the description which follows , and the embodiments described therein , are provided by way of illustration of an example , or examples , of particular embodiments of the principles of the present invention . these examples are provided for the purposes of explanation , and not limitation , of those principles and of the invention . in the description which follows , like parts are marked throughout the specification and the drawings with the same respective reference numerals . fig1 shows schematically a process for compressing cryptographic values , such as public keys or public key certificates , so that they are manageable for users . compression of a cryptographic value , such as a public key or a public key certificate , is to confine it to a restricted space . generally speaking , cryptographic algorithms involve values that are random within a certain space , or are indistinguishable from such random values . these spaces are of a size mat makes exhaustive search infeasible by computers of current technology . a space of 2 80 is considered out of reach today . representing a cryptographic value in such a space generally takes at least 80 bits , or 10 bytes . compression is to confine the cryptographic value to a subspace of such spaces so that a cryptographic value in such a space can be expressed in a shorter representation . the compression process 100 starts at step 110 by selecting a compression criteria for a cryptographic value . the criteria may be rule based , for example , by requiring all public keys to be selected from a pre - determined collection of words or pseudowords . the criteria may also be pattern based , for example , by requiring the selected cryptographic value to have 40 trailing zeros . the criteria may also be to select a particular string or text for a given number of trailing characters or the entire cryptographic text , for example , to correspond to an e - mail address or a website address . the criteria may also be based on any other user selected requirements that may make a cryptographic value more manageable . of course , the criteria may also be pre - determined in another process or fixed by a third party , such as a request submitted to the system . the purpose of the criteria is that certain bits of the cryptographic value can be omitted during transmission and storage and then reconstructed prior to a further cryptographic operation , for example , decryption , to be performed on the cryptographic value . at the next step 120 , a private key or other secret value that is required in a cryptographic operation is selected or generated . the nature of the secret value corresponds to the cryptographic operation . for example , a user may select a private key d at this step for finding a manageable public key . alternatively , a certification authority may select an initial secret contribution to a requester &# 39 ; s private key if an implicit certificate is to be compressed , or , when an encrypted text is required , the secret is an encryption key used to encrypt the text . next at step 130 , a cryptographic value is computed , incorporating the secret value as at least one of the inputs . for example , one may compute a public key p from a private key d using elliptic curve cryptography (“ ecc ”). the public key p may be computed from where g is a generator of a selected elliptic curve . of course , at this step , depending on the needs , the cryptographic value to be computed is not limited to a public key . it may be , for example , a public certificate as indicated above . next , at step 140 , the computed cryptographic value is evaluated to determine if it meets the pre - selected criteria . for example , one may verify at this step whether the public key has 40 trailing zeros , or if the cryptographic value matches the pre - selected text , such as an e - mail address . if the criteria is met , both the secret and the cryptographic values are output to the user at step 150 and the process terminates . for example , the private / public key pair may be provided to the user . as the trailing bits can be removed and later reconstructed , the compressed cryptographic value requires less bits to represent . this tends to make it more manageable for a human recipient as it is generally difficult for human users to manage a long string of apparent random bits . if the criteria is not met , the process is iterated by selecting a new secret value and computing a corresponding cryptographic value until the criteria is met . in certain applications , such as searching for a compressed elliptic curve public key , the cryptographic value is a constant multiple of the secret value . the secret value may be simply incremented at step 160 to arrive at a new value and the cryptographic value may be correspondingly incremented at step 170 , in order to avoid the need of a more expensive multiplication operation . the process then returns to step 140 until a secret value is found so that the corresponding cryptographic value is in a compressed form , namely satisfying the compression criteria selected at the beginning of the process . as an example , fig2 shows a process 200 of finding a public key that has 40 trailing zeros . this is accomplished by a trial and error process . for example , suppose one wants a compressed elliptic curve public key q whose last 40 bits ( five bytes ) are zero . in this example , g is the generator of a selected elliptic curve of order n . the following process can be followed to find such a public key : 1 . generate a random private key dε [ 1 , n − 1 ] ( step 210 ) 2 . compute the corresponding public key q = d g ( step 220 ) 3 . if the public key q , ends in 40 bits of value zero ( step 230 ) then stop and output the public and private key pair ( d , q ) ( step 240 ) 4 . otherwise , go back to the start of the process , step 210 this process takes on average 2 40 iterations . the process , as described , thus takes approximately 2 40 elliptic curve scalar multiplications . the process 200 described above can be improved to yield possibly an approximate hundredfold improvement . the modified process 300 shown in fig3 also starts from initializing a private / public key pair but it takes advantage of the multiplicative relationship between the private and public keys to avoid the multiplication operations otherwise required during the exhaustive search . the modified process 300 has the following steps : 1 . initialize a private / public key pair ( d 0 , q 0 ), namely , first generate a random private key d 0 ε [ 1 , n − 1 ] and set index i to 0 ( step 310 ), and then compute the corresponding public key q 0 = d 0 g ( step 320 ); 2 . in a loop , first evaluate whether the public key q i meets the compression criteria ( step 330 ), i . e ., if it ends in 40 bits of zero ; 3 . if q i is not in a compressed form , then ( a ) increment the private key : d i + 1 = d i + 1 ( step 340 ) ( b ) increment the public key : q i + 1 = q i + g ( step 350 ) ( c ) increment i by one ( d ) return to the beginning of the loop ( i . e ., step 330 ) 4 . output the private / public key pair ( d , q ) when a compressed key q is found ( step 360 ) this process also takes about 2 40 iterations . each iteration , however , costs mainly just one elliptic curve point addition . the saving of computation costs depends on the size of n . in view of today &# 39 ; s technology and the corresponding security level required of an encryption system , the saving can be approximately a hundred times faster than the process 200 based on elliptic curve multiplication , but would be greater if a longer key is required for better security , for example . the number of iterations 2 40 mentioned here is used in this example because it is considered to be just within reach of today &# 39 ; s desktop computers ( running for several days ). with a different number of iterations , a different savings will be realized . if public keys in a given system are generated in this manner , then they can be compressed by omission of the last 40 bits . for example , today 22 byte elliptic curve keys are commonly used . with 40 trailing zero bits , public keys compress to 17 bytes . different criteria on the public key can be used . for example , 32 trailing zero bits can be sought , or some other fixed pattern may be used . if a different criteria is used , the process described above will be adjusted so that at each iteration , it is the selected criteria that is tested . compression comes at a one - time computational cost during key generation . this cost can be amortized over the life of a public key . key generation and certification is a generally one - time operation . the extra cost of searching for a suitable key may be well worth the savings achieved by reduced storage and transmission costs . the methods described above in connection with fig1 to 3 can be applied to generation of digital signatures in certificates by certification authorities . by doing this , certificates can be compressed . certificates often need to be stored or transmitted . compressing certificates help reducing the associated storage and transmission costs . also , in theory certificate chains can be very long , in which case , compression generally tends to be beneficial . in a public key system , a public - key certificate is a data structure that consists of at least two parts , a data : part and a signature part . the data part contains cleartext data that includes at least the public key to be certified and a piece of information indicating the identity of the public key &# 39 ; s owner . the signature part consists of a digital signature over the data part . the digital signature is that of the certification authority , thereby binding the key owner &# 39 ; s identity to the key certified . the certification authority (“ ca ”) already has its public key and private key selected and , in general , already has its public key publicized . the certificate of a public key of a subject entity therefore can be compressed if a suitable public key of the subject entity is appropriately selected , such as in accordance with the general procedure outlined in fig1 . fig4 illustrates schematically how a public - key certificate can be compressed in an example embodiment . in this example , the compression criteria is to find a certificate that has 40 trailing zeros . the ca initializes the process 400 by initializing the data part . during initialization 410 , the ca selects an initial private key d 0 of the subject and computes the corresponding initial public key q 0 . the ca also selects the identity information i to be included in the certificate . at step 420 , the ca signs the initial data part to obtain an initial signature s . the signature s computed is evaluated at step 430 to determine whether it has 40 trailing zeros , i . e ., to determine if the signature meets the compression criteria . in general , an arbitrary initial public key does not lead to a compressed certificate . the ca then finds a new key pair at step 440 . advantageously , the ca can increment the private key and compute the corresponding public key by adding a corresponding increment : next , the process returns to step 420 and a digital signature corresponding to the new public key is computed . the new signature is evaluated at step 430 to determine whether it meets the criteria . if it does , the ca terminates the process and provides the subject entity with the key pair and the compressed public key certificate at step 450 . if the signature does not meet the criteria , steps 420 , 430 , and 440 are repeated until a compressed certificate is found . the public - key certificate so obtained is compressed in that its signature part is compressed . various embodiments of the invention have now been described in detail . those skilled in the art will appreciate that numerous modifications , adaptations and variations may be made to the embodiments without departing from the scope of the invention . since changes in and or additions to the above - described best mode may be made without departing from the nature , spirit or scope of the invention , the invention is not to be limited to those details but only by the appended claims .