A computer-implemented method, comprising: receiving, by a first aggregation server and from each of multiple client devices, impression data that includes, for each impression of a digital component recorded by the client device, (i) a first join key that is based on a first unique identifier for the client device or an application on the client device at which the impression occurred, (ii) encrypted impression data that has been encrypted using a first public key of the first aggregation server and using a second public key of a second aggregation server different from the first aggregation server, and (iii) encrypted impression time data that indicates a time at which the impression occurred; executing, by the first aggregation server in collaboration with a second aggregation server, secure multi-party computations using a secure multi-party computation protocol to generate chronological sequences of encrypted impression data and encrypted conversion data stored by the second aggregation server and to decrypt the encrypted impression data and the encrypted conversion data, including: identifying, based on the first join keys and second join keys corresponding to conversions for which the multiple client devices provided conversion data to the second aggregation server, groups of encrypted conversion data and corresponding encrypted impression data; ordering, for each chronological sequence, the encrypted conversion data and the corresponding encrypted impression data based on the encrypted impression time data and encrypted conversion time data corresponding to each second join key; and decrypting the impression data and the conversion data for each sequence of encrypted impression data and conversion data in multiple stages using a first private key that corresponds to the first public key and a second private key that corresponds to the second public key. receiving, by a first aggregation server and from each of multiple client devices, impression data that includes, for each impression of a digital component recorded by the client device, (i) a first join key that is based on a first unique identifier for the client device or an application on the client device at which the impression occurred, (ii) encrypted impression data that has been encrypted using a first public key of the first aggregation server and using a second public key of a second aggregation server different from the first aggregation server, and (iii) encrypted impression time data that indicates a time at which the impression occurred; executing, by the first aggregation server in collaboration with a second aggregation server, secure multi-party computations using a secure multi-party computation protocol to generate chronological sequences of encrypted impression data and encrypted conversion data stored by the second aggregation server and to decrypt the encrypted impression data and the encrypted conversion data, including: identifying, based on the first join keys and second join keys corresponding to conversions for which the multiple client devices provided conversion data to the second aggregation server, groups of encrypted conversion data and corresponding encrypted impression data; ordering, for each chronological sequence, the encrypted conversion data and the corresponding encrypted impression data based on the encrypted impression time data and encrypted conversion time data corresponding to each second join key; and decrypting the impression data and the conversion data for each sequence of encrypted impression data and conversion data in multiple stages using a first private key that corresponds to the first public key and a second private key that corresponds to the second public key. identifying, based on the first join keys and second join keys corresponding to conversions for which the multiple client devices provided conversion data to the second aggregation server, groups of encrypted conversion data and corresponding encrypted impression data; ordering, for each chronological sequence, the encrypted conversion data and the corresponding encrypted impression data based on the encrypted impression time data and encrypted conversion time data corresponding to each second join key; and decrypting the impression data and the conversion data for each sequence of encrypted impression data and conversion data in multiple stages using a first private key that corresponds to the first public key and a second private key that corresponds to the second public key.