Digital Signatures DS Message authentication does not address

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Digital Signatures (DS) Ø Message authentication does not address issues of lack of trust

Digital Signatures (DS) Ø Message authentication does not address issues of lack of trust Ø digital signatures provide the ability to: l l l verify author, date & time of signature authenticate message contents be verified by third parties to resolve disputes Ø DS includes message authentication function with additional capabilities

Digital Signature Properties must depend on the message signed Ø must use information unique

Digital Signature Properties must depend on the message signed Ø must use information unique to sender Ø l to prevent both forgery and denial must be relatively easy to produce Ø must be relatively easy to recognize & verify Ø be computationally infeasible to forge Ø l l Ø with new message for existing digital signature with fraudulent digital signature for given message be practical to save digital signature in storage

Direct Digital Signatures Ø involve only sender & receiver Ø assumed receiver has sender’s

Direct Digital Signatures Ø involve only sender & receiver Ø assumed receiver has sender’s public-key Ø digital signature made by sender signing entire message or hash with private-key Ø can encrypt using receivers public-key Ø important that sign first then encrypt message & signature Ø security depends on sender’s private-key

Digital Signature Model

Digital Signature Model

Digital Signature Model

Digital Signature Model

Arbitrated Digital Signatures Ø involves use of an arbiter who l l validates any

Arbitrated Digital Signatures Ø involves use of an arbiter who l l validates any signed message then dated and sent to recipient Ø requires suitable level of trust in arbiter Ø can be implemented with either private or public-key algorithms Ø arbiter may or may not see message

Authentication Protocols Ø used to convince parties of each others identity and to exchange

Authentication Protocols Ø used to convince parties of each others identity and to exchange session keys Ø may be one-way or mutual Ø key issues are l l confidentiality – to protect session keys timeliness – to prevent replay attacks Ø published protocols are often found to have flaws and need to be modified

Using Public-Key Encryption Ø have a range of approaches based on the use of

Using Public-Key Encryption Ø have a range of approaches based on the use of public-key encryption Ø need to ensure have correct public keys for other parties Ø using a central Authentication Server (AS) Ø various protocols exist using timestamps or nonces

Digital Signature Standard (DSS) US Govt approved signature scheme Ø designed by NIST &

Digital Signature Standard (DSS) US Govt approved signature scheme Ø designed by NIST & NSA in early 90's Ø published as FIPS-186 in 1991 Ø revised in 1993, 1996 & then 2000 Ø uses the SHA hash algorithm Ø DSS is the standard, DSA is the algorithm Ø FIPS 186 -2 (2000) includes alternative RSA & elliptic curve signature variants Ø

Digital Signature Algorithm (DSA) Ø creates a 320 bit signature Ø with 512 -1024

Digital Signature Algorithm (DSA) Ø creates a 320 bit signature Ø with 512 -1024 bit security Ø smaller and faster than RSA Ø a digital signature scheme only Ø security depends on difficulty of computing discrete logarithms Ø variant of El. Gamal & Schnorr schemes

Digital Signature Algorithm (DSA)

Digital Signature Algorithm (DSA)

DSA Key Generation Ø have shared global public key values (p, q, g): l

DSA Key Generation Ø have shared global public key values (p, q, g): l l choose 160 -bit prime number q choose a large prime p with 2 L-1 < p < 2 L • where L= 512 to 1024 bits and is a multiple of 64 • such that q is a 160 bit prime divisor of (p-1) l choose g = h(p-1)/q • where 1<h<p-1 and h(p-1)/q mod p > 1 Ø users choose private & compute public key: l l choose random private key: x<q compute public key: y = gx mod p

DSA Signature Creation Ø to sign a message M the sender: l l generates

DSA Signature Creation Ø to sign a message M the sender: l l generates a random signature key k, k<q NB! k must be random, be destroyed after use, and never be reused Ø then computes signature pair: r = (gk mod p)mod q s = [k-1(H(M)+ xr)] mod q Ø sends signature (r, s) with message M

DSA Signature Verification Ø having received M & signature (r, s) Ø to verify

DSA Signature Verification Ø having received M & signature (r, s) Ø to verify a signature, recipient computes: w = u 1= u 2= v = s-1(mod q) (H(M). w)(mod q) (rw)(mod q) (gu 1 yu 2(mod p)) (mod q) Ø if v=r then signature is verified Ø see book web sitehe text for details!

DSS Overview

DSS Overview