# Conference keying — the Burmester-Desmedt method

With conference keying, we have t participants, and each of these generates a secret value (r_i), and then transmit a public value generated from this (Z_i). Each of the participants then uses these values, and their secret value, and will generate the same secret key (K_i). In the following, we will use the Burmester-Desmedt method , and have five participants, and with varying sizes of a shared prime number (p), and for a common generator (g):

`import randomimport sysfrom Crypto.Util.number import getPrimefrom Crypto.Random import get_random_bytesp=997g=3t=5primebits=64msg="hello"if (len(sys.argv)>1):  primebits=int(sys.argv)if primebits>512: primebits=512p = getPrime(primebits, randfunc=get_random_bytes)z=*tX=*tr=*tK=*tfor i in range(0,t):  r[i] = random.randint(0,p)  z[i]=pow(g,r[i],p)  for i in range (0,t):  X[i]=pow(g,r[(i+1) % t]*r[i]-r[i]*r[(i-1) % t],p)  for i in range(0,t):  K[i] = pow(z[(i-1) % t],(t)*r[i],p)  for j in range(i+1,i+1+t):    if (i==j): continue    K[i]= (K[i]* pow(X[(j-1)%t],(t-j),p))% p  print ("Keys:",K)res=r*r+r*r+r*r+r*r+r*rprint ("Computing keys check: ",pow(g,res,p))`
`Random values (r): [226589242101802, 189829639746726, 188625714155186, 184735699686400, 116440993319309]Public values (z): [267704455905509, 50015333919247, 15916535078749, 264135697727188, 206738438540103]X values: [112085216125079, 87590296821257, 260726071053053, 50830423926144, 23766863138958]Keys: [155751430205915, 155751430205915, 155751430205915, 155751430205915, 155751430205915]Computing keys check:  155751430205915`

## Conclusions

Within conference keying, Eve sits and listens to Alice, Bob, Carol, Dave and Faith, and their broadcast values, but she cannot determine the shared key they will use for their secret communications.

## References

 Burmester, M., & Desmedt, Y. (1994, May). A secure and efficient conference key distribution system. In Workshop on the Theory and Application of of Cryptographic Techniques (pp. 275–286). Springer, Berlin, Heidelberg [here].

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