    hostname, the hostid, the internet address etc., for a fax machine
    or a modem it could be the international phone number.
    Furthermore, the description bitstring could contain key
    management data as the name of the SKIA (see below) which issued
    the key, the SKIA-specific serial number, the expiry date of the

Danisch Informational [Page 3] RFC 1824 TESS August 1995

    key, whether the secret part of the key is a software key or
    hidden in a hardware device (see section Enhancements), etc.
    Note that the numerical interpretation (the hash value) of the
    Identity Descriptor is an essential part of the mathematical
    mechanism of the TESS protocol. It can not be changed in any way
    without destroying the key structure.  Therefore, knowing the
    public part of a user key pair always means knowing the Identity
    Descriptor as composed by the SKIA which issued this key. This is
    an important security feature of this mechanism.
    The contents of the Identity Descriptor have to be verified by the
    issuing SKIA at key generation time. The trust level of the User
    Key depends on the trust level of the SKIA. A certain Identity
    Descriptor must not be used more than once for creating a User
    Key.  There must not exist distinct keys with the same Identity
    Descriptor.  Nevertheless, a user may have several keys with
    distinct expiration times, key lengths, serial numbers, or
    security levels, which affect the contents of the Identity
    Descriptor.
    However, it is emphasized that there are no assumptions about the
    structure of the Identity Descriptor.  The SKIA may choose any
    construction method depending on its purposes.
    The Identity Descriptor of a certain user A is referred to as
    Id[A].  Whereever the Identity Descriptor Id[A] is used in a
    mathematical context, its cryptographical hash sum H(Id[A]) is
    used.
 Encrypt(Key,Message)
 Decrypt(Key,Message)
    Encryption and Decryption of the Message with any common cipher.

1.2. Required mechanisms

 The protocols described in this RFC require the following
 submechanisms:
  1. A random number generator of cryptographic quality
  1. A prime number generator of cryptographic quality
  1. A hash mechanism H() of cryptographic quality
  1. An encryption mechanism (e.g. a common block cipher)

Danisch Informational [Page 4] RFC 1824 TESS August 1995

  1. An arithmetical library for long unsigned integers
  1. A method for checking network identities against real-world

identities (e.g. an authority which checks human identity cards

    etc.)

2. Setup

 This section describes the base method for the creation of the SKIA
 and the User key pairs. Enhancements and modifications are described
 in subsequent sections.
 The main idea of the protocols described below is to generate an
 ElGamal signature (r,s) for an Identity Descriptor Id[A] of a user A.
 Id[A] and r form the user's public key and s is the users secret key.
 The connection between the secret and the public key is the
 verification equation for the ElGamal signature (r,s). Instead of
 checking the signature (r,s), the equation is used in 'reverse mode'
 to calculate r^s from public data without knowledge of the secret s.
 The authority generating those signatures is the SKIA introduced
 above.

2.1. SKIA Setup

 By the following steps the SKIA key pair is created:
  1. p: choose a large prime p of at least 512 bit length.
  1. g: choose a primitive root g in GF(p)
  1. x: choose a random number x in the range 1 < x < p-1
  1. y:= ( g ^ x ) mod p
 The public part of the SKIA is the triple (p,g,y), the secret part is
 x.
 Since the public triple (p,g,y) is needed within the verification
 equation for the signatures created by the SKIA, this triple is also
 an essential part of all user keys generated by this SKIA.

2.2. User Setup

 The User Setup is the generation of an ElGamal signature on the
 user's Identity Descriptor by the SKIA. This can be done more than
 once for a specific User, but it is done only once for a specific
 Identity Descriptor.

Danisch Informational [Page 5] RFC 1824 TESS August 1995

 To create a User key pair for a User A, the SKIA has to perform the
 following steps:
  1. Id[A]: Describe the key owner A in any way (name, address, etc.),

convert this description into a bit- or byte-oriented

    representation, and concatenate them to form the Identity
    Descriptor Id[A].
  1. k[A]: choose a random number k[A] with gcd(k[A],p-1) = 1. k[A]

must not be revealed by the SKIA.

  1. r[A] := ( g ^ k[A] ) mod p
  1. s[A] := ( H(Id[A]) - x * r[A] ) * ( k[A] ^ -1 ) mod (p-1)
 The calculated set of numbers fulfills the equation:
    x * r[A] + s[A] * k[A] = H(Id[A])  mod (p-1).
 The public part of the generated key of A consists of Id[A] and r[A],
 referenced to as (Id[A],r[A]) in the context of the triple (p,g,y).
 (Id[A],r[A]) always implicitely refers to the triple (p,g,y) of its
 parent SKIA.
 The secret part of the key is s[A].
 k[A] must be destroyed by the SKIA immediately after key generation,
 because User A could solve the equation and find out the SKIAs secret
 x if he knew both the s[A] and k[A].  The random number k must not be
 used twice. s[A] must not be equal to 0.
 Since (r[A],s[A]) are the ElGamal signature on Id[A], the connection
 between the SKIA public key und the User key pair is the ElGamal
 verification equation:
    r[A] ^ s[A] =  ( g ^ H(Id[A]) ) * ( y ^  (-r[A]) )  mod p.
 This equation allows to calculate r[A] ^ s[A] from public data
 without knowledge of the secret s[A].  Since this equation is used
 very often, and for reasons of readability, the abbreviation Y[A] is
 used for this equation.
 Y[A] means to calculate the value of r[A] ^ s[A] which is
    ( g ^ H(Id[A]) ) * ( y ^ (-r[A]) )  mod p.

Danisch Informational [Page 6] RFC 1824 TESS August 1995

 Note that a given value of Y[A] is not reliable. It must have been
 reliably calculated from (p,g,y) and (Id[A],r[A]).  Y[A] is to be
 understood as a macro definition, not as a value.
 Obviously both the SKIA and the User know the secret part of the
 User's key and can reveal it, either accidently or in malice
 prepense.  The enhancements section below shows methods to avoid
 this.

3. Authentication

 This section describes the basic methods of applying the User keys.
 They refer to online and offline communication between two users
 A(lice) and B(ob).
 The unilateral and the mutual authentications use the KATHY protocol
 to generate reliable session keys for further use as session
 encryption keys etc.

3.1. Zero Knowledge Authentication

 The "Zero Knowledge Authentication" is used if Alice wants to
 authenticate herself to Bob without need for a session key.
 Assuming that Bob already reliably learned the (p,g,y) of the SKIA
 Alice got her key from, the steps are:
 1. Alice generates a large random number t, 1<t<p-1, where  t  should
    have approximately the same length as p-1.
 2. a := r[A] ^ t  mod p
 3. Alice sends her public key (Id[A],r[A]) and the number a to Bob.
 4. Bob  generates a large random number c, c<p-1, where c should have
    approximately the same length as p-1, and sends c to Alice.
 5. Alice calculates
    c' := (c * s[A] + t) mod (p-1)
    and sends c' to Bob.
 6. Bob verifies whether
    r[A] ^ c' = (Y[A] ^ c) * a    mod p.
 This is the Beth-Zero-Knowledge protocol [8] which is based on self-
 certified public keys and an improvement of the DLP-Zero-Knowledge
 identification protocol from Chaum, Evertse, and van de Graaf [9].

Danisch Informational [Page 7] RFC 1824 TESS August 1995

3.2. Unilateral Authentication

 The "Unilateral Authentication" (or "Half Authentication") can be
 used in those cases:
  1. Alice wants to authenticate herself to Bob without Bob

authenticating himself to Alice.

  1. Bob wants to send an encrypted message to Alice readable by her

only (offline encryption).

 A shared key is generated by the following protocol. This key can be
 known by Alice and Bob only.
 Assuming that Bob already reliably learned the (p,g,y) of the SKIA
 Alice got her key from, the steps are:
 1. Alice sends her public key (Id[A],r[A]) to Bob if he does not
    already know it.
 2. Bob chooses a random number 1 < z[A] < p-1 and calculates
    v[A] := r[A] ^ z[A] mod p
 3. Bob sends v[A] to Alice.
 4. Alice and Bob calculate the session key:
    Alice: key[A] := v[A] ^ s[A] mod p
    Bob:   key[A] := Y[A] ^ z[A] mod p
 Apply the equations of the User Key Setup section to Bob's equation
 to see that Alice and Bob get the very same key in step 4:
    key[A] = r[A] ^ ( s[A] * z[A] ) mod p
 A third party cannot calculate key[A], because it has neither s[A]
 nor z[A]. Therefore, Bob can trust in the fact that only Alice is
 able to know the key[A] (as long as nobody else knows her secret
 s[A]).
 This protocol is based on the Diffie-Hellman scheme [10], but avoids
 the weakness of the missing authenticity of the public keys.
 In this protocol Bob did not verify whether Alice really knew her
 s[A] and was able to calculate key[A]. Therefore, a final challenge-
 response step should be performed in case of online communication
 (see the subsection below).

Danisch Informational [Page 8] RFC 1824 TESS August 1995

 In case of sending encrypted messages, Bob can execute step 4 before
 step 3, use the key[A] to encrypt the message, and send the encrypted
 message together with v[A] in step 3.

3.3. Mutual Authentication

 The "Mutual Authentication" is used for online connections where both
 Alice and Bob want to authenticate to each other.
 Within this protocol description it is assumed that Alice and Bob
 have keys of the same SKIA and use the same triple (p,g,y). Otherwise
 in each step the triple has to be used which belongs to the user key
 it is applied to.
 The steps are as follows (where the first four steps are exactly
 twice the "Unilateral Authentication" and steps 5-9 form a mutual
 challenge-response step to find out whether the other side really got
 the key):
 1. Alice sends her (Id[A],r[A]) to Bob.
    Bob sends his (Id[B],r[B]) to Alice.
 2. Bob chooses a random number z[A] < p-1
    and calculates v[A] := r[A] ^ z[A] mod p
    Alice chooses a random number z[B] < p-1
    and calculates v[B] := r[B] ^ z[B] mod p
 3. Bob sends v[A] to Alice.
    Alice sends v[B] to Bob.
 4. Alice and Bob calculate the session keys:
    Alice: key[A] := v[A] ^ s[A] mod p
           key[B] := Y[B] ^ z[B] mod p
    Bob:   key[B] := v[B] ^ s[B] mod p
           key[A] := Y[A] ^ z[A] mod p
 5. Alice chooses a random number R[B]
    Bob   chooses a random number R[A]
 6. Alice sends Encrypt(key[B],R[B]) to Bob.
    Bob   sends Encrypt(key[A],R[A]) to Alice.
 7. Alice and Bob decrypt the received messages to R'[A] and R'[B].

Danisch Informational [Page 9] RFC 1824 TESS August 1995

 8. Alice sends Encrypt(key[A],T(R'[A])) to Bob.
    Bob   sends Encrypt(key[B],T(R'[B])) to Alice.
 9. Alice and Bob decrypt the received messages to R''[A] and R''[B]
10. Alice verifies whether T(R[B]) = R''[B].
    Bob   verifies whether T(R[A]) = R''[A].
 T()  is a simple bijective transformation function, e.g. increment().
 After step 4 Alice can trust in the fact that only Bob and herself
 can know key[B], but she still does not know whether she is really
 talking to Bob. Therefore, she forces Bob to make use of his key
 within steps 5-9. Alice now has checked whether she really talks to
 Bob. Since the scheme is symmetrical, Bob also knows that he talks to
 Alice.

3.4. Message Signing

 To sign a message m (where H(m) is a cryptographic hash value of the
 message), the message author A generates an ElGamal signature by
 using his r[A] as the generator and the s[A] as his secret:
  1. A generates a random number K with gcd(K,p-1) = 1.
  1. R := r[A] ^ K mod p
  1. S := ( H(m) - s[A] * R ) * (K ^ -1) mod (p-1)
 The calculated set of numbers fulfills the equation:
    ( s[A] * R + K * S ) = H(m) mod(p-1)
 The signed message consists of (m,Id[A],r[A],R,S).
 The receiver of the message checks the authenticity of the message by
 calculating the hash value H(m) and verifying the equation:
    r[A] ^ H(m) = ( Y[A] ^ R )  * ( R ^ S )  mod p

4. Enhancements

 This section describes several enhancements and modifications of the
 base protocol as well as other comments.

Danisch Informational [Page 10] RFC 1824 TESS August 1995

4.1. Non-Escrowed Key Generation

 Within the normal User Setup procedure for a User A, the SKIA gains
 knowledge about the secret key s[A]. The SKIA could use this key to
 fake signatures or decrypt messages, or to allow others to do so.
 To avoid this situation, a slight modification of the User Setup
 procedure may be applied. The SKIA Setup is the same as in the base
 protocol.
 Within the User Setup the SKIA does not use its primitive element g,
 but a generator created by the User instead.
 The modified scheme looks like this:
  1. User A generates a random number a with gcd(a,p-1)=1
  1. User A calculates g' := g^a mod p and forwards g' to the SKIA.
  1. The SKIA generates Id[A] and k[A] as in the base protocol
  1. The SKIA sets r[A] := ( g' ^ k[A] ) mod p and

s'[A] := ( H(Id[A]) - x * r[A] ) * (k[A] ^ -1) mod (p-1)

  1. The SKIA forwards (Id[A],r[A],s'[A]) to the user A
  1. The user A calculates his s[A] := s'[A] * (a^-1) mod (p-1)
 The SKIA is not able to find out the secret key s[A] of A.  This
 protocol is based on the idea of the 'testimonial' [11].
 The SKIA is still able to create a second key with the same Identity
 Descriptor (identical or at least having same contents), but with
 different r[A] and s[A]. If such a second key was successfully used
 for authentication or message signing, the real key owner can use his
 own key to proof the existence of two different keys with identical
 (equivalent) Descriptors. The existence of such two keys shows that
 the SKIA cannot be trusted any longer.
 If the key is generated by this method, it should be mentioned in the
 Identity Descriptor. This allows any communication partners to look
 up in the public part of a key whether the secret part is known to
 the SKIA.

4.2. Hardware Protected Key

 The protocol of the previous subsection guaranteed that the SKIA does
 not know the user's secret key.

Danisch Informational [Page 11] RFC 1824 TESS August 1995

 On the other hand, the SKIA may wish that the user himself does not
 know his own secret key. This may be necessary because the user could
 otherwise reveal his secret key accidently or intentionally.
 Especially if untrusted hard- or software or an environment without
 trusted process protection is used, the secret key can be spied out.
 For high-level security applications this might not be acceptable.
 The key owner must be able to use his key without being able to read
 this key. This contradiction can be solved by hiding the secret part
 of the User Key within a protected hardware device.
 Within the SELANE project, the protocols described in this RFC were
 implemented for SmartCards. The User Key is created using the non-
 escrowed key generation procedure described in the previous section,
 modified such that the random number is generated inside the card.
 The secret s[A] exists only inside the card and does not get outside.
 The SmartCard is able to execute all parts of the algorithms which
 need access to the secret key.  To make use of the SmartCard an
 additional password is required.
 If the key is hidden in such a hardware device, it should be
 mentioned in the Identity Descriptor. This allows any communication
 partners to look up in the public part of a key whether the key is
 hardware protected.

4.3. Key Regeneration

 If both methods of the previous subsections are used to protect the
 key, neither the SKIA nor the User himself knows the secret key. This
 could be harmful for the User if the hardware device is lost or
 damaged, because the User could become unable to decrypt messages
 encrypted with the public key.
 To prevent such a denial of service, there are two methods:
  1. If the protection factor 'a' was choosen by the User, the User

can deposit the factor 'a' in a secure way, e.g. give it as a

   shared secret to his friends. The SKIA can do the same and
   deposit s'[A] somewhere else.  If the SKIA and the User
   cooperate, they are able to create a second hardware device
   equivalent to the first.
  1. If the protection factor a was generated inside of the hardware

device, the device itself may give out the s[A] or the a in a

   secure way (e.g. as a shared secret).
 Since the recreation of a User key defeats the property of such a key
 to exist only once, the SKIA should restrict this to special cases
 only.  Furthermore it should be done only after the end of the

Danisch Informational [Page 12] RFC 1824 TESS August 1995

 lifetime of the key, if its lifetime was limited.

4.4. r ^ r

 A slight modification of the base protocol allows some speedup in the
 key exchange:
  1. The SKIA is created as in the base protocol
  1. For the User Setup the SKIA solves the equation

x * s[A] + r[A] * k[A] = H(Id[A]) mod (p-1)

    which differs from the base protocol in that r and s were swapped.
  1. The public key allows to calculate

y ^ s[A] = ( g ^ H(Id[A]) ) * ( r[A] ^ -r[A] ) mod p

    without knowing s[A]. Here the term  (  r[A]  ^  -r[A]  )  can  be
    precalculated for speedup.
  1. Bob calculates key[A] := ( g ^ H(Id[A]) * r[A] ^ -r[A] ) ^ z[A]

and v[A] := y ^ z[A] mod p

    Alice gets     key[A] := v[A] ^ s[A] mod p
    where key[A] = y ^ (s[A] * z[A])
 This protocol is similar to the AMV modification by Agnew et al.
 [12].

4.5. Implicit Key Exchange

 If the r ^ r protocol of the previous section is used, an implicit
 shared key can be calculated for Alice and Bob by using the Diffie-
 Hellman scheme:
  1. Alice: key[A,B] = ( g ^ H(Id[B]) * r[B] ^ -r[B] ) ^ s[A] mod p
  1. Bob: key[B,A] = ( g ^ H(Id[A]) * r[A] ^ -r[A] ) ^ s[B] mod p
 where key[A,B] = key[B,A] = y ^ (s[A] * s[B]).
 This can not be used with Non-escrowed keys.

4.6. Law Enforcement

 This will be subject of a separate RFC.

Danisch Informational [Page 13] RFC 1824 TESS August 1995

4.7. Usage of other Algebraic Groups

 Within this RFC calculations were based on a specific algebraic
 group, the multiplicative group of integers modulo a prime number p
 (which is the multiplicative group of a finite field GF(p)). However,
 any cyclic finite group with a strong discrete logarithm problem can
 be used, e.g., a subgroup of the multiplicative group or elliptic
 curves.
 As an example the subgroup used by the DSA (Digital Signature
 Algorithm) of length N can be used instead of the full multiplicative
 group of GF(p) for speedup (in this case the Secure Hash Algorithm
 SHA is recommended as the hash algorithm).  See [13, 14] for a
 description of DSA and SHA.

4.7.1. DSA subgroup SKIA Setup

  1. Generate large primes p and q such that p is at least 512 bit

long, q is 160 bit long, and q is a factor of (p-1).

  1. choose a primitive root h in GF(p)
  1. g:= h^1)
1)
p-1)/q)
    Note that g generates a subgroup G with |G|=q
  1. x: a random number of about 160 bit.
  1. y:= ( g ^ x ) mod p
 The public key of the SKIA is (p,g,y,q). (q is required for speedup
 only.)
 The secret key of the SKIA is x.
4.7.2. Escrowed DSA subgroup User Setup
  1. k[A]: a random number of 160 bit length with gcd(k[A],q)=1
  1. r[A]:= ( g ^ k[A] ) mod p
  1. s[A]:= (H(Id[A]) + x * r[A]) * (k[A] ^ -1) mod q
 Again, (Id[A],r[A]) is the public key and s[A] is the secret key.
 Note that r[A] has the length of p and s[A] has the length of q (160
 bit).
Danisch Informational [Page 14] RFC 1824 TESS August 1995 4.7.3. Non-Escrowed DSA subgroup User Setup
  1. User A generates a random number h of 160 bit length.
  1. User A calculates a := g^h mod p and sends a to the SKIA.
  1. The SKIA generates the user key with the secret key s'[A].
  1. User A calculates s[A]:= s'[a] * (h^-1) mod q
4.7.4. DSA subgroup Authentication
 The protocols for authentication are the same as described above,
 except that wherever the modulus (p-1) was used the smaller modulus q
 is used instead, and DSA is used for message signing.
 The abbreviation Y[A] still stands for r[A] ^ s[A], which is now (the
 sign of r[A] was changed for speedup)
    ( g ^ H(Id[A])) * ( y ^ r[A] ) mod p
 and can be calculated in a faster way as
    u1 * u2 mod p
 where
    u1 := g ^ ( H(Id[A])  mod q )  mod p
    u2 := y ^ ( r[A] mod q ) mod p.
5. Multiple SKIAs
 In the preceding sections it was assumed that everybody learned the
 (p,g,y) triple of a SKIA reliably.
 By default, a User reliably learns only the (p,g,y) of the SKIA which
 generated his own key, because he gets the triple with his key and
 can verify the triple with the signature verification equation.
 If the User wants to communicate with someone whose key was generated
 by a different SKIA, a method for authenticating the (p,g,y) of the
 other SKIA is needed.
5.1. Unstructured SKIAs
 This will be subject of a separate RFC.
Danisch Informational [Page 15] RFC 1824 TESS August 1995 5.2. Hierarchical SKIAs
 If there is a hierarchy between the SKIAs, their keys can be
 generated hierarchically:
  1. Every SKIA and every User has a level (expressed as a cardinal
number). The root SKIA has level 0. All Users and all other SKIAs
    have levels greater than 0.
  1. Each SKIA except the root SKIA is also a User, and each User can
be a SKIA.
    A SKIA of level n generates keys for Users of level n+1.
    A User of level n is also a SKIA of level n.
  1. Since every SKIA (except the root SKIA) is also a User, each SKIA
has an Identity Descriptor describing its Identity and perhaps its
    level  and  its  parent  SKIA. There is a function parent(A) which
    finds the parent SKIA for every user  A.  This  function  may  use
    informations stored in the Identity Descriptor.
    Thus,  the  parent()  function allows to find the path to the root
    SKIA for every node of the tree forming the hierarchy.
    The root SKIA may also have an Identity Descriptor.
  1. The root SKIA creates itself as in the base protocol.
  1. The key for a User A of level n (n>0) is generated by the parent
SKIA of level n-1. The public part is (Id[A],r[A]), the secret
    part is (s[A]).
    User A is automatically SKIA A:
    p[A] := p[parent(A)]  = p of the root SKIA
    g[A] := r[A]
    x[A] := s[A]
    y[A] := g[A] ^ x[A] = r[A] ^ s[A] = Y[A] =
           ( g[parent(A)] ^ H(Id[A]) ) * ( y[parent(A)] ^ -r[A]) mod p
    Therefore, the public data (p,g[A],y[A]) of  the  SKIA  A  can  be
    calculated  by everyone from the public data of the User A and the
    public data of its parent SKIA. The SKIA  A  itself  may  use  the
    faster  method  to  get  y[A]  by  calculating  r[A] ^ s[A], while
    everybody else has to use the slower but public method as  in  the
    lower  equation.  The  secret  of the "SKIA A" is identical to the
    secret of the "User A".
Danisch Informational [Page 16] RFC 1824 TESS August 1995
    Since a User A uses the very same data to act as either a user  or
    as a SKIA, and since message signing (subsection 3.4.) is the very
    same procedure as generating a User key (in fact it  is  the  same
    thing),   a  user  should  not  sign  a  message  which  could  be
    misunderstood  as  an  Identity  Descriptor.  An  attacker   could
    intercept  the  message  and  its signature and abuse it as a User
    key. This can be avoided by the use of tags  which  preceed  every
    set  of  data  being signed and show whether it is a message or an
    Identity Descriptor.
 This scheme allows any two users (even users of distinct hierarchies)
 to communicate reliably. They need to know the public data (p,g,y) of
 each other's root SKIA only. There is no need for online key servers.
 The communication is the same as in the base protocols but with an
 extension to the method of finding Y[A] (again with Alice and Bob):
  1. Bob reliably learned the (p,g,y) of Alice's root SKIA S(0).
  1. Where Alice presented (Id[A],r[A]) only in the first step, she now
presents (Id[S],r[S]) for each SKIA/User node S in her path to her
    root SKIA S(0).  Since  this  information  does  not  need  to  be
    reliable  or  signed,  it  can  be  provided  by any simple server
    mechanism.
  1. Bob iteratively calculates the public data (p,g,y) of each SKIA in
the path, starting with Alice's root SKIA, until he gets the
    (p,g,y) of Alice where y is Y[Alice].
 Note that Bob did not have to verify anything within the iteration.
 After the iteration he has a set of public SKIA data (p,g,y) to be
 used with Alice public key, but he still does not know whether he was
 spoofed with wrong data of Alice or her parent SKIAs.
 Since the iteration Bob calculated is a chain of nested signatures,
 the correctness of the (p,g,y) he gets depends on every single step.
 If there is at least one step with a bad Id[S] or r[S], Bob will get
 a wrong Y[S] in this step and all following steps, and the chain
 doesn't work.
 If the chain calculated by Bob was not completely correct for any
 reason, Alice cannot make use of her key: her signatures do not
 verify, she cannot decrypt encrypted messages and she cannot answer
 to the challenge response step in case of mutual authentication.
Danisch Informational [Page 17] RFC 1824 TESS August 1995 5.3. Example: A DNS-based public key structure
 Here is a simple example of the usage of the hierarchical SKIA scheme
 within the DNS name space:
 Let every domain also be a SKIA, and let the root domain be a root
 SKIA. Let the Identity Descriptor of any object within the name space
 be its name: the domain name for domains, the host name for machines,
 the mail address for humans and services.
 Consequently, a user with the mail address "danisch@ira.uka.de" got
 his key from the SKIA of the domain "ira.uka.de". This SKIA was
 authorized by the SKIA of "uka.de", which was authorized by the SKIA
 of "de", which is the root SKIA of Germany. It is assumed that
 everybody reliably learned the public key of the german root domain
 "de".
 The public key of danisch@ira.uka.de would look like:
    (  "danisch@ira.uka.de", r[danisch@ira.uka.de] ,
       "ira.uka.de"        , r[ira.uka.de]         ,
       "uka.de"            , r[uka.de]
    )
 For the reasons described in the previous subsection, this key is
 self-certified and does not need any further signature.
 The key can be presented by danisch@ira.uka.de within online
 communications, be appended to signed messages, or simply be
 retrieved by the domain name server of ira.uka.de.
 Someone who reliably learned the (p,g,y) of the root domain .de
 (Germany) can now build the chain:
    "de"                        (p,g,y)[de]
    "uka.de"                    (p,g,y)[uka.de]
    "ira.uka.de"                (p,g,y)[ira.uka.de]
    "danisch@ira.uka.de"        (p,g,y)[danisch@ira.uka.de]
 Thus it is possible to reliably obtain the Y[danisch@ira.uka.de].
 To communicate with the whole world, knowledge of the public keys of
 all root domain SKIAs only is needed. These keys can be stored within
 some tens of KBytes.  No third party is needed for doing an
 authenticated key exchange.
 The whole world could also be based on a single root SKIA; in this
 case a single (p,g,y) is needed only.
Danisch Informational [Page 18] RFC 1824 TESS August 1995
 In a more realistic example the Id[danisch@ira.uka.de] could contain:
    creator=      ira.uka.de
    created=      1-Jun-1995
    expiry=       31-Dec-1999
    protection=   non-escrowed, smartcard
    type=         human
    name=         Hadmut Danisch
    email=        danisch@ira.uka.de
    phone=        +49 721 9640018
    fax=          +49 721 696893
    photo=        <digitized compressed portrait>
Security Considerations
  1. The strength of TESS depends on the strength of the discrete
logarith problem, the strength of the ElGamal signature, and the
    confidentiality of the SKIAs.
  1. Attention should be paid to the security considerations of the
underlying mechanisms (ElGamal, DSA, Diffie-Hellman, etc.).
  1. Since the SKIA creates itself under normal circumstances, an
attacker could create his own SKIA and use it to create a User Key
    with  an  arbitrary  Identity  Descriptor.  This  shows  that  the
    Identity Descriptor is as reliable as the  origin  of  the  triple
    (p,g,y) of the SKIA it came from. The User Key creation process is
    a signature process  for  the  Identity  Descriptor  and  strongly
    depends on the trustworthyness of the signing SKIA.
  1. It is the SKIA's duty to give the s[A] only to the user the
Identity Descriptor belongs to.
  1. Since the very same procedure is used for signing messages and
generating user keys, it is important to distinguish between
    messages and keys.
  1. The authentication protocols work without an online authority.
Therefore, there is no simple way for revoking keys. For this
    reason keys should  have  an  expiration  date  mentioned  in  the
    Identity  Descriptor.  In  case  of  the hierarchical scheme a key
    expires if any key in the path to the root SKIA expires.
Danisch Informational [Page 19] RFC 1824 TESS August 1995 References 1. Th. Beth, F. Bauspiess, H.-J. Knobloch, S. Stempel, "TESS - A
    Security  System  based  on Discrete Exponentation," Computer
    Communcations Journal, Vol. 17, Special Issue, No.  7, pp.
    466-475 (1994).
2. T. ElGamal, "A Public Key Cryptosystem and a Signature Scheme
    Based on  Discrete  Logarithm,"  IEEE-Trans.  Information  Theory,
    IT-31, pp. 469-472 (July 1985).
3. B. Klein, H.-J. Knobloch, "ElGamal-Signatur" in
    Sicherheitsmechanismen, ed. Fries, Fritsch, Kessler, Klein, pp.
    171-176, Oldenburg, Muenchen (1993).
4. C. G. Guenther, "An Identity-Based Key-Exchange Protocol" in
    Advances in Cryptology, Proceedings of Eurocrypt '89,  pp.  29-37,
    Springer (1990).
5. B. Klein, H.-J. Knobloch, "KATHY" in Sicherheitsmechanismen, ed.
    Fries, Fritsch, Kessler, Klein, pp. 252-259,  Oldenburg,  Muenchen
    (1993).
6. F. Bauspiess, H.-J. Knobloch, "How to keep authenticity alive in a
    computer network" in Advances in Cryptology, Proceedings of
    Eurocrypt '89, pp. 38-46, Springer (1990).
7. F. Bauspiess, "SELANE - An Approach to Secure Networks" in
    Abstracts of SECURICOM '90, pp. 159-164, Paris (1990).
8. Th. Beth, "Efficient zero-knowledge identification scheme for
    smart  cards"  in Advances in Cryptology, Proceedings of Eurocrypt
    '88, pp. 77-84, Springer (1988).
9. D. Chaum, J. H. Evertse, J. van de Graaf, "An improved protocol
    for demonstrating possesion of discrete logarithms and some
    generalizations" in Advances in Cryptology, Proceedings of
    Eurocrypt '87, pp. 127-141, Springer (1988).
10. W. Diffie, M. Hellman, "New directions in cryptography," IEEE-
    Trans. Information Theory, 22, pp. 644-654 (1976).
11. Th. Beth, H.-J. Knobloch, "Open network authentication without an
    online  server"  in  Proc.  Symposium on Comput. Security '90, pp.
    160-165, Rome, Italy (1990).
Danisch Informational [Page 20] RFC 1824 TESS August 1995 12. G. B. Agnew, R. C. Mullin, S. A. Vanstone, "Improved digital
    signature scheme based on discrete exponentation," Electron.
    Lett., 26, pp. 1024-1025 (1990).
13. "The Digital Signature Standard," Communications of the ACM, Vol.
    35, pp. 36-40 (July 1992).
14. Bruce Schneier, Applied Cryptography, John Wiley & Sons (1994). Author's Address
 Dipl.-Inform. Hadmut Danisch
 European Institute for System Security (E.I.S.S.)
 Institut fuer Algorithmen und Kognitive Systeme (IAKS)
 University of Karlsruhe
 D-76128 Karlsruhe
 Germany
 Phone: ++49 721 96400-18
 Fax:   ++49 721 696893
 EMail: danisch@ira.uka.de
 WWW:   http://avalon.ira.uka.de/personal/danisch.html
Danisch Informational [Page 21]
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