Activity-ISAAC

Submitted By A18

Anoop Betigeri 2BV11CS014

Chaitra Besthar 2BV11CS024

Megha Byali 2BV11CS045

Radhika patil 2BV11CS073

WHAT IS STREAM CIPHER !!!

Key + Nounce =

Keystream

Plaintext Xor'd

With Keystream =

Ciphertext

Ciphertext Xor'd

With same

keystream=Plaintext

What is ISSAC is….

ISSAC stands for Indirection, Shift, Accumulate, Add, and Count.

It is a cryptographically secure pseudorandom number generator.

It is stream cipher designed by Robert J. Jenkins Jr in 1996.

ISAAC is fast especially when optimised and portable to most architectures in nearly all programming and scripting languages.

How ISSAC came up!!

● Based on the RC4 stream cipher

● Basic structure of RC4:

○ Starts with a 256-byte array, filled

with the golden ratio, then modified

with bytes of the key.

○ Each keystream bit modifies the

array

Issues addresssed

RC4 has a few issues, namely dealing with bias.

● Some sequences are more likely to occur than others- bias.

○ This is due to initialization of RC4 to avoid short cycles: sequences that will result in the keystream repeating earlier than expected.

● First few bytes of the keystream are significantly less random and give information about the key.

How Expansion Happened!!

● Robert Jenkins produced a number of ciphers attempting to expand on RC4

○ IA- gives values based on sum of values in array rather than individual values. Still prone to bias.

○ IBAA- adds an accumulator (rotating value based off array value) to deal with bias issues. Does not appear to have bias, and short cycles are significantly reduced from what would be expected in RC4.

ISSAC origin

The IBAA implementation is taken by

Robert and he adds a counter

incremented once per call.

○ This removes any chance of short

cycles, as even if the sequence would

normally cycle, the counter is different

and thus the sequence is different.

○ Estimated cycle length is 2^8287

calls.

Operation..

The ISAAC algorithm has similarities with RC4.

It uses an array of 256 four-octet integers as the internal state, writing the results to another 256 four-octet integer array, from which they are read one at a time until empty, at which point they are recomputed.

The computation consists of altering i-element with (i⊕128)-element, two elements of the state array found by indirection, an accumulator, and a counter, for all values of ifrom 0 to 255.

Since it only takes about 19 32-bit operations for each 32-bit output word, it is very fast on 32-bit computers.

Cryptanalysis on ISSAC

It has been undertaken by Marina

Pudovkina

Her attack can recover the initial state

with a complexity that is approximated to

be less than the time needed for

searching through the square root of all

possible initial states.

In practice this means that the attack

needs 4.67×10^1240 instead

of 10^2466. This result has had no

practical impact on the security of

ISAAC.

Cryptanalysis contd…

In 2006 Jean-Philippe Aumasson discovered several sets of weak states.

It is not clear if an attacker can tell from just the output whether the generator is in one of these weak states or not.

There was error in last attack made after Aumason and the reason was errorneousalgorithm rather than the real ISAAC.

An improved version of ISAAC is proposed, called ISAAC+.

Practical usage..Many implementations of ISAAC are so fast that they

can compete with other high speed PRNGs, even with

those designed primarily for speed not for security.

Only a few other generators of such high quality and

speed exist in usage.

ISAAC is used in the Unix tool ”shred” to securely

overwrite data.

This makes it suitable for applications where a

significant amount of random data needs to be

produced quickly, such solving using the Monte Carlo

method or for games.

How It happens…

The RNG should then be seeded with

the string "this is my secret key" and

finally the message "a Top Secret

secret" should be encrypted on that

key.

Your program's output ciphertext will

be a string of hexadecimal digits.

. Optional: Include a decryption check

by re-initializing ISAAC and

performing the same encryption pass

on the ciphertext.

Encryption method..

Two encryption schemes are possible:

XOR (Vernam)

Caesar-shift mod 95

Alternative sample view.

Message: a Top Secret secret

Key : this is my secret key

XOR : 1C0636190B1260233B35125F1E1D0E2F4C542

MOD : 734270227D36772A783B4A5F206266236978

XOR dcr: a Top Secret secret

MOD dcr: a Top Secret secret

About Isaac

No official seeding method for ISAAC has been published, but for this task we may as well just inject the bytes of our key into the randrsl array, padding with zeroes before mixing, like so.

ISAAC can of course also be initialized with a single 32-bit unsigned integer in the manner of traditional RNGs, and indeed used as such for research and gaming purposes.

PROGRAM ELEMENTS …1.MIX FUNCTION

Used with eight integers that will contain traces of the key: designed to ensure array elements will not reflect key.

mix(a,b,c,d,e,f,g,h) { a^=b<<11; d+=a; b+=c; b^=c>>2; e+=b; c+=d; c^=d<<8; f+=c; d+=e; d^=e>>16; g+=d; e+=f; e^=f<<10; h+=e; f+=g; f^=g>>4; a+=f; g+=h; g^=h<<8; b+=g; h+=a; h^=a>>9; c+=h; a+=b; }

PROGRAM ELEMENTS.. 2.INITIALIZATION 1

Loads eight elements of the key

into integers, runs the mix()

function to randomize them, then

loads them into eight elements of

the array. Repeats until key is

exhausted.

for (i=0; i<RANDSIZ; i+=8)

{

a+=r[i ]; b+=r[i+1]; c+=r[i+2];

d+=r[i+3];

e+=r[i+4]; f+=r[i+5]; g+=r[i+6];

h+=r[i+7];

mix(a,b,c,d,e,f,g,h);

m[i ]=a; m[i+1]=b; m[i+2]=c;

m[i+3]=d;

m[i+4]=e; m[i+5]=f; m[i+6]=g;

m[i+7]=h;

}

PROGRAM ELEMENTS-

3.INITIALIZATION 2

Routine then runs a second pass to mix more thoroughly, loading elements of the array instead of elements of the key into the integers this time.for (i=0; i<RANDSIZ; i+=8){a+=m[i ]; b+=m[i+1]; c+=m[i+2]; d+=m[i+3];e+=m[i+4]; f+=m[i+5]; g+=m[i+6]; h+=m[i+7];mix(a,b,c,d,e,f,g,h);m[i ]=a; m[i+1]=b; m[i+2]=c; m[i+3]=d;m[i+4]=e; m[i+5]=f; m[i+6]=g; m[i+7]=h;}

Program Elements4.GenerationThe rngstep function is the main function for the the ISAAC key generator.

rngstep(mix,a,b,mm,m,m2,r,x){

x = *m;

a = (a^(mix)) + *(m2++);

*(m++) = y = ind(mm,x) + a + b;

*(r++) = b = ind(mm,y>>8) + x;

}

What this essentially does is

stores the current memory into a register

set the new value of accumulator

set the next bit of memory to the addition of the 2-9 bits of x or the current memory with the accumulator and previous result

Lastly the results array is incremented and set to the addition of x and the 10-17 bits of y bit shifted right by 8

Program Elements5. Main Loop 1 b = ctx->randb + (++ctx-

>randc);

for (m = mm, mend = m2 = m+(RANDSIZ/2); m<mend; )

{

rngstep( a<<13, a, b, mm, m, m2, r, x);

rngstep( a>>6 , a, b, mm, m, m2, r, x);

rngstep( a<<2 , a, b, mm, m, m2, r, x);

rngstep( a>>16, a, b, mm, m, m2, r, x);

}

Adds the counter to element B, then calls rngstep()

function four times with different bitshifts of A for

the mix.

Program Elements:

6.Main Loop 2

Second loop just

iterates with M2

going from first

element to mend,

calling rngstep

four times

eachiteration.

Designed to

ensure that m2 is

at each array

index for at least

one rngstep.

ISSAC+

To fix some of weaknesses, we modify ISAAC’s algorithm,

We call the corresponding pseudo-random generator ISAAC+. The modifications: we add ⊕a to avoid the biases observed, perform rotations (symbols ≪, ≫) instead of shifts, so as to get more diffusion from the state bits, and replace an addition by a XOR to reduce the linearity

CONCLUSION and FUTURE PLAN

Its possible to understand the

thoroughly as stream cipher was

introduced in course.

ISSAC applications in real life can be

mapped with the learnt concept.

Its implementation can also be made

easily using C

“For every lock there is a Key…

It is better to KEEP SAFE YOUR LOCK THAN THE KEY”