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:
- a ^ b means the exponentiation of a to the power of b, which is
always used within a modulo context.
- a[b] means a with an index or subscription of b.
- 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:
- A random number generator of cryptographic quality
- A prime number generator of cryptographic quality
- A hash mechanism H() of cryptographic quality
- An encryption mechanism (e.g. a common block cipher)
Danisch Informational [Page 4]
RFC 1824 TESS August 1995
- An arithmetical library for long unsigned integers
- 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:
- p: choose a large prime p of at least 512 bit length.
- g: choose a primitive root g in GF(p)
- x: choose a random number x in the range 1 < x < p-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:
- 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].
- k[A]: choose a random number k[A] with gcd(k[A],p-1) = 1. k[A]
must not be revealed by the SKIA.
- r[A] := ( g ^ k[A] ) mod p
- 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:
- Alice wants to authenticate herself to Bob without Bob
authenticating himself to Alice.
- 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:
- A generates a random number K with gcd(K,p-1) = 1.
- R := r[A] ^ K mod p
- 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:
- User A generates a random number a with gcd(a,p-1)=1
- User A calculates g' := g^a mod p and forwards g' to the SKIA.
- The SKIA generates Id[A] and k[A] as in the base protocol
- 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)
- The SKIA forwards (Id[A],r[A],s'[A]) to the user A
- 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:
- 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.
- 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:
- The SKIA is created as in the base protocol
- 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.
- 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.
- 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:
- Alice: key[A,B] = ( g ^ H(Id[B]) * r[B] ^ -r[B] ) ^ s[A] mod p
- 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
- 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).
- choose a primitive root h in GF(p)
- g:= h^((p-1)/q)
Note that g generates a subgroup G with |G|=q
- x: a random number of about 160 bit.
- 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
- k[A]: a random number of 160 bit length with gcd(k[A],q)=1
- r[A]:= ( g ^ k[A] ) mod p
- 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
- User A generates a random number h of 160 bit length.
- User A calculates a := g^h mod p and sends a to the SKIA.
- The SKIA generates the user key with the secret key s'[A].
- 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:
- 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.
- 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.
- 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.
- The root SKIA creates itself as in the base protocol.
- 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):
- Bob reliably learned the (p,g,y) of Alice's root SKIA S(0).
- 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.
- 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
- 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.
- Attention should be paid to the security considerations of the
underlying mechanisms (ElGamal, DSA, Diffie-Hellman, etc.).
- 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.
- It is the SKIA's duty to give the s[A] only to the user the
Identity Descriptor belongs to.
- Since the very same procedure is used for signing messages and
generating user keys, it is important to distinguish between
messages and keys.
- 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]
|
