Dsa & Digi Cert

Presentation On Digital Signature Algorithm

DIGITAL SIGNATURES The most important development from the work on public key cryptography is Digital Signature. The Digital Signature provides a set of security capabilities that would be difficult to implement in any other way.

OUR REQUIREMENTS When two parties exchange message there is not complete trust between sender and receiver, something more than authentication is needed. The most attractive solution to this problem is Digital Signature. The Digital Signature is analogous to the handwritten signature .

It must verify the author and the date and time of signature. It must authenticate the contents at the time of the signature. It must verifiable by third parties, to resolve disputes. It must have the following properties

Properties (Contd..) The signature must be a bit pattern that depends on the message being signed. The signature must use some information unique to the sender, to prevent both forgery and denial. It must be relatively easy to produce the digital signature.

Properties (Contd..) It must be relatively easy to recognize and verify the digital signature. It must be computationally infeasible to forge a digital signature , either by constructing a new message for an existing digital signature. It must be practical to retain a copy of the digital signature in store.

Types of Digital Signature: #Direct Digital Signature: The direct digital signature involves only the communicating parties (source,destination). The destination knows public-key(assume) of the source. DS may be formed by encrypting the message with the sender`s private key. DS may also be formed by encrypting the HASH of message by shared secret keys

# Arbitrated Digital Signature : Every signed message goes first to an arbiter A, who subjects the message and its signature to a number of tests to check its origin and content. The message then dated and send to recipient with an indication that it has verified to the satisfaction of the arbiter.

(a) Conventional Encryption,Arbiter Sees Message X-> A : M || EKxa [ IDx || H(M)] A->Y : EKay [ ID x || M || EKxa [IDx || H(M) || T ] (b) Conventional Encryption, Arbiter Does Not See Message X -> A : IDx || EKxy [M] ||EKxa [ IDx || H(EKxy [M] ) ] || T ] A->Y:EKay[ IDX || EKxy [M] || EKxa [IDX || H(EKxy[M])] ||T] (c)Public Key Encryption, Arbiter Does Not See Message X -> A : IDx || EKRx [Idx || EKUy(EKRx[M])] A -> Y : EKRa [ IDx || EKUy [EKRx [M]] || T]

Function Of Signature # Evidence : Signature identifies the signer with the signed document. # Approval : Signature expresses the signer`s approval to the content. # Documents Authentication : Signature provides what is signed so that the contents can not be falsified without detection.

M | | H E M H D Compare KRa RSA Approach KUa E[H[M]]

M H Sig || M H Ver k s r Compare KUg KRa DSS Approach KUg KUa

Global Public Key Components p = Prime number where 2 L-1 < p <2 L for 512<=L<=1024 and L is multiple of 64 bits i.e. bit length of between 512 and 1024 in increment of 64 bits q = Prime divisor of (p-1) where 2 159 < q < 2 160 i.e. bit length of 160 bits g = h (p-1)/q mod p: Where h is any integer with 1< h < (p-1) and g>1

User’s Private Key k = Random or pseudorandom integer with 0< k < q x = Random or pseudorandom integer with 0 < x < q User’s Public Key y = g x mod p User’s Per Message Secret Number

Singing in DSS f2 M H f1 x q P q g r s k

Signing r = (g k mod p) mod q s = [k -1 (H(M)+ xr)] mod q Signature = (r,s)

Verifying in DSS M ’ s ’ r ’ H f4 f3 y q g q v Compare

Verifying w = (s r ) -1 mod q u1 = [ H(M’) w ] mod q u2 = (r’) w mod q v = [ (g u1 y u2 ) mod p ] mod q Test :-> v = r’ M = Message to be Signed H(M) = Hash of M using SHA-1 M’ , s’ , r’ = Received version of M , s , r

Proof Of The DSA LEMMA 1 For any Integer t – If g=h (p-1)/q mod p Then g t mod p = g t mod q mod p LEMMA 2 For non Negative Integer a and b g (a mod q +b mod q) mod p = g (a+b) mod q mod p

LEMMA 3 y ( rw ) mod q mod p = g ( rxw ) mod q mod p LEMMA 4 ( ( H(M) + xr ) w ) mod q = k

= ((g (H(M)w) mod q y (rw) mod q) mod p) mod q = ((g (H(M)w) mod q g (xrw) mod q) mod p) mod q = ((g (H(M)w) mod q + (xrw) mod q) mod p) mod q = (g k mod p) mod q = r THEOREM If v = r Then Signature is Valid PROOF = ((g (H(M)w) + xrw) mod q) mod p) mod q =(( g (H(M)w) mod q + (xrw) mod q) mod p) mod q v = ((gu1 yu2) mod p) mod q

X.509 Authentication Service part of CCITT X.500 directory service standards distributed servers maintaining user info database defines framework for authentication services directory may store public-key certificates with public key of user signed by certification authority also defines authentication protocols uses public-key crypto & digital signatures algorithms not standardised, but RSA recommended X.509 certificates are widely used

X.509 Certificates issued by a Certification Authority (CA), containing: version (1, 2, or 3) serial number (unique within CA) identifying certificate signature algorithm identifier issuer X.500 name (CA) period of validity (from - to dates) subject X.500 name (name of owner) subject public-key info (algorithm, parameters, key) issuer unique identifier (v2+) subject unique identifier (v2+) extension fields (v3) signature (of hash of all fields in certificate) notation CA<<A>> denotes certificate for A signed by CA

Obtaining a Certificate any user with access to CA can get any certificate from it only the CA can modify a certificate because cannot be forged, certificates can be placed in a public directory

CA Hierarchy if both users share a common CA then they are assumed to know its public key otherwise CA's must form a hierarchy use certificates linking members of hierarchy to validate other CA's each CA has certificates for clients (forward) and parent (backward) each client trusts parents certificates enable verification of any certificate from one CA by users of all other CAs in hierarchy

Certificate Revocation certificates have a period of validity may need to revoke before expiry, eg: user's private key is compromised user is no longer certified by this CA CA's certificate is compromised CA’s maintain list of revoked certificates the Certificate Revocation List (CRL) users should check certificates with CA’s CRL

Authentication Procedures X.509 includes three alternative authentication procedures: One-Way Authentication Two-Way Authentication Three-Way Authentication all use public-key signatures

One-Way Authentication 1 message ( A->B) used to establish the identity of A and that message is from A message was intended for B integrity & originality of message message must include timestamp, nonce, B's identity and is signed by A may include additional info for B eg session key

Two-Way Authentication 2 messages (A->B, B->A) which also establishes in addition: the identity of B and that reply is from B that reply is intended for A integrity & originality of reply reply includes original nonce from A, also timestamp and nonce from B may include additional info for A

Three-Way Authentication 3 messages (A->B, B->A, A->B) which enables above authentication without synchronized clocks has reply from A back to B containing signed copy of nonce from B means that timestamps need not be checked or relied upon

X.509 Version 3 has been recognised that additional information is needed in a certificate email/URL, policy details, usage constraints rather than explicitly naming new fields defined a general extension method extensions consist of: extension identifier criticality indicator extension value

Certificate Extensions key and policy information convey info about subject & issuer keys, plus indicators of certificate policy certificate subject and issuer attributes support alternative names, in alternative formats for certificate subject and/or issuer certificate path constraints allow constraints on use of certificates by other CA’s

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