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The code of the bean continues with the declaration of the obligatory methods related to the EJB lifecycle:

r[1] = 5, r[2] = 10, r[3] = 15, r[4] = 20, r[5] = 25

public void ejbPostCreate(OrderMaster orderMaster) {} public void ejbActivate() {} public void ejbPassivate() {} public void thisctx = ctx; } setEntityContext(EntityContext ctx) {

public void unsetEntityContext() { thisctx = null; }

(4-6)

public void ejbLoadO { } public void ejbStoreO { }

second input which has the same hash value as any given input Thus given an input x, it should be infeasible to nd any other input y such that both x and y hash to the same value Note that the function x 2 mod n does not have this property as both x and x have the same hash value Strong collision resistance implies that it is computationally infeasible to nd any two distinct inputs which hash to the same value Thus, in this case, it is infeasible to nd any x and y values such that both x and y have the same hash value Note that this is stronger than weak collision resistance since for the weak collision resistance property we x one of the inputs while for the strong collision property we do not x either of the inputs Thus, strong collision resistance does imply weak collision resistance In addition there are other properties such as noncorrelation, near-collision resistance and partial pre-image resistance that are desirable in hash algorithms used as cryptographic primitives Noncorrelation ensures that the input and output bits of the hashing function are not correlated In fact, an avalanche property, whereby any change in one of the input bits causes at least half of the output bits to change randomly, is desirable Near-collision resistance ensures that it is dif cult to nd any two inputs whose hash values differ in only a small number of bits Partial pre-image resistance makes it as hard to recover any portion of the input as it is to recover the entire input given the hash value A hash value is very frequently used to create a digital signature In this case, the hash value of a message is created and the signer signs the hash value rather than signing the message This is more ef cient from the point of view of performance since a hashing primitive is much faster than an asymmetric cryptographic primitive In addition, a hash value can be used to detect changes to a message provided that the corresponding hashing algorithm has been designed such that collisions are computationally dif cult to nd Thus, the hashing functions are used mainly to ensure data integrity and message authentication Secure hash algorithm (SHA) is a widely used hashing algorithm SHA was designed by NIST and NSA in 1993 and revised in 1995 as SHA-1 This algorithm takes an arbitrarily sized input and produces 160 bit hash values A message is processed in terms of 512 bit chunks over four rounds of 20 steps each SHA-256, SHA-384, and SHA-512 have also been speci ed These produce 256, 384 and 512 bit hash values Given that SHA-1 produces 160 bit hash values, the probability of nding a collision is negligibly small More precisely, this probability is one in 280 (follows from the birthday paradox) Thus, if we hashed 280 messages, we would nd one pair of messages that hashed to the same value This is the brute force approach to nding collisions for hashing algorithms It is clear that the dif culty of this approach depends on the size of the output hash value It is desirable that the brute force approach be the best way to determine collisions for a given hash algorithm To break a hash algorithm, an adversary will have to be able to nd collisions while expending fewer cycles than needed by the brute force approach SHA-1 has been broken using this de nition The authors in [9] have shown the ability to nd collisions in SHA-1 using about 263 calculations In order to understand the gravity of the problem, note that using today s technology it is expected that 260 calculations might require a couple of days On the positive side, however, note that these are collision attacks and not attacks on the pre-image property of SHA-1, and collision attacks are typically important in the case of digital signatures As a result, many protocols will not be impacted by this result In addition, leveraging these theoretical results to design software.

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public void ejbRemove() throws RemoveException {}}

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