Abstract: A method for mutual authentication between user equipment and a communications network. The network includes a mobility management entity and a home subscriber server. The method, implemented by the user equipment, includes: receiving an authentication challenge having an token based on a first index and a first authentication message calculated by the home subscriber server and based on a first sequence number; checking that a condition of a set is true, the set including: the first sequence number is the same as a second sequence number stored in the user equipment, and the first sequence number is the same as a preceding value of the second sequence number and the first index is higher than a second index stored in the client equipment; and calculating and sending, when a condition is true, an authentication result and an authentication message, based on the preceding value of the second sequence number.

Abstract: A method for mutual authentication between user equipment and a communications network. The network includes a mobility management entity and a home subscriber server. The method, implemented by the user equipment, includes: receiving an authentication challenge having an token based on a first index and a first authentication message calculated by the home subscriber server and based on a first sequence number; checking that a condition of a set is true, the set including: the first sequence number is the same as a second sequence number stored in the user equipment, and the first sequence number is the same as a preceding value of the second sequence number and the first index is higher than a second index stored in the client equipment; and calculating and sending, when a condition is true, an authentication result and an authentication message, based on the preceding value of the second sequence number.

Abstract: A cryptographic device performs modular addition between a first integer value x and a second integer value y in a processor by: obtaining a first masked input {circumflex over (x)}, a second masked input ?, a first mask rx and a second mask ry, the first masked input {circumflex over (x)} resulting from the first integer value x masked by the first mask rx and the second masked input ? resulting from the second integer value y masked by the second mask ry; computing a first iteration masked carry value ?1, using the first masked input {circumflex over (x)}, the second masked input ?, the first mask rx, the second mask ry and a carry mask value ?; recursively updating the masked carry value ?i to obtain a final masked carry value ?k?1, wherein the masked carry value is updated using the first masked input {circumflex over (x)}, the second masked input ?, the first mask rx, the second mask ry, and the carry mask value ?; combining the first masked input {circumflex over (x)} and the second masked input ? and t

Abstract: A cryptographic device performs modular addition between a first integer value x and a second integer value y in a processor by: obtaining a first masked input {circumflex over (x)}, a second masked input ?, a first mask rx and a second mask ry, the first masked input {circumflex over (x)} resulting from the first integer value x masked by the first mask rx and the second masked input ? resulting from the second integer value y masked by the second mask ry; computing a first iteration masked carry value ?1, using the first masked input {circumflex over (x)}, the second masked input ?, the first mask rx, the second mask ry and a carry mask value ?; recursively updating the masked carry value ?i to obtain a final masked carry value ?k?1, wherein the masked carry value is updated using the first masked input {circumflex over (x)}, the second masked input ?, the first mask rx, the second mask ry, and the carry mask value ?; combining the first masked input {circumflex over (x)} and the second masked input ? and t